The Foreign Exchange Market

XXXXX FX Annual Cover 2009_Gra24309_FX Annual Cove#781.qxd 22/10/2009 09:31 Page 1

The Foreign Exchange Market

ANNUAL

2009

n n n n n

GSDEER re-estimation and equity investments Extended BBoP and real TWI analysis Robustness of cross-asset proxy baskets Portfolios of macro-thematic FX Currents baskets Output gaps and growth differentiation in FX markets

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

The Foreign Exchange Market October 2009 Introduction and Summary

1

1. GSDEER—Re-Estimation and Test-Based Adjustment

2

Thomas Stolper, Anna Stupnytska and Malachy Meechan

2. Using GSDEER to Trade Equities

14

Dominic Wilson and Roman Maranets

3. Measuring Global Output Gap Dispersion as a Guide for Relative Growth Strategies

18

Mark Tan

4. The Benefits of Investing in Portfolios of FX Currents

22

Themistoklis Fiotakis

5. Updating our Trade-Weighted Exchange Rates and Looking at the Real TWIs

27

Fiona Lake, Roman Maranets and Swarnali Ahmed

6. Empirical Links Between the Major Currencies and their BBoP Flows

32

Fiona Lake and Thomas Stolper

7. Over-fitting in Cross-Asset Proxy Baskets

37

Thomas Stolper

8. FX Volatility Still Looks Expensive Relative to Cyclical Factors

48

Themistoklis Fiotakis

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Introduction and Summary Welcome to the 13th edition of The Foreign Exchange Market. As usual, the book is designed to supplement our ongoing FX and financial market research. In this issue we have once again combined deeper work on some of our existing toolkit with new research into the FX market. Chapter One re-estimates our flagship GSDEER ‘fair value’ model, incorporating the additional data published since the last update nearly two years ago. The framework remains broadly the same but the estimated coefficients change slightly. We also introduce a new test-based adjustment procedure to correct biases in the level of some of our ‘fair value’ estimates. Chapter Two presents an innovative use of GSDEER FX valuation signals to trade equity markets. The basic idea is that the real appreciation of undervalued currencies will occur through nominal appreciation and/or rising prices in goods and asset markets. FX unhedged exposure to equity markets with undervalued currencies is a way of capturing both possible appreciation channels simultaneously. Chapter Three analyses the performance of FX growth differentiation strategies through the business cycle. It appears that during the early stages of recovery, such as the current juncture, the change in output gaps is a particularly valuable differentiation signal for FX investors. We also introduce a new growth dispersion measure that can be used to identify periods of likely outperformance of growth differentiation strategies. Chapter Four provides guidance on how to construct baskets of FX Currents with high Sharpe ratios. The Currents are the fully tradable replacements of our old FX Slices. Chapter Five introduces real trade-weighted exchange rate indices to complement our nominal GS TWIs. We also publish the latest annual revision of the underlying weights. Once again, the weights for EM currencies have increased, reflecting continued globalisation. Chapter Six builds on the BBoP modelling framework introduced in the previous edition and analyses empirically the balance of payments components that drive the main currencies. We find further evidence for the validity of our BBoP concept, although country-specific differences persist. Chapter Seven pushes the cross-asset correlation analysis to the limit. By constructing deliberately over-fitted FX proxy baskets for non-FX assets, we can illustrate the limits of this approach. However, we also find clusters of relative robustness, which suggest FX proxy baskets may work precisely when they are also most useful for investors. Chapter Eight looks at the cyclical patterns in FX volatility, and suggests that both realised and implied volatility will likely continue to decline as the business cycle advances. Thomas Stolper October 22, 2009

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Goldman Sachs Global ECS Research

The Foreign Exchange Market

Chapter 1: GSDEER—Re-Estimation and Test-Based Adjustment We have updated our GSDEER model, while maintaining the same framework as before. The primary aim was to re-estimate the coefficients on the basis of 11 additional quarters of new data, now covering the period from 1Q1980 to 4Q2008. In addition, we have adjusted the fixed effects for 12 countries using a cross-sectional link between GDP per capita relative to the US and deviation from PPP. This kind of adjustment had previously been used for CEE countries only. The new ‘fair value’ estimates have barely changed for most major currencies; however, there are some notable shifts in EM. The Dollar remains broadly undervalued.

Overview and Modelling Philosophy

Table 1: Changes to Coefficients

Back in May 2005, we introduced a new unified GSDEER framework for Major and Emerging Market (EM) currencies, which is based on the idea that long-run variations in the real exchange rate can be explained through productivity and terms of trade (ToT) differentials.1

Variable

Old coefficient

New coefficient

Productivity

-0.239

-0.189

Terms of trade

-0.484

-0.378

Source: GS Global ECS Research

fixed effects for all currencies. As we explain in more detail below, this adjustment helps correct for level problems linked to short sample size or heavily managed exchange rate regimes. For those countries where our test favours an adjustment, we will adjust the estimated fixed effect to make it consistent with a second crosssectional model, which is a more sophisticated version of the one already used for the CEE countries in the past. This second model is based on the idea that over, long timeframes and across countries, currencies become less ‘cheap’ as the population becomes wealthier on a GDPper-capita basis.

We occasionally re-estimate our model to incorporate the additional data that has been released since the previous update. The stability of the coefficients is one important test to assess the robustness of our framework. We also use the opportunity to introduce additional modifications to address issues that may have appeared since the latest re-estimation. For example, in the previous re-estimation in 2007, we dropped a right-hand variable, the international investment position, which had lost all explanatory power. Our latest model update includes the following changes (Chart 1 illustrates the procedure schematically):

New Coefficients Incorporate the Commodity Boom As Table 1 shows, both coefficients are now lower than in the previously estimated model. The fall in the value of the terms of trade coefficient is consistent with the fact that the additional data used in the extended sample contains a lot more commodity-related volatility than the earlier periods. With more variation in the variable, it is normal that the coefficient can decline to explain similar levels of exchange rate variation. This change in the coefficient also has to be seen as a welcome change given

We have re-estimated the model once again, using additional data that has been released since the last reestimation. The coefficients have changed slightly but in line with what we would have expected given the substantial increase in commodity market volatility in recent years. We have replaced the CEE-specific adjustment factors in favour of a test-based framework that helps calibrate the Chart 1. GSDEER Re-Estimation and Adjustment Procedure GSDEER Re-estimation Longer Sample: 1Q1980-4Q2008

Estimation of PPP-Implied Fair Values

Calculation of Adjustment Factors from PPP-Implied Misalignment and GSDEER Misalignment

New Coefficients and Country-Specific Fixed Effects

Unit Root Test of Residuals for Each Country

Unit Root Probability Ranking

Country Selection for Fixed Effects Adjustment

Adjustment of Fixed Effects for Selected Countries

New GSDEER Fair Values for All Currencies Source: GS Global ECS Research

1. Global Economics Paper 124, “Merging GSDEER and GSDEEMER: A Global Approach to Equilibrium Exchange Rate Modelling”, May 2005. Chapter 1

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October 2009

Goldman Sachs Global ECS Research

The Foreign Exchange Market

Eastern European countries2. We then adjusted the ‘fair values’ of the CZK, HUF, PLN and RUB and have been using these estimates since then. However, a number of countries from other regions also potentially fall into this group, and we have therefore decided to make equivalent adjustments to all countries and currencies where the aforementioned issues cause concern.

that large fluctuations in recent commodity prices had become a source of rapid change in the ‘fair values’ of commodity-exporting countries. The coefficient on productivity has become smaller as well, and this could also have resulted from more variation in the explanatory variable. In particular, over the last few years of globalisation, a growing cross-country divergence of productivity growth may have been a factor, in particular in the emerging world. Both coefficients remain highly significant.

While our approach rests on the same logic as before, it is now a more structured two-step procedure. First, we determine which countries are mostly likely to be subject to the level bias by running residual-based tests for cointegration for each currency in our model. Second, we adjust GSDEER ‘fair values’ for the selected currencies by estimating the PPP-implied equilibrium values from a cross-sectional PPP regression. This involves calibrating the individual countries’ fixed effects from the panel, while keeping the estimates of the long-run elasticities for differentials in terms of trade and productivity unchanged.

Issues Related to ‘Fair Value’ Level Estimates As explained in more detail in the original GSDEER paper mentioned above, we estimate ‘fair value’ on the basis of a panel cointegration framework with so-called country-specific ‘fixed effects’. This simply means a currency-specific constant, which ensures that the average of the observations equals the average of the much smoother ‘fair value’ estimates over the sample period. This is fine as long as we have a long timeframe and a large number of swings of the exchange rate around the true fundamental ‘fair value’.

GSDEER Adjustment: Testing for Cointegration Technical aspects. Standard tests for cointegration are closely related to unit root tests3. If a long-run relationship between the fundamentals in our model and the real exchange rate exists (i.e., the variables are cointegrated), then the error term (or residuals from the model) must be stationary. If there is no cointegration, the residuals will follow a unit root process.

However, most countries in our cross-section, particularly EMs, have had a number of currency regimes over time— pegs, various floats and currency boards. Artificial management of currencies, transitions between regimes and other factors have in most cases caused movements in exchange rates, which were not necessarily reflective of fundamentals. Even very long-term averages of managed exchange rates may be considerably different from the true fundamental ‘fair value’. Arguably, inflation differentials would compensate for nominal pegs and still allow some real exchange rate variation, which we would capture in our GSDEER model. However, any form of stickiness in inflation processes or data problems linked to selection of the most appropriate inflation measure would likely introduce new sources of error.

A number of residual-based tests for cointegration exist. But tests of this nature tend to be very sensitive to finite (short) samples, specific features of the data-generating process (heteroskedasticity, serial correlation) that are generally unknown, structural breaks and seasonally adjusted data. This leads to severe reductions in power (the ability to reject the null hypothesis of a unit root (no cointegration) when it is actually false) and means that failure to reject noncointegration may provide only weak evidence that the series of interest are in fact not cointegrated.

An additional problem arises in some countries where the data sample may be too short to gain a good sense of what the long-term averages are (even in the case of a freely floating exchange rate). For example, looking at EUR/$ over just the last five years could create the impression that ‘fair value’ is somewhere in the region of 1.30-1.40, whereas most long-term models suggest ‘fair value’ is in the 1.00 to 1.20 area. As we have pointed out in the past, this problem is particularly severe in Eastern Europe, which has still relatively short time series data.

In our case, the finite samples and structural breaks are exactly the problems we are facing (and trying to correct for), which means that the unit root tests on the residuals from GSDEER are bound to have low power. As a result, some residual series that are identified as unit roots according to the tests could in theory still be stationary. There is no simple mechanical solution to this problem and largely any decision must involve a judgement call. To avoid any ad hoc and arbitrary selection procedure, we choose to concentrate on the ranking of currencies according to their test results rather than on the actual test statistics and corresponding critical values.

Interestingly, these data problems will almost certainly show up in standard cointegration tests. While our full panel satisfies the usual criteria, individual countries with the problems described above will likely show signs of non-stationarity in the country-specific residuals.

We use the Phillips-Perron unit root test, which has an advantage of being non-parametric and thus does not require specification of the exact form of serial correlation

We have acknowledged this issue before and argued that it was particularly pertinent in the context of Central and

2. Refer to Global Viewpoint 07/03: “The Evolving GSDEER Currency Model”, January 25, 2007. 3. Tests for cointegration are effectively unit root tests on residuals, although the asymptotic distributions of the corresponding test statistics are not the same as those of ordinary unit root test statistics—as a result, different critical values have to be used. Chapter 1

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Goldman Sachs Global ECS Research

The Foreign Exchange Market

Table 2: Phillips-Perron Test Results

CZK HUF TRY HKD PEN TWD MYR BRL CNY SGD ARS PLN

P-value*

Fixed Effect Adjustment Factor*

0.8791 0.8146 0.7724 0.7521 0.7199 0.6609 0.6359 0.6051 0.5873 0.5738 0.5525 0.3790

-29.8 -13.7 -13.9 -16.3 15.5 -11.3 -6.9 9.7 -8.6 -36.8 0.9 -29.8

bias problems recede and more cycles in the data appear to have reduced the importance of structural breaks. We thus chose to leave the RUB unadjusted. In a similar vein, we would expect the number of currencies requiring re-adjustment to decrease over time as the availability of longer time series with more cyclical swings makes the estimation of long-term equilibrium values in our regular GSDEER panel much more reliable.

GSDEER Adjustment: Estimating PPP-Implied ‘Fair Values’ In our previous adjustment of CEE currencies, we exploited the cross-sectional link between the gap between PPP exchange rate and spot exchange rate, and GDP per capita levels in PPP relative to the US.

* The probability of the null hypothesis of unit root (i.e. non-stationarity of residuals) being true ** Difference betw een PPP-implied misalignment and GSDEER misalignment on average over 1995-2007 Source: GS Global ECS Research

One problem we encountered in this PPP-based framework is that some countries still have very large agricultural sectors with very low output per head. In some cases it almost appears as if the countries were split in two: a competitive industrial and services sector versus a largely self-sufficient and very poor agricultural sector that plays a very small role in global trade. We see abundant evidence that global trade barriers remain disproportionally high for agricultural goods. We therefore found it more appropriate to focus on GDP per capita in the industrial and services sectors for all countries. Industry and services also account for the largest share of the tradable sector in most countries, and we use the GDP and employment shares of these two sectors to estimate a rough measure of tradable GDP per capita. For countries such as China, India, Indonesia and Turkey, where agriculture accounts for a relatively high share of GDP, the difference is especially significant.

4

(which is certainly an issue in our context) . We rank the countries according to their test results—by the probability of the null hypothesis (of a unit root) being true. Currencies that score high are most likely to have nonstationary residuals and thus require adjustment to their ‘fair values’. Table 2 shows the top countries ranked by probability and the corresponding adjustment factors. As we explain in more detail below, these adjustment factors represent the difference between PPP-implied misalignment and GSDEER misalignment for each currency. These factors are used to calibrate fixed effects. Country selection. The countries topping the ranking fall into two broad unifying groups. One group contains those that have undergone periods of rapid economic transition and experienced major structural shocks and/or currency crises (the Czech Republic, Hungary, Turkey and Brazil). Another group includes countries that used to manage, or still manage or peg, their exchange rates (Hong Kong, Taiwan, Malaysia, China, Singapore and Argentina). These results are reassuring as it appears our unit root test ranking identifies the countries most affected by the potential biases in ‘fair value’ levels discussed above.

With the new measure in hand, we run a pooled least squares regression across 37 countries from 1995 to 2007. This time period is chosen to exclude the initial transition years in the CEE countries, as the currency movements over that period hardly reflected the fundamentals and would therefore bias the results. The equation takes the following form:

In order to decide how far down we go in our unit root ranking, we decided to use the first free-floating G10 currency for which we are reasonably certain that the stationarity assumption has been wrongly rejected, because neither structural breaks nor data issues should affect the cointegration relationship. Based on the highest ranked major currency, the Canadian Dollar, used as a cut-off point, we end up with 11 currencies needing adjustment. In addition, we choose to include the PLN in this list—even though it ranks below the CAD, the issues of structural change and small sample bias are highly likely to distort its ‘fair value’, as we argued before.

ln(

GDPinUSDi ,t GDPinPPPi ,t

) = α + β ln(

GDPinPPPi ,t × ai USGDPinPPPt × aUS

) + εt

w h e r e GDPinUSD i ,t is per capita GDP of country i i n year t in current US Dollar terms, GDPinPPPi ,t is per capita GDP of country i in year t in PPP terms, USGDPinPPPt is per capita US GDP in t year in PPP terms, ai is a ratio of value added in industry and services as a share of GDP to employment in industry and services as a share of total employment for country i on average over 1995-2007, ε t is the residual term, α and β are the intercept and slope, respectively.

Russia, which previously used to be adjusted, comes much lower in the ranking (on this and other tests), indicating that the above issues may no longer be important—as time series become longer, small sample

4. We tried several alternative unit root tests, such as the ADF, KPSS and others. Although they do not yield identical rankings, the broad result holds across all of them. So we chose the test that requires minimal assumptions. Chapter 1

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October 2009

Goldman Sachs Global ECS Research

The Foreign Exchange Market

Chart 2: PPP Exchange Rates and GDP per capita 0.8 0.6 0.4

0.0 -0.2 -0.4 -0.6 -0.8

AUD

BRL

CAD

CHF

CLP

CNY

COP

CZK

DEM

ESP

EUR

FRF

GBP

HKD

HUF

IDR

ILS

INR

ITL

JPY

KRW

MXN

MYR

NOK

NZD

PEN

PHP

PLN

RUB

SEK

SGD

THB

TRY

TWD

VEB

ZAR

PPP exchange rate (logs)

0.2

ARS

-1.0 -1.2 -1.4 -1.6 Tradable GDP per capita relative to US (logs)

-1.8 -2.8

-2.4

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4

Source: GS Global ECS Research

we have now produced two GSDEER valuation tables: one with the Dollar crosses and one with the corresponding EUR crosses.

This cross-sectional relationship accounts for 67% of the variation in PPP gaps. We use the fitted values to calculate the long-term equilibrium value for each currency, which we call ‘the PPP-implied fair value’. The difference between fitted and actual values (residuals) for each country is the PPP-implied currency misalignment. We then compare these estimates to the GSDEER misalignments for each currency, on average over the same 1995-2007 period. The difference between the two gives the factors by which our GSDEER fixed effects have to be calibrated, translating into corresponding adjustments in ‘fair values’. Table 2 illustrates the results for the 12 currencies.

This direct comparison throws up some interesting conclusions. For example, Asian currencies appear broadly in line with GSDEER when looking at the Dollar crosses—some are overvalued and some undervalued. However, with the Dollar itself undervalued against most majors, Asian currencies are substantially undervalued when using a non-Dollar benchmark. There is not a single Asian currency, including the AUD and the NZD, that is not undervalued against the EUR currently. In the subsequent sections, we focus mainly on the changes in ‘fair value’ estimates due to our re-estimation, and hence on the comparable USD values. But in terms of valuation signals, it appears increasingly important to assess ‘fair value’ relative to both the Dollar and the Euro.

Valuation Benchmark: USD versus EUR Given that our model is consistently estimated on the basis of USD crosses, the primary valuation reference automatically remains the USD as well. This is not an issue when the Dollar is about fairly valued on a tradeweighted basis. However, it becomes a problem when the Dollar is substantially overvalued—as it currently is.

Summary of PPP-Adjusted GSDEER Estimates We now briefly discuss the impact of the latest reestimation and adjustment on the currencies in our selection, highlighting clear regional and structural themes.

The problem becomes even more complicated if the foreign exchange world gradually drifts towards a dual reserve currency standard, with the Dollar still dominating but the Euro becoming increasingly more dominant. Furthermore, with shifting global trade patterns and a trend slowdown in US consumption, the Dollar may naturally become less of a dominating reference point.

EUR/CZK, EUR/HUF and EUR/PLN. As expected, the ‘fair values’ of the CE-3 currencies have become stronger as the convergence process becomes firmly established. GDP per capita has increased since the last estimation and this has led to stronger ‘fair value’ levels, as explained in our adjustment procedure. The PLN now looks especially ‘cheap’ versus the EUR. This is, of course, partly also the result of the rapid depreciation during the recent crisis.

For these reasons, it is very important to compare valuation signals against the Dollar with trade-weighted valuation signals, but also against the Euro. The latter is particularly intuitive as a directly quotable FX cross, and Chapter 1

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Goldman Sachs Global ECS Research

The Foreign Exchange Market

Table 3: GSDEER Values and Misalignment for USD Crosses Spot G3 EUR/$ $/JPY Europe £/$ $/NOK $/SEK $/CHF $/CZK $/HUF $/PLN $/RUB $/TRY $/ILS $/ZAR Americas $/ARS $/BRL $/CAD $/MXN $/CLP $/PEN $/COP $/VEB Asia AUD/$ $/CNY $/HKD $/INR $/KRW $/MYR NZD/$ $/SGD $/TWD $/THB $/IDR $/PHP USD TWI

GSDEER Current (4Q09)

Table 4: GSDEER Values and Misalignment for EUR Crosses

Bilateral Misalignment, %

21-Oct-09

Old

New*

Old

New*

1.49 90.84

1.19 114.00

1.19 108.75

24.80 25.50

24.86 19.71

1.64 5.59 6.96 1.01 17.32 177.33 2.79 29.21 1.47 3.70 7.37

1.54 4.63 7.07 1.24 22.54 224.80 3.43 35.91 2.38 3.81 6.30

1.55 5.01 7.06 1.24 19.83 235.85 3.03 34.96 1.97 4.58 6.70

6.49 -17.20 1.56 22.08 30.19 26.77 22.89 22.93 62.13 2.97 -14.45

5.69 -10.40 1.38 22.21 14.49 33.00 8.53 19.66 34.15 23.76 -9.05

3.82 1.75 1.05 13.05 543.75 2.86 1913.60 2.15

2.43 2.43 1.15 12.60 381.19 2.90 1991.13 2.18

2.69 2.76 1.17 12.83 476.57 3.54 2252.90 2.65

-36.44 38.26 9.43 -3.50 -29.90 1.11 4.05 1.64

-29.56 57.25 11.80 -1.69 -12.36 23.43 17.73 23.46

0.92 6.82 7.75 46.17 1183.60 3.37 0.75 1.40 32.27 33.42 9395.00 46.61 211.49

0.91 6.93 7.02 46.14 1395.21 2.97 0.60 1.62 29.72 34.12 9191.20 53.62

0.80 6.87 6.20 46.62 1303.30 2.71 0.62 1.14 26.83 34.94 9495.27 53.57

1.80 1.64 -9.44 -0.08 17.88 -11.89 24.21 16.43 -7.92 2.12 -2.17 15.04

15.79 0.69 -20.01 0.96 10.11 -19.58 20.42 -18.31 -16.86 4.57 1.07 14.93 -11.96

Spot

GSDEER Current (4Q09)

21-Oct-09 Old G3 EUR/$ 1.49 1.19 EUR/JPY 135.39 136.14 Europe EUR/GBP 0.91 0.78 EUR/NOK 8.34 5.53 EUR/SEK 10.38 8.45 EUR/CHF 1.51 1.48 EUR/CZK 25.81 26.92 EUR/HUF 264.29 268.45 EUR/PLN 4.16 4.09 EUR/RUB 43.54 42.89 EUR/TRY 2.19 2.84 EUR/ILS 5.51 4.55 EUR/ZAR 10.98 7.53 Americas EUR/ARS 5.69 2.90 EUR/BRL 2.61 2.90 EUR/CAD 1.56 1.37 EUR/MXN 19.46 15.04 EUR/CLP 810.40 455.22 EUR/PEN 4.27 3.46 EUR/COP 2852.03 2377.81 EUR/VEB 3.20 2.61 Asia AUD/EUR 0.62 0.76 EUR/CNY 10.17 8.28 EUR/HKD 11.55 8.38 EUR/INR 68.82 55.10 EUR/KRW 1764.04 1666.16 EUR/MYR 5.02 3.54 NZD/EUR 0.50 0.51 EUR/SGD 2.08 1.94 EUR/TWD 48.10 35.49 EUR/THB 49.80 40.75 EUR/IDR 14002.30 10976.11 EUR/PHP 69.47 64.03 USD TWI 211.49

Bilateral Misalignment, %

New*

Old

New*

1.19 129.81

24.80 0.56

24.86 -4.12

0.77 5.98 8.43 1.48 23.67 281.53 3.61 41.73 2.35 5.46 8.00

-14.68 -33.65 -18.62 -2.18 4.32 1.57 -1.53 -1.50 29.91 -17.50 -31.45

-15.35 -28.23 -18.80 -2.12 -8.31 6.52 -13.07 -4.16 7.44 -0.88 -27.15

3.21 3.29 1.40 15.32 568.87 4.22 2689.25 3.16

-49.07 10.79 -12.32 -22.68 -43.83 -18.98 -16.63 -18.56

-43.59 25.95 -10.46 -21.26 -29.80 -1.14 -5.71 -1.12

0.67 8.20 7.40 55.65 1555.73 3.23 0.52 1.36 32.03 41.71 11334.38 63.94

-18.43 -18.56 -27.44 -19.94 -5.55 -29.40 -0.47 -6.71 -26.22 -18.18 -21.61 -7.83

-7.26 -19.35 -35.94 -19.14 -11.81 -35.59 -3.56 -34.57 -33.41 -16.25 -19.05 -7.95 -11.96

* Adjusted currencies: CZK, HUF, TRY, HKD, PEN, TWD, MYR, BRL, CNY, SGD, ARS, PLN

* Adjusted currencies: CZK, HUF, TRY, HKD, PEN, TWD, MYR, BRL, CNY, SGD, ARS, PLN

Source: GS Global ECS Research

Source: GS Global ECS Research

$/TRY. The ‘fair value’ of the Lira has strengthened, correcting the previous overvaluation of over 60% to around 30%. This is more in line with our bullish stance on Turkey’s current growth story and its long-term potential as part of the N-11. The Turkish Lira ‘fair value’ has also benefited substantially from the adjustment procedure.

$/CNY. The ‘fair value’ of the $/CNY rate has gained enough strength to align it with the current spot, correcting the previous overvaluation. China is where the focus on non-agricultural output has made the biggest difference, as a very large part of the population remains employed in the agricultural sector. One fact often forgotten is that China remains a very poor country on a per-capita basis. If we were to include the vast but poor agricultural population in our adjustment model, the CNY would look substantially overvalued currently. On the other hand, the highly productive export sector could probably live with a stronger CNY, as also illustrated by China’s pace of reserve accumulation. Overall, the CNY therefore looks too strong for parts for the Chinese economy and too weak for others. Thus, a GSDEER ‘fair value’ estimate that puts ‘fair value’ close to current spot sounds about right. It also highlights the need for more domestic rebalancing in China.

$/HKD, $/TWD and $/MYR. The re-estimation and adjustment have strengthened the ‘fair values’ of these Asian currencies, contributing further to their current undervaluation. Of the three, the $/HKD rate has seen the most substantial change, linked to Hong Kong’s relatively high GDP per capita, which has translated into a relatively large adjustment factor. The $/MYR is also one of the ‘cheapest’, probably consistent with a very large current account surplus.

Chapter 1

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$/SGD. The $/SGD has gained considerable strength, switching from an overvaluation of over 16% to an undervaluation of around 18%. This is an extreme move but remains well within the magnitude of misalignment seen in other crosses and through time. Moreover, an undervalued $/SGD is far more consistent with the extremely large and stable current account surplus position in this managed currency regime.

Conclusion: GSDEER Model Further Improved The latest round of GSDEER model maintenance incorporated two major changes: The re-estimation of coefficients with more data led to a reduced sensitivity to commodity prices via the ToT variable. We have introduced a test-based fixed effect adjustment procedure for all countries that reveal certain data or estimation issues. So far this procedure had only been applied to CEE countries.

$/BRL, $/PEN and $/ARS. These three Latin American countries have seen the ‘fair values’ of their exchange rates weaken post re-estimation and adjustment. The $/BRL is even more ‘expensive’ than before, and is now the most overvalued currency in our list of specially adjusted currencies. However, it is important to remember that Brazil is one of the world’s least open economies. External trade accounts for a disproportionally small share of GDP, so the cyclical impact of either an over- or undervalued currency is quite limited.

The resulting changes are broadly in line with expectations and ‘fair value’ estimates do not change dramatically in many cases, in particular for freely floating major currencies with long data histories. In EM space and for commodity-exposed currencies, we have seen more substantial changes but in general they were in the direction of what our intuition would have suggested. For example, a notable undervaluation for the $/SGD is more consistent with the large structural trade surplus than our previous estimate of a currency that was broadly ‘fairly valued’.

The $/ARS undervaluation has been corrected through the adjustment, bringing the ‘fair value’ more in line with the current spot, although it still looks to be the ‘cheapest’ currency in the group. The $/PEN has switched from being almost in line with its fair value to being significantly ‘expensive’, and is now one of the most overvalued currencies in Latin America.

Brazil and Turkey have the most overvalued currencies, consistent with the fact that they are also among the highest-yielding currencies globally. In terms of the cyclical position, Brazil has proven a lot more resilient to the global recession than most other countries and, from a growth differentiation point of view, this alone warrants a currency that trades substantially stronger than ‘fair value’. We are therefore not concerned about a sudden sell-off, although further appreciation may be limited.

Summary of Non-Adjusted GSDEER Estimates As we discussed above, the re-estimation of ‘fair value’ should not materially affect the well-behaved crosses for which our test suggests an adjustment is not necessary. Indeed, the fair values of the EUR, JPY, GBP, SEK, CHF and CAD have barely changed. On the other hand, we do see some changes in the reestimated ‘fair values’ of commodity-exposed currencies. Because of the declining coefficient on terms of trade, exporting countries have seen their ‘fair value’ revised down from generally high levels. That said, importing countries, which have seen their ‘fair value’ decline rapidly on rising commodity prices in recent years, have been re-adjusted to a slightly stronger level. As we pointed out above, this pattern was in line with what we expected given the huge rise in commodity prices since the previous re-estimation.

The RUB is also one of the more overvalued currencies against the Dollar, although it remains slightly undervalued vis-à-vis the Euro. As before, the EUR and the JPY are also substantially overvalued against the USD. The Dollar remains significantly undervalued on a trade-weighted basis and against most currencies on a bilateral basis. On the other hand, the Euro is overvalued against all but a handful of high-yielding currencies, such as the TRY, BRL and HUF. The ‘cheapest’ currencies are the SEK, NOK and SGD. The latter two effectively have managed exchange rates and sovereign wealth funds with rapidly growing reserves; therefore any substantial move back to ‘fair value’ would be conditional on a policy change.

The Australian Dollar is a good example of this terms of trade related change, as its ‘fair value’ has been revised down from 0.91 to 0.80 in the re-estimated model. Similarly, we have seen the ‘fair value’ in other commodity exporters weaken, such as the MXN, NZD, ZAR, CLP and VEB. Importing countries, such as Japan, have at the margin seen their ‘fair value’ strengthen. However, many other commodity-importing countries in Asia and CEE were among those needing adjustment, and hence it is less obvious how the impact from a declining ToT coefficient compares with the impact from the PPPbased level adjustment.

Chapter 1

As before, the CNY is about ‘fairly valued’ against the Dollar but undervalued against most other major currencies. Thomas Stolper, Anna Stupnytska and Malachy Meechan

7

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Appendix $/ARS

AUD/$

4.5

1.6

4.0 Australia New

1.4

3.5

Australia Prior

3.0

1.2

AUD

2.5 1.0

2.0 Argentina New

1.5

ARS

0.5 0.0 2Q98

0.8

Argentina Prior

1.0

3Q00

4Q02

1Q05

2Q07

0.6 0.4 1Q74

3Q09

Source: GS Global ECS Research

1Q79

1Q84

1Q89

1Q94

1Q99

1Q04

Source: GS Global ECS Research

$BRL

$/CAD

4.0

1.6

3.5

Brazil New

1.5

3.0

Brazil Prior

1.4

2.5

BRL

1.3

2.0

1.2

1.5

1.1

Canada New

1.0

Canada Prior

1.0 0.5 0.0 1Q94

1Q97

1Q00

1Q03

1Q06

0.8 1Q74

1Q09

1Q79

1Q84

1Q89

1Q94

1Q99

1Q04

1Q09

Source: GS Global ECS Research

EUR/CHF

$/CLP 800

2.3 2.2

700

Switzerland New

2.1 2.0 1.9

Switzerland Prior

600

CHF

500

1.8

400

1.7

300

1.6

200

1.5

Chile New Chile Prior CLP

100

1.4 1Q79

1Q84

1Q89

1Q94

1Q99

1Q04

0 2Q83 3Q86 4Q89 1Q93 2Q96 3Q99 4Q02 1Q06 2Q09

1Q09

Source: GS Global ECS Research

Source: GS Global ECS Research

Chapter 1

CAD

0.9

Source: GS Global ECS Research

1.3 1Q74

1Q09

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Goldman Sachs Global Economics, Commodities and Strategy Research

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$/COP

$/CNY

CNY/USD

10.0

3000

9.0

2500

8.0

2000

7.0

1500

Colombia New Colombia Prior

China New

6.0

COP

1000

China Prior 500

CNY

5.0

0 1Q80 2Q83 3Q86 4Q89 1Q93 2Q96 3Q99 4Q02 1Q06 2Q09

4.0 4Q87 2Q90 4Q92 2Q95 4Q97 2Q00 4Q02 2Q05 4Q07 2Q10 Source: GS Global ECS Research

Source: GS Global ECS Research

EUR/CZK

EUR/$

40.0

1.6

35.0

1.4

30.0

1.2

25.0

1.0

20.0

0.8

Czech Republic New Czech Republic Prior

15.0

EURO New EURO Prior

0.6

CZK

EUR

10.0 1Q95 1Q97 1Q99 1Q01 1Q03 1Q05 1Q07 1Q09

0.4 1Q81 3Q84 1Q88 3Q91 1Q95 3Q98 1Q02 3Q05 1Q09

Source: GS Global ECS Research

Source: GS Global ECS Research

$/HKD

GBP/$ 12.0 2.4

10.0

UK New

2.2

UK Prior

2.0

8.0

GBP

1.8

6.0

1.6

4.0

Hong Kong New Hong Kong Prior

1.4

2.0

HKD

1.2 1.0 4Q74

4Q79

4Q84

4Q89

4Q94

4Q99

4Q04

0.0 2Q81

4Q09

2Q91

2Q96

2Q01

2Q06

Source: GS Global ECS Research

Source: GS Global ECS Research

Chapter 1

2Q86

9

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Goldman Sachs Global Economics, Commodities and Strategy Research

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$/IDR

EUR/HUF 400

14000.0

350

12000.0

300

10000.0

250

8000.0

Indonesia New Indonesia Prior

Hungary New

200

6000.0

Hungary Prior

150

4000.0

HUF

2000.0

100 50 2Q96

INR

3Q98

4Q00

1Q03

2Q05

3Q07

0.0 1Q83

4Q09

1Q88

1Q93

1Q98

1Q03

1Q08

Source: GS Global ECS Research

Source: GS Global ECS Research

$/ILS

$/INR

5.0

60.0

4.8 50.0

4.6 4.4

India New India Prior

40.0

INR

4.2 30.0

4.0 3.8 3.6

Israel New

3.4

Israel Prior

3.2

ILS

3.0 2Q96

3Q98

4Q00

20.0 10.0

1Q03

2Q05

3Q07

0.0 1Q80

4Q09

1Q85

1Q90

1Q95

1Q00

1Q05

1Q10

2Q00

2Q05

2Q10

Source: GS Global ECS Research

Source: GS Global ECS Research

$/KRW

$/JPY 1600

300

1500

Japan New

250

JPY

200

South Korea New

1400

Japan Prior

1300

South Korea Prior

1200

KRW

1100 150

1000 900

100

800 700

50 1Q74

1Q79

1Q84

1Q89

1Q94

1Q99

1Q04

600 2Q80

1Q09

Chapter 1

2Q85

2Q90

2Q95

Source: GS Global ECS Research

Source: GS Global ECS Research

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October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

$/MYR

$/MXN 4.5

16.0 14.0

Mexico New

12.0

Mexico Prior

10.0

MXN

Malaysia New Malaysia Prior MYR

4.0 3.5

8.0

3.0

6.0 4.0

2.5

2.0 2.0 3Q83

0.0 2Q85 2Q88 2Q91 2Q94 2Q97 2Q00 2Q03 2Q06 2Q09

3Q88

3Q93

3Q98

3Q03

3Q08

Source: GS Global ECS Research

Source: GS Global ECS Research

NZD/$

EUR/NOK 10.0

1.4

9.0

1.2

New Zealand New New Zealand Prior

8.0

NZD

1.0

7.0 0.8

6.0 Norway Prior 0.4

NOK

4.0 3.0 1Q74

0.6

Norway New

5.0

1Q79

1Q84

1Q89

1Q94

1Q99

1Q04

0.2 1Q74

1Q09

4.5

1Q94

1Q99

1Q04

1Q09

50.0

3.5

40.0

3.0 2.5

1.0

1Q89

60.0

4.0

1.5

1Q84

$/PHP

$/PEN

2.0

1Q79

Source: GS Global ECS Research

Source: GS Global ECS Research

30.0

Peru New Peru Prior

20.0

PEN 10.0

Philippines New Philippines Prior PHP

0.5 0.0 1Q91 3Q93 1Q96 3Q98 1Q01 3Q03 1Q06 3Q08

0.0 1Q83 2Q86 3Q89 4Q92 1Q96 2Q99 3Q02 4Q05 1Q09

Source: GS Global ECS Research

Source: GS Global ECS Research

Chapter 1

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Goldman Sachs Global Economics, Commodities and Strategy Research

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EUR/PLN

$/RUB

5.0

45.0 40.0

4.5 4.0

Russia Prior

30.0

RUB

25.0

3.5

20.0

Poland New

3.0

15.0

Poland Prior

10.0

PLN

2.5 2.0 4Q95

Russia New

35.0

5.0 4Q97

4Q99

4Q01

4Q03

4Q05

4Q07

0.0 1Q95 1Q97 1Q99 1Q01 1Q03 1Q05 1Q07 1Q09

4Q09

Source: GS Global ECS Research

Source: GS Global ECS Research

EUR/SEK

$/SGD

12.0

2.4

11.0

Singapore Prior

2.0

9.0

SGD

8.0

1.8

7.0

1.6

6.0

Sweden New

5.0

1.4

Sweden Prior

4.0 3.0 1Q74

Singapore New

2.2

10.0

1.2

SEK 1Q79

1Q84

1Q89

1Q94

1Q99

1Q04

1.0 1Q80 2Q83 3Q86 4Q89 1Q93 2Q96 3Q99 4Q02 1Q06 2Q09

1Q09

Source: GS Global ECS Research

Source: GS Global ECS Research

$/TRY

$/THB 50.0

3.0

45.0

2.5

Turkey New Turkey Prior

40.0

2.0

TRL

35.0 30.0 25.0 20.0

Thailand New

1.5

Thailand Prior

1.0

THB

0.5

15.0 2Q83 3Q86 4Q89 1Q93 2Q96 3Q99 4Q02 1Q06 2Q09

0.0 4Q95

Source: GS Global ECS Research

Source: GS Global ECS Research

Chapter 1

12

4Q97

4Q99

4Q01

4Q03

4Q05

4Q07

4Q09

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Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

$/VEB

$/TWD 50.0

4.0

45.0 40.0

Taiwan New

3.5

Venezuela New

Taiwan Prior

3.0

Venezuela Prior

TWD

2.5

VEF

35.0

2.0 1.5

30.0

1.0 25.0

0.5

20.0 1Q80 2Q83 3Q86 4Q89 1Q93 2Q96 3Q99 4Q02 1Q06 2Q09

0.0 1Q83 2Q86 3Q89 4Q92 1Q96 2Q99 3Q02 4Q05 1Q09

Source: GS Global ECS Research

Source: GS Global ECS Research

$/ZAR 12.0 10.0

South Africa New South Africa Prior

8.0

ZAR

6.0 4.0 2.0 0.0 1Q80 2Q83 3Q86 4Q89 1Q93 2Q96 3Q99 4Q02 1Q06 2Q09 Source: GS Global ECS Research

Chapter 1

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Chapter 2: Using GSDEER to Trade Equities Our GSDEER current valuation tool provides an important signal not just for relative FX returns but for equities too. Since real currency misalignments can be resolved through local prices as well as through nominal currency shifts, we have always suspected this might be the case. It is striking, though, that the Sharpe ratio from using GSDEER to trade equities in common currency is better than it is for FX, suggesting that those allocating across equity indices may want to pay more attention to currency valuation than they often do. There are commonly cited intuitive reasons for thinking that countries with undervalued currencies may have better equity performance. Those with undervalued currencies may see stronger export-led growth—a notion we have exploited from time to time when recommending equity markets where financial conditions are easier. And when countries resist appreciation in undervalued currencies, the result is often a liquidity injection into the local economy and asset markets that is reflationary. But these channels are really examples of how the basic real adjustment process can take place, not separate dynamics.

Currency Valuation as a Guide to Real Misalignments We have shown on many occasions over the past decade or so how our GSDEER currency valuation models help to predict forward FX returns, particularly over long horizons. We described our GSDEER currency valuation model in more detail in Chapter 1, where we re-estimated the latest version. Although convergence on ‘fair value’ in FX markets is relatively slow, we pay a great deal of attention to the signals from GSDEER in trading FX, particularly when currencies are a long way from equilibrium and when the market itself appears to be in the process of focusing on imbalances, as it has done over the past 12 months.

We look here at whether those equity markets whose currencies are undervalued on the basis of GSDEER tend to outperform those with more overvalued currencies over time. We find that FX valuation seems to provide a good signal for relative equity, as well as FX, performance, as theory would predict. What is even more striking is that using GSDEER to guide investment in equity indices in common currency to capture both the FX and relative index performance seems to deliver higher Sharpe ratios for FX than using it for equity alone.

Because of this convergence to ‘fair value’, the strategy of being long the most undervalued currencies and short the most overvalued—which is what our FX Valuation Current1 (formerly FX Valuation Slice) essentially captures—tends to be profitable on average over time, although there are many specific periods when it is not. And the Valuation Current rises over time, delivering an average annual return of around 3.6% since 1998 and 7.5% over the last 12 months. We have long been aware that a real exchange rate misalignment such as those signalled by GSDEER can be resolved in one of two ways: by a nominal exchange rate adjustment or by a shift in the relative domestic prices of goods and services, and hence through local asset prices— or some combination of the two. As a result, focusing only on the FX implications potentially misses part of the adjustment and the opportunity, particularly where currencies are heavily managed. Given that many emerging market (EM) exchange rates are still a long way from being free-floating, that problem can be particularly acute: it may be possible to identify a significantly undervalued exchange rate (as at times in the past few years with the CNY) but harder to benefit from that view in FX markets than for a truly floating currency. Local asset prices (equities) may adjust instead.

A Higher Sharpe Ratio Using GSDEER to Trade Equities/FX Together To look at this issue, we start by replicating the methodology of the FX Valuation Slice in equities. We take a universe of 20 reasonably liquid international equity indices (Table 1). We again use GSDEER to Index

380 360 340 320 300 280 260 240 220 200 180 160 140 120 100 80

Table 1: Our Universe of 20 Countries Australia Brazil Canada China EMU

Hong Kong India Japan Mexico Norway

Poland Russia Singapore South Africa South Korea

Sweden Switzerland Taiwan Turkey United Kingdom

Equity Slice (USD) Equity Slice (Local Currency) FX Slice

98

Source: GS Global ECS Research

Chart 1: Historical Performance of Equity (USD), Equity (Local Ccy) and FX Slices

99

00

01

02

03

04

05

06

07

08

Source: GS Global ECS Research, MSCI International Equity Indices

1. Although the FX Valuation Slice is a predecessor of the investable GS FX Valuation Current, technically these two products are slightly different from the weighting methodology and the USD component inclusion perspectives. For more information on GS FX Currents, please see Global Viewpoint 09/12 “‘FX Slices’ Become New Tradable ‘FX Currents’”. Chapter 2

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Goldman Sachs Global Economics, Commodities and Strategy Research

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Table 3: Panel Regressions: 1m & 6m Fwd Returns as a Function of Currency Misvaluations

identify the markets with the six most overvalued and undervalued currencies, but using the total return series based on the relevant MSCI indices, we now look at going long and short their equity markets. We look at this on a ‘currency unhedged’ basis (where the investments essentially benefit from both FX and local equity market appreciation), which is what the theory suggests is the most logical instrument. But we also construct a version that looks only at local currency equity returns and a matching version of our FX Slice for this specific universe, which allows us to decompose the overall return effectively into its equity and FX components.

Fwd Return Horizon EQ Slice 1-month USD 6-month 1-month EQ Slice Local Ccy 6-month

Intercept

Beta

T-Stat

RSquared

0.83 4.08 0.82 4.16

-0.03 -0.07 -0.02 0.00

-2.73 -1.02 -1.62 -0.03

0.3% 0.3% 0.1% 0.0%

Source: GS Global ECS Research, MSCI International Equity Indices

past for GSDEER itself. Specifically, we used a panel regression to attempt to explain 1- and 6-month forward returns as a function of GSDEER misvaluations over our sample period. Table 3 displays the statistical results of these regressions. In all cases, even at this very short horizon, GSDEER is statistically significant in predicting both the USD and local currency equity returns, although, as is usual with these kinds of tests, the amount of overall variation it helps to explain is extremely low. This is why diversified strategies work better and why long-term performance is more reliable than shorter-term.

Chart 1 illustrates the performance of the three indices created along these lines (equities in USD, equities in local currency and FX). All three trend upwards over time, suggesting that the convergence to FX valuation does help in determining cross-country equity performance. The highest returns over time come from the USD equity strategy, followed by local currency equities and then FX returns. The decomposition indicates that the USD equity strategy benefits from both the impact on currency returns and the impact on local currency equity performance.

Are We Picking Up Something Else? We are wary of the possibility that in using GSDEER, we are unintentionally picking up exposure to some other factor (such as market risk, etc.) that would help explain why returns are positive over time.

The volatility of the underlying assets does, of course, differ substantially. That said, a comparison of a basic version of the Sharpe ratio (returns divided by realised volatility) in Table 2 shows that the USD equity strategy is the most reliable of the three combinations on that front too, at least over the last 11 years since data have been easy to obtain. Both the FX and local currency equity components alone deliver inferior (and comparable) Sharpe ratios, although both are positive over time. Each strategy has periods of superior performance and periods of weakness; hence, for shorterterm trading it remains helpful—when possible—to identify periods when valuation is and is not a market driver. But the USD equity index has had only two negative years in our sample, compared with four for each of the other two components.

To cross-check against that risk, we look at the correlations between the three versions of the strategy (USD equity, local currency equity, FX) and a range of other macro asset measures that may conceivably be driving the results. We find that the USD equity and local currency equity indices are highly correlated with each other, and that the USD equity index is also well correlated (albeit less so) with the FX index. This is probably largely a reflection of the relative volatility of the two assets. What is more interesting is that the local currency equity index and the FX index have almost zero correlation with each other. As a result, the equity and FX components of returns do appear to be picking up generally different kinds of convergence.

To validate the notion that GSDEER matters for returns in the way the strategy suggests, we also tested the predictive power more formally, as we have done in the

Table 2: Sharpe Ratios, Returns and Standard Deviations for Equity (USD), Equity (Local Ccy) and FX Slices Year

Eq Slice (USD)

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Overall

2.1 1.4 1.2 0.8 0.3 0.7 -0.7 1.3 -0.5 0.9 0.6 0.8

Sharpe Ratio Eq Slice (Local Ccy) 0.9 1.5 1.4 -0.5 -0.5 0.5 -1.5 1.8 -0.2 0.6 0.1 0.5

FX Slice

Eq Slice (USD)

3.3 -1.2 -0.1 1.9 1.7 0.3 0.9 -1.0 -1.5 0.7 0.7 0.6

40% 27% 22% 12% 4% 8% -7% 15% -6% 19% 8% 13%

Return (Ann.) Eq Slice (Local Ccy) 16% 29% 25% -7% -5% 5% -13% 18% -2% 11% 1% 7%

FX Slice 21% -8% -1% 13% 9% 2% 4% -4% -7% 5% 6% 4%

Stardard Deviation (Ann.) Eq Slice Eq Slice FX Slice (USD) (Local Ccy) 19% 19% 19% 15% 13% 11% 9% 12% 14% 20% 13% 15%

18% 19% 17% 12% 11% 10% 9% 10% 14% 18% 12% 14%

6% 7% 10% 7% 5% 5% 4% 4% 5% 7% 9% 7%

Source: GS Global ECS Research, MSCI International Equity Indices Chapter 2

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Goldman Sachs Global Economics, Commodities and Strategy Research

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Table 4: Returns Correlations for Equity (USD), Equity (Local Ccy) & FX Slices and Macro Factors

Eq Slice (USD) Eq Slice (Local Ccy) FX Slice Oil 10-year Yields SPX USD TWI VIX WF Growth WF China WF Cons. Growth WF Foreign WF Housing WF Oil WF Oil Growth WF Rates WF Turbo Growth

Correlations of 1-week Returns Eq Slice (Local Eq Slice (USD) FX Slice Ccy) 100% 85% 47% 85% 100% 4% 47% 4% 100% 5% 3% 4% 1% -1% 6% -1% -5% 1% 7% 9% 1% 4% 3% 8% 12% 9% 3% 3% 3% 0% -2% -5% 0% 10% 11% 1% -8% -11% 3% -4% -5% 0% -4% -2% 1% 9% 4% 10% 11% 7% 3%

Correlations of 2-week Returns Eq Slice (Local Eq Slice (USD) FX Slice Ccy) 100% 84% 46% 84% 100% 0% 46% 0% 100% -7% -3% -8% -1% -5% 8% 2% -3% -3% 12% 10% 12% 0% 4% 5% 8% 7% -4% 4% 5% -12% -4% -7% 0% -1% 0% 1% -15% -15% -1% -11% -4% -13% -10% -3% -9% -1% -3% 2% 12% 9% -2%

Source: GS Global ECS Research, MSCI International Equity Indices

We checked the correlation of each index (in 1- and 2week returns) with:

By taking into account relative volatilities and betas in terms of equity selection. By taking account of equity valuations as well as currency valuations. In particular, we would like to see whether equity valuations are more or less useful than FX valuations as a determinant of cross-sectional returns.

SPX and VIX – to measure market risk. Oil – to see if we are picking up a commodity proxy. Our Wavefront Growth basket in equities – to see if we are picking up cyclical risk.

By looking at whether different thresholds matter in terms of identifying the valuation signal.

10-year yields – to gauge rates exposure and cyclical risk.

It would also be helpful to understand more about what characterises those periods when the strategy works better and those when it works less well. Is this a function of when valuation dispersion is less extreme, so that ranking on a signal is less effective? Or is it a function of growing global imbalances that are tending to drive currencies away from ‘fair value’, as we saw in 2007 for instance, when currencies moved particularly strongly against their valuation signals?

The USD TWI – to see if we have a closet Dollar view embedded in this method. Overall, the results (Table 4) show extremely low correlations to all of these factors (in general, less than 15% in absolute terms). So whatever we are capturing here seems to be a genuinely independent source of return, not an accidental linkage with some other source of risk. This is encouraging too, although it raises the challenge of identifying those moments when valuation is likely to be particularly strongly rewarded and those when it is not, as is also the case with our Valuation Current in FX.

A preliminary look at these issues provides promising results, which deserve to be studied in more detail. We compared the returns on our strategy to both the dispersion of misvaluation and the average gap in misvaluation between longs and shorts. Both are simple measures of how ‘strong’ the valuation sorting signal actually is. We do find—as the charts on the next page

We also looked at how often the composition of the basket changes. The answer is that there is roughly a 10% chance in a given month that a member on the long or short side is replaced, so the baskets are reasonably stable over time, consistent with the relatively slow-moving system that generates them.

Table 5: Current Constituents (October 2009) Undervalued (Long) Country Hong Kong India Mexico Norway South Africa Taiwan

Looking Forward—A Fruitful Area Given Low Focus from Equity Investors The basic insight opens up a number of avenues. We would like to understand more about whether the simple notion can be improved into a more effective strategy. This can be done in a number of ways: Chapter 2

Weight 16.7% 16.7% 16.7% 16.7% 16.7% 16.7%

Overvalued (Short) Country Brazil EMU Japan Singapore Switzerland Turkey

Weight 16.7% 16.7% 16.7% 16.7% 16.7% 16.7%

Source: GS Global ECS Research

16

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Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market Equity Slice (Local Ccy) 1yr Fw d Return

Equity Slice Chart 2: Dispersion of Currency Misvaluation (USD) 1yr vs 1-year Fwd Returns of Equity (USD) Slice Fw d Return

30%

30%

y = -0.03 + 0.84x R2 = 10%

25%

Chart 3: Dispersion of Currency Misvaluation vs 1-year Fwd Returns of Equity (Local Ccy) Slice y = -0.03 + 0.55x R2 = 5%

25%

20%

20%

15%

15% 10%

10%

5%

5%

0%

0%

-5%

-5%

-10%

Dispersion of Currency Misvaluation

-10% 5%

10%

15%

20%

25%

Dispersion of Currency Misvaluation

-15% 5%

30%

10%

15%

20%

25%

30%

Source: GS Global ECS Research, MSCI International Equity Indices

Source: GS Global ECS Research, MSCI International Equity Indices

show—that returns from the strategy are highest on average after periods when valuation dispersion has been high and so currencies are in very different places to where they ‘belong’. This suggests we may be able to refine the signals according to how strong they are. Consistent with this observation, the performance so far this year is striking after a period of unusually high deviations from ‘fair value’. Across all three strategies, 2009 has been a year in which valuation has had strong predictive power, and the second half of 2008 had similar features. The unwinding of global imbalances and dislocations that we have documented over the past 12 months appears to have been a powerful force in driving currencies and other assets back towards ‘fair value’. It is equally clear that, in the process, both equities and FX— and even more so a combination of the two—have been rewarded by paying attention to GSDEER. Dominic Wilson and Roman Maranets

FX Slice 1yr Chart 4: Dispersion of Currency Misvaluation Fw d Return vs 1-year Fwd Returns of FX Slice

Index

20%

1.12

y = -0.01 + 0.21x R2 = 1%

15%

Chart 5: Year-To-Date Performance of Equity (USD), Equity (Local Ccy) and FX Slices

1.1 1.08

10%

1.06

5%

1.04

0%

1.02 1

-5%

0.98

Dispersion of Currency Misvaluation

-10% 5%

10%

15%

20%

25%

0.96 Jan-09

30%

Source: GS Global ECS Research, MSCI International Equity Indices

Chapter 2

EQ Slice USD EQ Slice Local Ccy FX Slice Mar-09

May-09

Jul-09

Sep-09

Source: GS Global ECS Research, MSCI International Equity Indices

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Chapter 3: Measuring Global Output Gap Dispersion as a Guide for Relative Growth Strategies In this chapter we try to identify the stage of the business cycle at which growth differentiation strategies reap the most returns for FX. We find broad evidence that differentiation strategies start to outperform when economies are emerging from the troughs of the cycle. More specifically, the key is to identify when output gaps are at their most dispersed across countries. This dispersion creates the most scope for exchange rates to help redistribute excess capacity across countries, given their role as a measure of relative prices. Our research suggests that growth differentiation strategies tend to underperform as we approach the peak of the global business cycle, where growth differentiation gradually disappears. which encourages more imports to free up even more resources for the booming export sector. Compared with the standard Mundell-Fleming model (in which a country’s export sector competes with foreign producers), this special case assumes complementarities between exporters and foreign producers.

Output Gaps Matter for FX performance1 Economics theory can provide reasonable explanations for the relationship between output gaps and FX. For example, we can take the approach of a Mundell-Fleming open economy framework, where the exchange rate, as an expression of relative prices, is the facilitating mechanism in the reallocation of resources across countries. Faster growth and capacity constraints shift the demand curve out, leading to a rise in prices and a rising domestic interest rate. The resultant appreciating pressures on the exchange rate act as a redistributive tool, and the impact on a country’s trade flows (lower exports and higher imports) eventually rebalances demand across countries over time.

In practice, the central bank reaction function is also an important factor in the transmission from output gaps into FX. Where capacity constraints lead to inflationary pressures, tighter monetary policy and appreciating currencies follow—either through market forces such as carry, or through explicit FX management, as in many Asian countries. Another possible channel is through capital inflows. Stronger growth prospects boost investment opportunities and attract the inflow of capital, which also drives FX appreciation.

A caveat to this simple framework is that the domestic cycle of some countries may be highly geared to the global cycle, with a beta greater than one, i.e., these countries mainly have externally-driven domestic cycles. Growing external demand may lead to an even greater increase in domestic demand and a stronger currency,

While the theoretical underpinnings are straightforward, it is not clear if it is the change in or level of the output gap that matters. It is also unclear whether global or local

Summary Table of Regression Results: Changes in Domestic Output Gaps Matter Most, Especially for EM Countries (Coeffecients, t-stat)

Domestic OP Gap Level

AUD NZD SEK CAD GBP CHF JPY NOK USD CNY INR IDR KRW MYR MXN PHP SGD TRY TWD THB

√ (1.7, 1.6)

Domestic OP Gap Change

Global OP Gap Level

√ (1.8, 3.9)

Global Output Gap Change

√ (3.7, 3.8) √ (3, 2.5)

√ √ √ √ √ √

(1.95, (2.18, (4.94, (1.22, (0.80, (3.18,

2.03) 2.43) 5.16) 2.68) 2.29) 2.88)

√ (2.63, 3.49)

√ (2.40, 2.42)

√ (5.63, 1.8) √ (0.29, 1.78) √ (1.91, 2.4) √ (1.18, 1.77)

√ (0.6, 4.26)

√ (2.34, 2.09)

R-sq 0.27 0.44 0.43 0.65 0.45 0.29 0.41 0.33 0.26 0.37 0.50 0.66 0.69 0.63 0.59 0.53 0.68 0.47 0.45 0.74

Source: GS Global ECS Research

1. This section provides a recap of our previous work on the links between output gaps and FX (see Global Viewpoint 09/13, “Focusing on Output Gaps—A Guide to FX Differentiation in the Recovery Cycle”, August 12, 2009). Chapter 3

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Goldman Sachs Global Economics, Commodities and Strategy Research

Change In Output Gaps Drives FX Returns Over Cycles, Especially for Small Open Economies—Example of Mexico

%

8 6 4

The Foreign Exchange Market

%

20

10

15

0

10

-10

5

0

-20

0

-2

-30

2

-4

Change in output gap from year ago

-6 -8

nominal TWI returns (RHS)

-10

-40

-15

-50

-20

-60

-25

2007

2005

2003

2001

1999

1997

1995

1993

1991

1989

1987

1985

1983

-30 -14

These results are better reflected in emerging market economies, which are typically small open economies, providing the most scope for exchange rates to act as a redistributive tool of excess capacity.

115 M ixed perfo rmance in the do t co m 'bo o m' phase

100 Outperfo rmance in the po st bubble burst reco very

Underperfo rmance during the glo bal credit 'bo o m' years

Outperfo r mance emerging fro m the tro ughs

85 80 99

00

01

02

03

04

05

06

07

08

09

10

Source: GS Global ECS Research

Chapter 3

-4

-2

0

2

4

6

Measuring the dispersion of output gaps worldwide. The observations described above seem to imply that the scope for FX as a redistributive tool is the greatest when the dispersion of output gap changes is the greatest across countries. This would logically concur with the period around the troughs of a global recession and during the ensuing stages of recovery, when there are differences in the pace of recovery across countries. It is not until later in the business cycle, closer to the peak, when economies are all growing at maximum capacity, that we see little dispersion in the speed at which output gaps narrow. The charts on the next page show the changes in output gap in 2009 and in 2007: we see little dispersion in 2007 when all economies were close to their peak and ‘overheating’, while 2009 shows economies during the trough of the business cycle with very large differences in the pace at which the output gap widens. This in turn sets the stage for differences in the pace of subsequent output gap

Output Gap Differentiation Basket Shows Interesting Differential Performance Corresponding to Stages of the Cycle

90

-6

A cursory look at the performance of our output gap differentiation basket (we constructed a basket of currencies grouped according to differences in output gaps) reveals years of good performance following periods of stalled performance, as seen in the chart below. A closer look at the series seems to show a relatively good correspondence with the boom/bust fluctuations through the cycles. For example, the index shows mixed performance during the height of the tech bubble years in the early part of this decade. This was followed by returns of around 30% from 2002 to 2005 as the global economy emerged from the troughs of the ‘dot com’ bust and steadily grew from there. However, as we approached the peak of the cycle, the index stalled again. The index did not start to show signs of life again until after we emerged from the troughs of the most recent crisis.

The local output gap tends to matter more than the global output gap.

95

-8

Having pinned down the relationship between output gaps and FX, we then identified the periods of the cycle that provide the most fertile ground for growth differentiation strategies to take root.

The changes in output gaps are more important for FX performance than the absolute levels of the gap.

105

-10

Which part of the cycle best rewards growth differentiation for FX?

The table on the previous page summarises the results of our regressions: a positive result indicates that the variables of domestic or global output gaps are statistically significant (we have included the coefficient of the variable in question, followed by its t-statistic in brackets). Our three main findings are as follows:

110

-12

Source: GS Global ECS Research

output gaps matter more. We have attempted to define the relationship empirically: we performed a regression analysis, running trade-weighted FX returns against the levels of and changes in both domestic and global output gaps, and controlling for certain exogenous factors (see the box at the end of this chapter for further details on the exact specification).

120

OP gap change (%)

-5

Source: GS Global ECS Research

Index

Nominal TWI returns (%)

-10

-70 1981

-12

Mexico: TWI Returns vs Output Gap Change Since 1981

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Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Changes in Output Gaps: Least Dispersion at the Peak of the Cycle (2007)...

11

…And Most As We Emerge From the Troughs (2009) 1

10

0 -1

9 8 7

-2 -3 -4

6 5

-5

4 3

-6 -7

2007

2

HUF CAD SEK EUR NZD NOK USD TRY CLP GBP MXN AUD IDR THB ZAR CHF KRW VND JPY INR ILS MYR BRL CZK HKD PLN PEN PHP TWD RUR VEB CNY COP SGD ARS

-10 -11

Source: GS Global ECS Research

Source: GS Global ECS Research

returns in our output gap FX basket (see chart below). Specifically, FX returns appear to be high when output gap dispersion is also high, which in turn corresponds to the periods when the global economy emerges from recession, as we showed in the previous section.

narrowing during the recovery. Growth differentiation strategies seem to work best during this latter stage. To arrive at a measure of dispersion of output gaps across countries, we take the standard deviation of the output gap changes across the different countries for any given year. This measure of output gap dispersion has a fairly good inverse correlation with global GDP growth (see chart below). And it lends support to our earlier reasoning that output gaps are at their most dispersed across countries when the world is emerging from the trough of a business cycle and, conversely, are least dispersed close to the peak of the cycle.

The same can be shown more formally through a simple linear regression. We find a rather tight relationship with an R-squared of 0.7, as can be seen in the chart on the next page. This regression also reveals that a dispersion of global output gap changes of more than 1.6 standard deviations typically results in positive returns for our output gap FX basket. We currently expect an output gap dispersion of around 2.9 standard deviations for 2009, which is well above the level that would normally result in positive FX returns, and implies great scope for FX trades based on growth differentiation strategies into 2010 and beyond. Indeed, our Growth Current—the tradable version of a basket of currencies differentiated in practice according to variations in the output gap—has started to outperform, after months of stalled performance.

FX growth differentiation strategies outperform when output gaps most dispersed across countries. Having established the links between the business cycle and output gap dispersion, we can now return to our initial hypothesis that FX growth differentiation provides the best returns during the early stages of a recovery. We find that a good relationship exists between the dispersion of output gap changes and 1-year lagged

Std Dev

3.5

Output Gaps Are Most Dispersed Emerging From Cycle Troughs

% chg yoy

Measure of output gap dispersion across the w orld

3

w orld GDP grow th (Inverted RHS)

2.5 2

%

-2.0

10

-1.0

8

0.0 Increasing output gap dispersion

1.5

1.0

0.5

3.5 3

4

2.5

2009 YTD returns

2.0 2

2

0

4.0

1

Dispersion in Output Gaps Across Countries Std. Dev Drive FX Returns

6

3.0

5.0

-2

6.0

-4

7.0

-6

95 96 97 98 99 00 01 02 03 04 05 06 07 08 09

1.5 1

OP gap basket returns (lagged 1 year) OP gap dispersion (RHS)

0.5

96 97 98 99 00 01 02 03 04 05 06 07 08 09

Source: GS Global ECS Research

Chapter 3

TRY MXN TWD SGD HUF CZK THB MYR HKD JPY SEK GBP AES ILS EUR ZAR CLP USD CAD KRW COP BRL PHP NZD CHF PEN PLN VEF NOK AUD VND INR IDR CNY

-8 -9

1 0 -1

2009

Source: GS Global ECS Research

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The Impact of the Output Gap on FX—Our Methodology SPX is the S&P 500 index, intended to capture underlying risk sentiment and the impact on FX; GSCI is the Goldman Sachs Commodity index included to account for the link between commodity prices and currencies, important for commodity currencies in particular; the TWIs are the GS trade-weighted exchange rates and we have included the Dollar TWI as a RHS variable to account for currency moves driven by broad Dollar moves. We ran these regressions for countries where we have sufficient data across the G10 and emerging markets. The sample period for this runs from 1981 to 2008.

We attempt to test the relationship between output gaps and FX. We calculate the output gap as the difference between real actual GDP over potential GDP, expressed as a ratio of potential GDP. To obtain a consistent measure of output gaps across countries, we have estimated potential GDP here using the Hodrick and Prescott filter, a simple statistical procedure. This is just one of various ways to estimate a country’s trend GDP. The purpose of our discussion here isn’t to establish the best technique for estimating potential growth or to replace the more formal models that we have for some individual countries. But rather to subject each country to a consistent method of estimation and in so doing obtain a ranking for relative FX performance.

Note that we used real TWIs instead of nominal exchange rates as the LHS variable. We think the implications for real TWIs can be mapped onto our nominal exchange rate views given the assumption that relative inflation differentials should be fairly stable over our trade implementation horizon, especially given increased and more successful inflation targeting over the years.

We ran OLS regressions, looking at the changes in real trade-weighted exchange rates versus moves in the domestic and global output gaps, while controlling for risk sentiment, commodity moves and broad Dollar moves. We ran our regressions according to the following specification:

As a cross-check, we also tried different specifications of the model, including output gap levels alone, output gap changes alone, and the changes in output gap as a share of the levels. We find that the specification presented above has the ‘best fit’ among the various specifications and produces results that are largely consistent across countries.

Equation 1 ∆ Real TWI = α+ β1*LGAP + β2*(LGAP-LGAP(-1)) + β3*GGAP+ β4*(GGAP-GGAP (-1)) + β5* ∆SPX + β6*∆ GSCI+ β7*∆USD TWI + µ where LGAP is the local or domestic OP gap; GGAP is the global output gap as proxied by the G7 output gap;

Positive FX Returns When Output Gap Dispersion Above 1.6 Std. Dev. 3.5 Global Output Gap Dispersion (Std dev)

3 2.5

y = 0.1x + 1.6 R 2 = 0.7

2 1.5 1 0.5

% return in output gap FX basket

0 -6

-4

-2

0

2

4

6

8

10

Source:GS Global ECS Research

Overall we expect the next couple of quarters to present attractive opportunities for FX strategies based on relative growth strategies and, in particular, those that focus on relative changes in the output gap. Mark Tan

Chapter 3

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The Foreign Exchange Market

Chapter 4: The Benefits of Investing in Portfolios of FX Currents Following the introduction of the new tradable FX Currents to replace our purely analytical FX Slices, we look at the construction of portfolios of FX Currents with high Sharpe ratios. One key result is that very Sharpe ratios can theoretically be obtained—even when taking into account indicative trading costs. In addition, certain FX Currents tend to perform particularly well in certain macro environments. We intend to apply the results of our analysis when formulating FX strategy and recommendations in the future. We then look at the composition of these portfolios over time to extract lessons on the combinations of tradable themes that have provided the best returns over the different stages of the last cycle.

FX Slices Become FX Currents Our FX Currents are based on the FX Slices concept, which we introduced four years ago in the 2005 issue of The Foreign Exchange Market. The purpose of the Currents project was to create long-short portfolios of currencies that were meant to capture the performance of a particular macro theme in the FX market. Since then, we have used the Currents to analyse the trading environment, assess the potential for different crosscurrency trades to perform (given the market trends), and express our views on the potential future performance of the different Currents.

We have identified the relevant patterns in each Current, and these broad patterns should help us formulate our strategy.

Portfolios of FX Currents: Combining Themes offers Higher Sharpe Ratios An FX Current represents a simple approach to implementing a specific theme in the FX market. For example, the Growth Current offers a simple benchmark to quantify the market’s preference for high growth currencies. To the extent that strong growth is one of the key themes driving the FX market, this Current aims to capture the shifts in this theme.

As we wrote recently (see Global Viewpoint 09/12, July 20, 2009), the FX Currents replace our FX Slices, making them fully tradable instruments. We have six FX Currents at present: the G10 & Emerging Markets Carry Current, the BRIC/N-11 Current, the Energy Current, the Valuation Current, the Growth Current and the Current Account Current. We constantly monitor their performance for analytical purposes but also intend to use them for our trade recommendations.

However, even from a theoretical perspective, an index approach (which is what the FX Currents are) is not the most pure expression of a theme. This is because typically a combination of themes drive price action and it is difficult to disentangle the individual impact of each theme. In that sense, the price action in each Current may reflect a set of underlying macro drivers and, vice versa, each theme may have multiple expressions in different Currents or in different combinations of Currents.

Different FX Currents tend to outperform during different stages of the business cycle. For example, Chapter 3 in this publication shows that the FX Growth Current typically posts good returns during early stages of a global recovery. However, beyond focusing on the likely performance of one individual FX Current, it is also important to look at the linkages between them. This chapter forms part of this effort. Here, we look at FX Currents from a portfolio perspective, and examine how individual Currents and portfolios of Currents have performed over time.

We have attempted to gauge the overall impact of combinations of different macro themes on the FX markets in the past. In the 2006 issue of The Foreign Exchange Market we introduced our ‘Multivariate Slices’ analytical framework, which used rolling cross-sectional regressions to de-compose moves across currencies into different factors. Although that approach was not based on tradable macro factors, it did indicate that interest rates, volatility and Dollar direction were among the most important drivers of price action in the FX markets.

We find that, although some individual Currents (such as the Carry Current) do offer high Sharpe ratios, combining Currents in portfolios offers better reward for risk than individual ones, especially if we adjust for trading costs. We also look at ‘optimal’ portfolios of Currents, designed ex-post to give the highest Sharpe ratios among different combinations of Currents (under specified constraints).

In this piece we approach the problem from a new angle. We combine our tradable FX Currents in portfolios and try to gauge the returns that combinations of FX themes can offer.

Table 1: How to Find FX Currents in Bloomberg FX Currents

Bloomberg Tickers

G10 & Emerging Markets Carry Index

GSCUEMCC Index

BRIC/N11Core Index

GSCUBRIC Index

Energy Currencies Index

GSCUENER Index

Valuation Index

GSCUVALU Index

Growth Index

GSCUGROW Index

Current Account Index

GSCUCACC Index

To place FX Currents in the context of a broader portfolio of FX indices, it is useful to look first at some simple descriptive statistics. Table 2 shows the average volatilities and returns for different FX Currents over the period from 1999 to mid-2009. A first observation is that most Currents have very comparable volatilities of

Source: GS Global ECS Research

Chapter 4

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Goldman Sachs Global Economics, Commodities and Strategy Research

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Table 4: Correlations Across Currents

Table 2: Historical Risk Reward in Different Currents Average

Carry Valuation Growth

Return

7.2% 4.3%

Vol

1.7

S.R.

2.0%

2.3%

3.3%

2.7%

0.6

0.8

CA -1.3% 3.3% -0.4

Carry Valuation Growth

BRIC/N11 Energy 2.0% 3.5% 0.6

BRIC/N11 Energy

100%

2.0%

YLD

2.7%

VAL

-6.4%

100%

0.7

GRO

13.4%

-2.5%

100%

CA

-58.6%

8.1%

-13.1%

100%

EM

43.0%

1.4%

-15.2%

-3.9%

100%

ENER

44.6%

7.3%

21.2%

-46.9%

-33.5%

Source: GS Global ECS Research

between 2.7% and 3.5% p.a.; the exception is Carry, which is far more volatile than other Currents, with an average annualised volatility of 4.3%.

There is no single year in which portfolios of FX Currents have yielded negative returns. During years when cyclical pressures have been more supportive towards risk-taking (e.g., 2005-2007), equallyweighted baskets offered better returns relative to volatility-adjusted baskets, as they had more exposure to riskier Currents, and vice versa. Overall, it appears that there are diversification benefits to holding broader baskets of FX Currents. This should also be visible in the correlation structure among Currents. In Table 4 we highlight the correlation in historical returns between Currents. We focus on the correlations above 30% (or below -30%).

This simple set of statistics provides further evidence that carry trading strategies tend to be among the most profitable FX strategies over time.

The most important correlation seems to be between the Carry Current, the Energy Current and the Current Account Current. Historical observation suggests that the Current Account Current and the Carry Current are negatively correlated. We have written extensively about the fact that risk-on types of environment favour carrydriven investments, and that at times of risk aversion, current account surplus countries tend to benefit.

However, this does not mean that investors need only buy high-yielding currencies. Table 3 shows the Sharpe ratios of baskets of FX Currents over the whole sample (19992009), as well as in individual years. We use two simple weighting methodologies to create our baskets of Currents: equal and volatility-adjusted weights (higher vol Currents are assigned lower weights). Three key things emerge as most interesting on first examination:

The cross-linkages between the Energy Current and the Current Account Current are also interesting, since the large uptrend in commodities over recent years is responsible for a significant part of the external surpluses/deficits across the world. Potentially, the link between the Energy Current and the Carry Current can be related to the impact of global growth expectations on risky assets and commodity prices alike.

Simple baskets of FX Currents such as these offer better Sharpe ratios on average than any individual Current does. Equally-weighted baskets offer higher risk-adjusted returns compared with volatility-weighted baskets, which is an argument for allocating more capital on higher-risk Currents.

Lastly, it is interesting to note that the Valuation and Growth Currents can be sources of relatively uncorrelated returns.

Table 3: Sharpe Ratios of Simple Static Portfolios of Currents Sharpe Ratio

Equal weights

Vol Weights

1999

3.05

3.03

2000 2001 2002 2003 2004

0.87 1.81 3.13 2.77 1.64

0.95 1.70 3.25 3.06 1.97

2005 2006 2007 2008 2009

3.11 0.85 1.36 1.70 3.12

2.87 0.59 1.23 1.49 3.25

Whole Sample

1.82

1.77

100%

Source: GS Global ECS Research

And while the volatilities of the different Currents are broadly comparable, the average annual returns are substantially different, creating disparities among Currents in terms of Sharpe ratios. At one extreme, the Carry Current (the FX index that mostly captures global markets’ risk sentiment) has an annualised Sharpe ratio of almost two, combining the highest volatility with the highest average return. At the other extreme, the ‘defensive’ Current Account Current exhibits negative returns and high volatility.

Constructing an Optimal Portfolio of Currents; Lessons from Past Experience So far we have discussed evidence that there may be benefits to investing in portfolios of FX Currents and that these benefits may come from the effects of correlations between themes. However, we have looked at portfolios of FX Currents in a static way, disregarding the fact that some of these correlations may be stronger or weaker over time, or that one can change basket weights to adapt to different market conditions. In order to better understand how the shifts in the macro trading environment create different sets of opportunities for different FX Currents, we created ‘optimal’ portfolios

Source: GS Global ECS Research Chapter 4

CA

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Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

of FX Currents for every year from 1999 to 2008 and for the first half of 2009. We used daily data for each year to find the combination of FX currents that provided the highest possible Sharpe ratio. We assume long only positions in FX Currents (so the minimum weight of a current in a basket is no less than zero) and we assume that weights always have to sum up to 100%.

Chart 2: Carry Weights 80.0% 70.0% 60.0% 50.0%

These assumptions replicate an investor profile of a portfolio manager who has a particular capital to allocate to FX Currents without extra leverage and without keeping any of the amount in any form of cash in any currency outside those invested in the Currents. This is a reasonably realistic set of assumptions. Moreover, these restrictions help us to avoid corner solutions during the optimisation process.

40.0% 30.0% 20.0%

Overw eight

10.0%

Underw eight

0.0% 1999 2000 20012002 2003 20042005 20062007 2008 2009 Source: GS Global ECS Research

For every year we optimise a portfolio of Currents to offer the highest (ex-post) Sharpe ratio. Chart 1 shows the Sharpe ratios achieved through this optimisation process. The chart suggests that very high excess returns can be achieved in FX markets by investing through portfolios of Currents, as long as investors combine them in an optimal way. That said, it is important to highlight that ex-post optimisation is not particularly fair—there will always be an optimal portfolio of FX Currents that offers the maximum possible Sharpe ratio. Nonetheless, it is still interesting that, in certain years, Sharpe ratios reached 5.00—a significantly high level of excess returns in a cross-asset context.

Current: at one extreme, in 2008 our framework shows that it would be optimal to be long carry with a weight less than 14% (underweight relative to an equallyweighted basket). At the other extreme, during 2000, the weight of the carry basket rose above 70%. As implied by our correlation analysis earlier, owning the Current Account Current can offer substantial diversification benefits. Given the large negative correlation to risky assets, it is unsurprising that the Current account Current entered the optimal basket in 2002, 2007 and 2008. What is more interesting is that during the peak of the ‘carry fever’, in 2006, the CA basket received its largest weight of more than 40%. Lastly, we note that in 2001 and 2007/2008 it was worth holding a combination of the Carry basket and the Current Account basket, rather than simply holding a defensive position by being long the current account. In other words, it was more profitable to hold a diversified position than go outright short risk in the FX markets.

In addition, we can extract useful information by looking at the weights of different optimal portfolios, and understand during what types of trading environments it is optimal to hold different combinations of FX Currents: It is no big surprise that it was worth owning the Carry Current in every year (we have written extensively on the systemic reward for risk in carry trading strategies). However, it is also interesting that during years of cyclical downturns the weight of the Carry basket in the optimal portfolio falls. There is an element of cyclicality in the weights of the Carry

There appears to be very little relationship between cyclical forces and EM outperformance. However, our exercise here is to look at the BRIC/N-11 Current Chart 3: CA Weights

Chart 1: Sharpe Ratios of "Optimal Baskets" 5.0

45.0%

4.5

40.0%

4.0

35.0%

3.5

30.0%

3.0

25.0%

2.5

20.0%

2.0 1.5

15.0%

1.0

10.0%

0.5

5.0%

0.0

Underw eight

0.0%

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

1999 2000 20012002 2003 20042005 20062007 2008 2009

Source: GS Global ECS Research

Chapter 4

Overw eight

Source: GS Global ECS Research

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Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Chart 6: Valuation Weights

Chart 4: BRIC/N11 Weights 35.0%

40.0%

30.0%

35.0% 30.0%

25.0%

25.0% 20.0% 15.0%

Overw eight

20.0%

Underw eight

15.0%

10.0%

10.0%

5.0%

Underw eight

5.0%

0.0%

0.0% 1999 2000 20012002 2003 20042005 20062007 2008 2009

1999 2000 20012002 2003 20042005 20062007 2008 2009

Source: GS Global ECS Research

Source: GS Global ECS Research

11 Current re-enters the optimal basket in 2008— when many EMs had to allow currency appreciation to fight inflation pressures (up until the third quarter).

within the context of a broader portfolio. Within that portfolio, a number of other Currents reflect cyclical risks and broader swings in risk appetite in a more straightforward way (including the Carry Current, as we showed above).

As the correlation analysis above also showed, there is a large idiosyncratic component to the Growth and Valuation Current. In the previous cycle, growth became a great theme to own, and in high percentages, during the early stages of the recovery (2002-2004) and in the late part of the cycle (2007-2009). This is an intriguing result in the context of Mark Tan’s work on output gaps mentioned earlier. He argues that changes in the output gap tend to matter most for FX outperformance during the early stages of the recovery.

In this context the BRIC/N-11 Current represents the potential for genuine EM outperformance beyond risk swings. Overall, the BRIC/N-11 Current tends to enter the ‘optimal portfolio’ in years of thematic outperformance of emerging markets. For example, the BRIC/N-11 Current only entered the optimal basket with a significant weight in 1999 (the year of recovery after the EM crises of 1998), in 2005 (which saw significant EM outperformance preceding the 2006 EM sell-off) and in 2008-2009 (when EMs held up well despite broader pressures in risky assets).

Our Growth Current is based on growth relative to trend and therefore reflects shifts in the output gap. And it is during the recession and the early stages of the cycle that these shifts tend to be larger and more visible. In other words, the Growth Current appears to be better at capturing the shifts in the output gap when these shifts are most noticeable.

Another point to be made here is that the BRIC/N-11 Current includes a number of currencies that are managed tightly relative to the USD. It therefore tends to stagnate performance-wise during times of significant overall Dollar depreciation pressures, such as in 2003 or 2006. Equivalently, changes in FX policy in emerging markets can result in significant shifts in FX performance. For example, the BRIC/N-

The easiest way to identify patterns in the Valuation Current is to identify the years when it DOES NOT

Chart 5: Growth Weights

Chart 7: Energy Weights

80.0%

40.0%

70.0%

35.0%

60.0%

30.0%

50.0%

25.0%

40.0%

20.0%

30.0%

15.0%

20.0%

Overw eight

10.0%

Underw eight

10.0%

Overw eight Underw eight

5.0% 0.0%

0.0%

1999 2000 20012002 2003 20042005 20062007 2008 2009

1999 2000 2001 20022003 2004 20052006 2007 2008 2009 Source: GS Global ECS Research

Chapter 4

Overw eight

Source: GS Global ECS Research

25

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From a practical perspective it is important to verify the levels of risk/reward in the most realistic set-up possible to see if our conclusions about the Sharpe ratios of the baskets still hold.

Table 5: Sharpe Ratios of Currents Subtracting Trading Costs Average

YLD

VAL

GRO

CA

EM

ENER

Return Vol S.R.

6.0% 4.3% 1.4

0.5% 3.3% 0.2

0.7% 2.7% 0.3

-2.6% 3.3% -0.8

1.0% 3.5% 0.3

1.1% 2.7% 0.4

Finally, there are different costs attached to different FX Currents. It is therefore important to see whether the conclusions from the previous section hold or if different cost structures influence the optimal basket weights.

Source: GS Global ECS Research

enter the optimal basket. Those years tend to be towards the late part of the cycle: 1999, 2006, 2007 and 2008. There is no rigorous way of explaining why markets tend to focus away from valuation late in the cycle but one can intuitively see why this may be the case. During the later stage of the cycle, investment themes with solid fundamental justification tend to overshoot as market speculation drives prices beyond what fundamental benchmarks imply. One example in the most recent cycle has been the FX valuation misalignments created and sustained late in the cycle in commodity currency space (due to the sharp spike in commodity prices).

According to an early estimate of trading costs, fixed baskets such as the BRIC/N-11 Current or the Energy Current cost the least. The Valuation and Growth Currents are the most costly, while the Current Account and Carry Current costs lie somewhere in the middle. Including those trading costs reduces Sharpe ratios significantly. The Carry Current still stands out as the only Current offering a Sharpe ratio above 1, overall a decent reward for risk. Given that Sharpe ratios were fairly similar for the Growth, Valuation, Current Account, Energy and BRIC/N-11 Currents, the different cost structures make a difference. The lower costs for Energy and BRIC/N-11 Currents keep Sharpe Ratios somewhat higher than in the Valuation Current, whose Sharpe ratio is reduced significantly by trading costs on a buy and hold basis. The Current Account Sharpe ratio becomes even more negative.

The patterns in the Energy Current are less obvious. At the very least, the best years to hold the Current were not necessarily the best-performing years for oil. This may well be due to the fact that other Currents may be capturing the macro impact of underlying shocks that also move energy prices. For example, the Carry Current, which is closely correlated with the Energy Current, may be capturing the pro-cyclical nature of commodity price fluctuations to a large extent.

As we showed earlier, although holding these Currents over time may not have resulted in high Sharpe ratios, including them in portfolios and managing them according to certain patterns may offer high reward for risk.

Including Trading Costs in Our Analysis; From Theoretical to Practical Considerations

Including trading costs does not change our results for when returns on holding each individual Current were better. Looking at our optimal basket, the only thing that changes is that, on average, our optimisation gives the Carry Current a larger weight than without trading costs. But that is to be expected given the reduction in Sharpe ratios for other currents, as noted above.

So far our analysis has not taken into account trading costs. From a theoretical perspective, fixed trading costs over time should not alter our broad conclusions about how the optimal combinations of FX Currents within broader portfolios change over time and along the cycle. However, it is still worth cross-checking that assumption.

5.00 4.50 4.00

Combining Currents Offers Better Reward for Risk

Chart 8: Sharpe Ratios After Transaction Costs Remain High

Although some individual Currents do offer high Sharpe ratios, combining the Currents in portfolios offers substantially better reward for risk than individual ones, especially if we adjust for trading costs.

Without Trading Costs With Trading costs

Another key result from our analysis is that there are periods in the business cycle when specific Currents are expected to be relatively more valuable. Our plan is to conduct more detailed research in this area, which will be critical to using Currents to express shorter-term views on macro themes.

3.50 3.00 2.50 2.00 1.50 1.00

Themistoklis Fiotakis

0.50 0.00 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Source: GS Global ECS Research

Chapter 4

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Chapter 5: Updating Our Trade-Weighted Exchange Rates and Looking at the Real TWIs Trade-weighted indices are a universally used measure of a currency’s broad strength. We use such indices both to generate trading recommendations and in our modelling work. In this chapter we present our latest trade weights and some innovations to the way we calculate the weights, making them a better reflection of a country’s evolving trade links. We also introduce real trade-weighted indices for all the currencies we cover. Our TWIs are available on GS Plottool for client use. developed markets. In extreme cases, hyperinflation can significantly distort a nominal TWI. Real trade-weighted indices take account of such differences by incorporating relative price levels into the calculation. As a consequence, real exchange rates are better-placed to capture longer-term changes in competitiveness than their nominal cousins.

Why look at Trade-Weighted Exchange Rates? In any given day and over any given period, a currency is likely to strengthen against some currencies while weakening against others. Although bilateral exchange rate movements invariably capture the headlines, such moves often belie the broader performance of a particular currency. A prime example recently has been the CNY. Since last summer, it has essentially been fixed against the Dollar and thus the CNY is broadly assumed to be stable. However, if we look at the CNY on a TWI basis, it had appreciated by 15% to early March but has since depreciated by 10%.

Method of Calculation Our TWI weights are based on a large sample of 53 countries. The weights for each TWI are derived from this selection. If a country has a weight of 0.5% or more, it is then included in the index—otherwise it is dropped and the weights are then rebalanced to sum to 1. This process is repeated annually; consequently, the country selection can change every year. Reflecting a trend of continued globalisation, the number of countries in a particular TWI tends to increase over time. In the case of Brazil, for example, the number of countries in the TWI has expanded from 16 in 1980 to 30 in 2008.

Consequently, to gain a sense of a currency’s overall performance, we need to combine each of the bilateral exchange rates into a single index. The logical weighting system for such an index is to choose weights that reflect the importance of trading relationships. There is a long history of using trade-weighted indices (TWIs) in the analysis of currency movements and their wider economic implications (for example, the implications of broad currency movements for net trade). Such indices are also an appropriate input into Financial Conditions Indices, whereby an appreciation of a currency tends to loosen financial conditions. It is also instructive to look at the ‘fair value’ of a currency in broader terms.

Each weight is made up of three components: import share, export share (which would be found in a ‘simple’ trade-weighted index) and third-country competition. The latter requires some explanation. Goods produced in one country face competition in two places: in the domestic market (with imports from other countries) and in export markets (where the goods face competition from both the local goods in the target market and third-country exports to that target market). Relative exchange rate changes can affect such competition. We include third-country effects in the weighting scheme to capture these dynamics. The calculation also takes into consideration how open an economy is by including imports as a share of GDP (for more details on the calculation method, refer to The Foreign Exchange Market 2004, Chapter 2).

Nominal TWIs implicitly assume that inflation is the same across countries. In the short run, this is not a particularly bad assumption. However, in the longer run it is less appropriate; for instance, many emerging market economies exhibit higher rates of inflation than more $/CNY

CNY has Appreciated on a TWI Basis

7.4 7.3

Index

38.0 37.0

TWI Appreciation

36.0

7.2 7.1 7

The bulk of the underlying data used in the weighting calculations comes from the IMF, both the Direction of Trade Statistics and International Financial Statistics. We aim to update the weights for the previous year in the following spring, when the latest IMF trade data becomes available.

34.0 $/CNY (lhs) CNY TWI (rhs)

6.9

Data Considerations

35.0

33.0 32.0 31.0

There is much debate in the economic literature over which price measure to use in the calculation of real exchange rates. Given that a TWI is designed to capture

6.8 30.0 Jan-08 May-08 Sep-08 Jan-09 May-09 Sep-09 Jan-10 Source: GS Calculations

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competitiveness, more appropriate measures of inflation are provided by PPI, WPI or unit labour costs, as these measures are more reflective of the prices facing producers. In contrast, CPI tends to include prices for services and other non-tradable products. However, while not the optimal choice, CPI often pans out as the inflation measure of choice because it is timely, widely available and calculated in a broadly similar fashion across countries. We have therefore opted for this measure. Lastly, our model of ‘fair value’—GSDEER—also uses CPI inflation for similar reasons. As with the rest of the data, the IMF is the principal source.

index

260 240 220

Nominal Real

200 180 160 140 120 100

The Weights

80

The tables in the appendix to this chapter provide the latest weights for the TWIs of the currencies we cover. Unsurprisingly, the largest countries in the world (e.g., the G3) appear in all the indices. However, given increasing globalisation, the growth of emerging market economies and rising commodity prices, many of the indices now also ascribe high weights to countries such as China, Brazil and Russia. India is not as dominant as the other three BRICs countries.

80 82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 Source: GS Calculations

China and Mexico has intensified. In 1980, 64% of the US TWI weights were accounted for by the so-called major markets. By 2007, this had slipped to 50.9%. Trade dynamics are a slowly evolving process and it would be unsurprising if this proportion declined further in coming years.

Looking at the history of the TWI weights, we can trace the rise of globalisation, particularly as the weights of the BRICs economies become larger over time. The weights of the N-11 are also likely to become more prominent. That said, a particular country’s trade links are still strongest with its neighbours. A glance at the set of Asian weights indicates a different set of important countries in comparison to the countries that make up the weights in the Latin American and New European Markets’ TWIs. Taking a more detailed look at the US TWI, we can see the rise in importance of emerging markets in USD trade weights. The accompanying chart shows that while the importance of Japan, and to a certain extent Canada, has declined in US trade since the early 1980s, trade with

%

US$ TWI: Real vs Nominal

280

To supplement the nominal TWI analysis, we have introduced a set of real TWIs to remove the distortion of inflation from the nominal TWIs.1 The difference between the nominal and real US TWIs are shown in the chart above. Fiona Lake, Roman Maranets and Swarnali Ahmed

Evolving weights in the Dollar TWI

25.0%

20.0% 1

Clients can access our TWIs on GS Plottool

CAD 15.0%

CNY

Nominal TWIs are found using the code: GS_CCC_TWI For instance, the Dollar TWI is GS_USD_TWI

JPY MXN

10.0%

Real TWIs are found using the code: GS_CCC_RTWI For instance the real Dollar TWI is GS_USD_RTWI

5.0%

0.0% 80 82 84 86 88 90 92 94 96 98 00 02 04 06 08 Source: GS Calculations

Chapter 5

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Appendix TWI Weights (%) ARS TWI AUD TWI BRL TWI CAD TWI CHF TWI CLP TWI CNY TWI COP TWI CZK TWI EUR TWI GBP TWI HKD TWI HUF TWI IDR TWI ILS TWI INR TWI JPY TWI KRW TWI MXN TWI MYR TWI NOK TWI NZD TWI PEN TWI PHP TWI PLN TWI RUB TWI SEK TWI SGD TWI THB TWI TRY TWI USD TWI VEB TWI ZAR TWI

AED

ARS

1.1 0.8 0.7 0.5 0.6 0.7 4.0 4.1 2.6 1.1 1.1 1.5 1.8 4.1 1.5 1.0

8.9 6.0 0.8 1.3 0.6 0.6 3.0 2.3 1.6

AUD BGL

BRL

CAD CHF

0.6 0.9 0.6 0.7 0.8 3.1 1.1 1.1 1.3 3.7 1.0 3.8 5.1 3.3 3.5 20.7 2.0 0.9 3.4 4.2 0.6 1.4 2.4

30.3 0.8 0.8 1.1 8.6 2.6 5.2 2.1 0.9 0.7 1.1 1.5 1.8 1.3 1.4 2.0 0.9 1.0 6.6 1.0 1.5 0.8 0.7 1.2 0.8 2.5 7.1 2.1

1.1 1.3 2.0 1.2 2.4 1.9 2.4 1.5 1.9 0.9 1.3 1.5 1.4 2.0 1.5 4.5 1.1 2.8 1.6 4.5 1.3 0.7 0.8 0.9 1.0 0.9 18.3 2.4 1.3

1.0 -

0.7 0.8 1.1 0.6 0.7 1.4 1.4 4.7 1.6 1.1 1.3 4.8 0.9 0.8 0.7 1.1 0.6 1.5 1.1 1.8 1.1 0.7 1.7 2.8 1.2 0.8 1.4

CLP 3.6 2.5 0.9 3.0 0.5 0.7 0.8 1.0 0.8 5.2 0.7 1.8 -

CNY COP 12.6 15.9 12.9 7.1 3.5 14.6 7.0 3.9 9.8 6.1 44.7 5.6 12.7 6.7 16.2 19.8 24.4 5.5 15.0 4.8 11.5 13.1 19.6 3.6 10.9 3.9 13.5 13.1 6.3 13.5 7.7 11.7

0.6 1.0 2.7 0.6 0.8 3.5 0.9 10.3 -

CZK

DKK

DZD

ECS

EEK

EGP

EUR

1.0 3.1 1.0 3.5 0.9 4.0 1.5 1.2 0.8 -

0.6 0.9 2.3 1.3 0.9 5.6 0.6 1.8 0.7 8.5 0.7 -

0.6 1.0 1.1 1.5 1.7 0.6 -

2.0 2.6 3.5 1.0 -

0.6 -

0.6 0.8 -

17.2 12.4 20.3 8.1 57.0 15.3 15.0 13.0 58.4 48.5 8.8 54.2 9.4 30.2 18.3 10.8 10.0 9.3 10.1 40.5 11.5 13.2 8.8 57.0 38.3 45.0 11.6 9.6 35.2 16.6 11.5 26.5

Continued on the next page…

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TWI Weights (%) GBP ARS TWI AUD TWI BRL TWI CAD TWI CHF TWI CLP TWI CNY TWI COP TWI CZK TWI EUR TWI GBP TWI HKD TWI HUF TWI IDR TWI ILS TWI INR TWI JPY TWI KRW TWI MXN TWI MYR TWI NOK TWI NZD TWI PEN TWI PHP TWI PLN TWI RUB TWI SEK TWI SGD TWI THB TWI TRY TWI USD TWI VEB TWI ZAR TWI

1.7 4.8 2.4 3.3 5.2 1.4 2.5 2.1 4.9 13.7 2.2 4.2 1.4 4.7 4.5 2.0 1.8 1.1 1.9 16.3 3.5 1.2 1.5 5.4 4.0 8.1 2.4 2.1 5.5 4.2 1.6 8.3

HKD HRK HUF 0.8 1.5 0.8 1.0 4.1 0.7 0.9 0.9 0.8 2.7 2.2 2.6 1.1 1.9 0.7 3.3 1.1 0.7 3.5 0.6 1.7 1.6 0.9 1.0

0.8 -

0.6 2.6 2.0 0.7 1.9 1.4 0.7 0.7 -

IDR

ILS

INR

JPY KRW KZT

0.7 2.5 0.8 1.7 1.0 3.0 3.5 2.4 4.6 2.8 2.6 5.9 3.8 0.7 0.9 0.8

1.2 0.7 0.8 1.0 1.2 1.1 0.7

1.2 3.4 1.6 0.7 0.9 2.0 2.8 1.0 1.8 1.6 2.2 0.5 4.0 3.7 1.4 2.0 0.7 2.7 0.5 1.4 0.9 1.1 1.2 0.9 3.8 2.2 1.2 1.7 2.6

2.2 16.6 5.0 3.7 3.1 8.3 14.1 2.8 1.8 4.1 2.6 8.4 2.1 17.3 3.5 5.2 14.0 3.2 11.6 2.1 10.3 5.9 15.1 1.0 5.8 2.0 9.8 19.1 2.0 7.5 1.8 9.3

1.3 4.6 2.6 1.3 0.7 5.4 9.0 1.8 0.6 1.8 1.1 3.3 1.4 5.7 1.8 3.6 5.7 3.2 4.3 1.2 3.3 2.7 4.4 1.4 3.5 0.8 5.5 3.9 1.7 2.7 2.4

0.7 0.7 2.9 1.1 -

LBP

LVL

-

0.7 -

MXN MYR NGN NOK 2.9 0.7 2.4 3.4 0.5 3.5 1.0 5.9 1.2 0.6 0.6 0.9 1.1 1.3 0.6 0.8 2.8 0.6 11.3 4.6 -

0.6 3.1 0.8 2.5 0.8 0.5 1.9 5.6 2.5 2.4 1.9 1.2 3.2 3.3 0.6 8.8 4.4 0.6 1.2 1.1

2.7 0.8 0.6 0.7 1.3 1.8

0.5 1.1 0.6 2.8 4.2 1.6 9.5 -

NZD 3.6 0.6 0.6 0.6 0.6 -

Continued on the next page…

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TWI Weights (%) OMR PEN PHP PLN QAR ROL RUB SAR SEK SGD SKK THB TRY TWD UAH USD VEB VND ZAR ARS TWI AUD TWI BRL TWI CAD TWI CHF TWI CLP TWI CNY TWI COP TWI CZK TWI EUR TWI GBP TWI HKD TWI HUF TWI IDR TWI ILS TWI INR TWI JPY TWI KRW TWI MXN TWI MYR TWI NOK TWI NZD TWI PEN TWI PHP TWI PLN TWI RUB TWI SEK TWI SGD TWI THB TWI TRY TWI USD TWI VEB TWI ZAR TWI

Chapter 5

0.6 0.7 0.8 1.1 -

0.9 0.8 2.8 2.1 1.6 -

0.6 1.7 1.3 1.1 1.3 1.0 1.8 0.9 1.9 1.6 0.6 -

1.0 6.6 4.5 1.5 4.3 0.6 2.3 3.7 3.2 1.5 0.6

0.9 2.2 1.6 1.8 1.6 1.1 -

1.0 1.4 3.3 1.0 0.8 2.4 -

1.9 0.6 2.5 0.6 3.5 0.5 2.9 5.6 7.3 2.3 7.7 0.9 2.0 2.2 2.3 2.7 0.7 2.1 0.5 0.9 9.1 4.2 0.8 1.4 13.2 1.4 1.4 0.6

0.8 1.6 0.6 2.2 1.4 0.6 2.5 1.8 4.6 4.3 1.1 1.4 3.4 3.1 3.1 2.0 2.1 3.9

0.9 4.5 0.8 0.9 1.0 0.8 2.2 1.6 3.7 0.8 2.2 0.8 4.0 1.2 10.1 1.0 0.8 0.8 3.7 1.5 2.5 0.7 13.0 11.1 0.6 3.3 0.7 6.4 3.0 1.6 3.4 1.1 0.6 0.9 0.6 1.4 1.0

31

5.2 1.4 3.0 1.8 1.1 -

0.7 3.3 0.8 1.0 0.6 2.0 0.8 0.6 1.7 3.8 0.9 1.6 2.9 1.3 4.6 2.3 0.7 3.7 3.6 0.6 1.0 1.5

0.7 0.6 2.2 1.2 0.7 0.8 2.8 1.4 1.2 0.9 3.2 0.9 0.6 0.7 1.3 4.4 1.1 0.6 1.7

0.6 2.2 1.2 1.2 4.6 0.7 0.9 0.6 4.9 3.1 0.9 1.4 3.2 2.4 0.6 2.8 1.9 1.1 4.5 0.5 3.2 2.6 0.6 1.6 1.2

0.9 0.8 1.5 1.9 5.5 2.6 -

14.5 1.1 11.5 18.2 1.6 67.5 11.8 18.8 1.2 17.6 35.7 10.5 2.9 13.6 13.6 11.0 3.3 10.5 26.9 14.7 17.5 13.0 64.3 0.8 12.9 7.0 12.1 0.7 25.1 2.5 14.8 2.9 6.2 6.3 13.8 11.9 7.2 2.0 42.9 12.3 -

1.6 0.6 0.8 0.9 1.2 1.1 0.9 0.8 -

0.9 0.9 0.7 0.8 1.0 1.3 0.9 1.0 1.0 0.6 0.5 0.6 0.7 0.9 0.6 -

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Chapter 6: Empirical Links Between the Major Currencies and their BBoP Flows Following the template of the US BBoP analysis published in the previous issue of The Foreign Exchange Market, we empirically select the balance of payments components that best explain variations in the real tradeweighted exchange rate of other major currencies. We again find strong evidence that the BBoP matters, although the exact composition is slightly different for each country. In almost all cases, trade flows and the components of the current account are key drivers of exchange rates. The relevance of FDI and portfolio flows is less systematic. While these capital flows matter a lot for the EUR, CAD and AUD, the results are more mixed for countries with large financial centres (UK, CHF) or stronger FX policy influence (JPY, NOK). The BBoP framework has long been part of our currency analysis. Introduced in 1999 as an extension of the academic Basic Balance (current account + FDI), we included portfolio flows to gain a better sense of overall ‘commercial’ demand and supply factors in currency markets. Our basic thesis runs that, if a country with a current account deficit is able to attract enough FDI and portfolio inflows to finance that deficit, then demand and supply factors are currency neutral. By focusing on the current account deficit alone, one could wrongly conclude that the currency is under depreciation pressure. Thus, we consider a BBoP surplus to be a positive factor for a currency, and a deficit to be a negative.

for New Zealand due to limited historical data; however, other research we have conducted indicates that the BBoP model is useful in explaining developments in the NZD (see The Foreign Exchange Market 2007, Chapter 5: “Empirical and Theoretical Links between the US BBoP and the Dollar”). As in the previous analysis on US data, we again tried to find the best cointegrating vector that links the level of the exchange rate to a combination of cumulative crossborder capital flows. We ran the same model selection routine, which tries to optimise the fit of a linear regression, while using as few additional variables as possible. We use the Akaike Information Criterion (AIC) to decide if any n+1 variable combination helps improve on the best n variable model. More specifically, our program first regresses the level of the exchange rate on each individual right-hand-side variable and a constant, and selects the one with the highest AIC. In the second step, it iterates through all possible two variable combinations and checks whether the best solution improves on the optimal combination from the previous one-variable step. If positive, we iterate through all three variable combinations, and add increasing numbers of variables until the inclusion of an additional variable no longer improves the result from the previous step.

In the 2007 edition of this publication (Chapter 5: “Empirical and Theoretical Links between the US BBoP and the Dollar”), we examined the empirical links between the real US$ TWI and the BBoP flows in some detail, and explained in more depth the theoretical links between balance of payments flows and exchange rates. Building on standard results of academic FX microstructure literature, namely that a strong relationship exists between order flows and changes in the exchange rates, we showed that such a relationship also holds on a macro level, when using balance of payments data. Specifically, we showed that there is a particularly strong long-run relationship (cointegration) between cumulative BBoP flows and the level of exchange rates.

Once the optimal model is found, we test the cointegration properties more formally and critically examine the coefficient estimates. As a general rule, all coefficients should have the same positive sign, as balance of payments conventions prescribe that inflows (credits) are positive and hence expected to be associated with currency appreciation. However, depending on how FX-relevant the individual balance of payments components are, the size of the coefficients can be quite

Using an automated variable selection procedure, we achieved particularly strong results with a subset of the components in the BBoP, namely goods imports and exports, foreign purchases of US equity and foreign purchases of US debt. We extend this analysis here to the rest of the major currencies and discuss the results.

Variables Included in the Selection Process

Regression and Variable Selection Procedures Mirroring the analysis published last year on the USD, we have attempted to find the best combination of components of the BBoP to explain the real tradeweighted exchange rates of the other major currencies. The variables included in the selection process are listed in the table alongside. Certain countries do not publish the full breakdown of the BBoP components; thus we have used the balances when the separate credit and debit data was not available. We did not undertake the analysis

Chapter 6

Goods: Exports

Goods: Imports

Services: Exports

Services: Imports

Income: Receipts

Income: Payments

Current Transfers: Receipts

Current Transfers: Payments

Domestic Direct Investment

Direct Investment Abroad

Foreign purchases of US Equity

US Purchases of Foreign Equity

Foreign Purchases of US Debt

US Purchases of Foreign Equity

Source: GS Global ECS Research

32

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The Foreign Exchange Market Index

Euroland Real TWI Model

160

JPY Real TWI Model

240

155

220

150

200

145 140

180

135 160

130 Actual

125

140

Fitted

120

Actual 120

115 110

Fitted

100 99

00

01

02

03

04

05

06

07

08

09

10

91

Source: GS Global ECS Research, Haver Analytics

Results Broadly In Line With US BBoP Analysis In general, the results are intuitive and in line with our analysis of the US BBoP, although each individual country represents specific issues. We examine each country’s results in turn.

97

99

01

03

05

07

09

On the transfer component, Euroland residents may shift relatively more deposits into foreign currency denominated accounts abroad when the Euro is relatively strong, and vice versa. In terms of volumes, both services exports and transfers matter relatively less than the other flows selected.

Euroland. The variable selection procedure selected a broad range of Euroland BBoP constituents (see the accompanying table below for details). It is particularly interesting to see the selection of the FDI and equity components. This reflects what we have long held to be important drivers of the EUR. In its early days, the single currency was under a lot of pressure due to FDI and equity outflows, particularly to the US, associated with the ‘dot com’ boom and the serial underperformance of the Euroland economy. In subsequent years, Euroland’s growth outperformance relative to expectations has helped attract capital and provide a backdrop for Euro appreciation. More recently, repatriation of foreign holdings of overseas assets has been important for the Euro.

Japan. As with the other currencies we cover, we have always paid close attention to the Japanese BBoP. However, the flows have had an inverse relationship with the Yen, i.e., when the BBoP was in strong positive territory in recent years, the Yen was weak. Through this period the carry trade outweighed the influence of portfolio flows when it came to driving the Yen. Thus, we looked forward to the results of the model. We are intrigued to see that goods and services trade have been selected as important with the correct sign, as have income debits. The selection of trade reflects the importance of the externally facing parts of the Japanese economy, and the highly significant coefficients underline the importance of goods trade for Japan.

The most striking result is the negative sign on services credits and transfer debits, which points to an inverse relationship between these two variables and the Euro.

JPY Real TWI: Model Results* Variable

Euroland Real TWI: Model Results* Coefficient

Std. Error

t-Statistic

Prob.

135.484

1.633

82.941

0.000

Goods Exports Services Credit Transfers Debit FDI Abroad

0.085 -0.308 -0.197 0.053

0.016 0.040 0.054 0.006

5.417 -7.672 -3.658 8.357

0.000 0.000 0.000 0.000

FDI Domestic Equity Assets Equity Liabilities R-squared Adjusted R-squared

0.039 0.079 0.031 0.897 0.891

0.008 5.135 0.006 12.484 0.004 7.767 Akaike info criterion Schwarz criterion

0.000 0.000 0.000 5.203 5.384

Constant FDI Domestic Equity Assets

*Monthly data since 1999. Source: Haver Analytics, GS Global ECS Research

Chapter 6

95

The sign on services exports and transfers is likely to pick up reverse causalities. In particular, European tourism is likely to be benefit from a weak currency. Therefore, a stronger EUR would be associated with fewer services exports. This also suggests that services exports are quite sensitive to FX.

different. In particular, the coefficients for largely FXhedged inflows (more common in fixed-income-related flows) tend to be smaller.

Constant

93

Source: GS Global ECS Research

Coefficient Std. Error

t-Statistic

Prob.

163.1265 -0.0006 -0.0004

4.2255 0.0001 0.0001

38.6055 -4.3317 -4.2108

0.0000 0.0000 0.0000

Equity Liabilities Goods Exports Goods Imports

-0.0001 0.0005 0.0007

0.0000 0.0000 0.0001

-4.5004 13.8976 12.3370

0.0000 0.0000 0.0000

Services Credits Services Debits Income Debits Transfer Credits

0.0007 0.0002 0.0003 -0.0044

0.0002 0.0001 0.0000 0.0007

3.8807 2.6807 6.4341 -6.4663

0.0001 0.0079 0.0000 0.0000

R-squared Adjusted R-squared

0.8360 0.8289

Akaike info criterion Schwarz criterion

7.415 7.569

*Monthly data since Jan 1991.Source: Haver Analytics, GS Global ECS Research

33

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research Index

The Foreign Exchange Market Index

CAD Real TWI Model

125

110

120

105

115

100

110

AUD Real TWI Model

Actual Fitted

95

105

Actual

100

Fitted

90 85

95

80

90 85

75

80

70

75

65 90

92

94

96

98

00

02

04

06

08

10

88

92

94

96

98

00

02

04

06

08

One puzzle is the wrong sign on transfer credits, which suggests that transfers into Canada have an inverse relationship with the Canadian Dollar direction. Again, as already seen for the Euro-zone and Japan, this may simply reflect another reverse causality, i.e., that foreign investors shift deposits into CAD-denominated accounts when the Canadian Dollar appears relatively cheap and vice versa. Given their size relative to other components, transfer payments are unlikely to materially affect the BBoP relationship in any case.

Given the dominance of Japanese buying of foreign bonds in Japanese portfolio flows, it is interesting that this component of the capital account has not been selected. This suggests that these flows are fully hedged. Instead, FDI abroad and both sides of the equity ledger are selected as important variables. However, they have the wrong sign, which may reflect reverse causalities. With the Japanese equity market dominated by exporting companies, foreign purchases of Japanese stocks may pick up when a falling Yen improves exporters’ profitability. For similar reasons, Japanese investors may pull out of overseas equities and re-allocate to domestic stocks.

Australia. The model for the real AUD TWI throws up some interesting results. Although Australia is a large commodity exporter, exports are not selected. That said, the much smaller flows associated with services exports appear important. FDI flows on both sides of the ledger are selected as important. Equity and bond liabilities are also selected as important, reflecting strong foreign interest in Australian assets. Foreign buying of Australian debt has been strong in recent years, reflecting the influence of the carry trade, but also the need to fund the chronic current account deficit. The anomaly is the negative sign on the income credit variable, possibly hinting at some FX sensitive behaviour by Australian overseas investors. Specifically, the negative sign could suggest that overseas profits are more likely to be repatriated when the AUD is particularly weak.

Canada. We modelled the Real CAD TWI over two periods, from 1980, when the balance of payments data begins, and from 1990. The results presented here are those from 1990, which coincides with the period that was influenced to a far lesser extent by capital controls. Similar to the Real EUR TWI results, those for the Real CAD TWI indicate that a broad range of BBoP components are key drivers of the currency. The results are intuitive and highly significant. It is no surprise that goods exports and imports are selected, given that Canada is a small open economy. FDI is also a selected variable; indeed, Canada has benefited from strong net FDI inflows into the commodity sector. The selection of equity assets may reflect the influence of the large Canadian pension funds and their activities in foreign assets. Canada Real TWI: Model Results* Variable

90

Source: GS Global ECS Research

Source: GS Global ECS Research

Coefficient Std. Error

Australian Dollar Real TWI: Model Results* t-Statistic

Prob.

Contant Goods exports Goods imports Services exports

174.9978 0.0003 0.0006 0.0024

6.5365 0.0000 0.0000 0.0002

26.7725 7.0244 19.5680 10.2857

0.0000 0.0000 0.0000 0.0000

Income credits Transfer Credits FDI Abroad

0.0006 -0.0082 0.0002

0.0001 0.0009 0.0000

8.5672 -8.9786 4.9597

0.0000 0.0000 0.0000

FDI Domestic Equity Assets R-squared Adjusted R-squared

0.0001 0.0003 0.954 0.948

0.0000 3.8752 0.0001 4.4886 Akaike info criterion Schwarz criterion

0.0002 0.0000 4.820 5.096

Variable

Coefficient

Std. Error

t-Statistic

Prob.

Constant

94.0710

1.1759

79.9989

0.0000

Services Exports Income Credits Transfer Debits FDI Abroad

0.0013 -0.0015 0.0079 0.0004

0.0001 0.0001 0.0007 0.0001

11.6533 -10.7137 11.5443 4.8066

0.0000 0.0000 0.0000 0.0000

FDI Domestic Equity Liability Bonds Liability R-squared Adjusted R-squared

0.0005 0.0006 0.0002 0.873 0.861

0.0001 5.1657 0.0001 6.5392 0.0000 9.2543 Akaike info criterion Schwarz criterion

0.0000 0.0000 0.0000 5.363 5.596

*Quarterly data from 2Q1988. Source: Haver Analytics, GS Global ECS Research

*Quarterly data from 1990. Source: Haver Analytics, GS Global ECS Research

Chapter 6

34

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

Index

The Foreign Exchange Market

Index

GBP Real TWI Model

115

SEK Real TWI Model

80

110 75

Actual

105

Fitted

100

70

95 90

65

85 80

Actual

60

Fitted

75 70

55 90

92

94

96

98

00

02

04

06

08

10

98

Source: GS Global ECS Research

99

00

01

02

03

04

05

06

07

08

09

10

Source: GS Global ECS Research

UK. The model selection for the real Sterling TWI picks variables from the current account and capital account. The components of the current account have the correct sign; however, the components of the financial account tend to have a negative sign. Interpreting the UK capital account from an FX perspective has always been fraught with complications, largely because the transactions are not recorded with the location of the person doing the transaction in mind. For instance, a German investor buying a US bond through London is a transaction that does not involve the Pound—but it is potentially recorded as a UK purchase of a US bond. Thus we are not surprised that some of the variables have a negative sign. It is also interesting that bond liabilities have the correct sign and may reflect the importance of foreign investors in the Gilt market.

Sweden. Given that Sweden is a small open economy, it is unsurprising to see exports and imports selected as a key driver of the SEK. The model also finds that Swedish direct investment abroad is a key driver of the SEK but FDI into Sweden is not. It is interesting to see Swedish buying of foreign debt selected but with the wrong sign. Swedes are large buyers of foreign debt due to their pension fund program. The negative sign could reflect the hedging of that debt. Overall, however, the fit is not as good as for a number of other countries, possibly affected by the heavy weight of the EUR in the Swedish TWI, which may not reflect the regional distribution of cross border flows.

GBP Real TWI: Model Results

SEK Real TWI: Model Results*

Variable

Coefficient

Std. Error

t-Statistic

Prob.

Variable

Coefficient Std. Error

t-Statistic

Prob.

Constant Goods exports Income debits Transfer credits

86.3289 0.0003 0.0001 0.0024

5.5368 0.0000 0.0000 0.0004

15.5917 8.6016 6.5381 5.5686

0.0000 0.0000 0.0000 0.0000

Constant

87.8824

5.6289

15.6128

0.0000

Goods exports

0.0400

0.0090

4.4426

0.0001

Goods imports

0.0457

0.0112

4.0812

FDI Abroad

0.0266

0.0002

0.0044

5.9966

0.0000

Transfer debits Equity liability Bonds liability FDI abroad

0.0039 -0.0002 0.0001 -0.0002

0.0006 0.0000 0.0000 0.0000

6.9846 -4.6007 2.5641 -5.5191

0.0000 0.0000 0.0126 0.0000

Debt assets

-0.0251

0.0087

R-squared

0.7369

S.D. dependent var

-2.9010

0.0060 3.8167

Adjusted R-squared

0.7106

Akaike info criterion

4.3812

Bonds assets R-squared Adjusted R-squared

-0.0001 0.8852 0.8717

0.0000 -8.3191 S.D. dependent var Akaike info criterion

0.0000 9.9253 5.4841

*Quarterly data starting 1998. Source: Haver Analytics, GS Global ECS Research

Source: Haver Analytics, GS Global ECS Research

Chapter 6

35

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research index

The Foreign Exchange Market Index

NOK Real TWI Model

CHF Real TWI Model

100

115

Actual

98 110

94

Fitted

105

Fitted

96

Actual

92 90

100

88 95

86 84

90

82 85

80 99

94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 Source: GS Global ECS Research

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

Norway. Norway’s balance of payments is complicated by the management of the country’s oil wealth. In principle, the oil revenues in the current account should offset much of the portfolio flows abroad. However, the non-oil mainland economy also has trade and investment relationships with other countries, and these should become visible via our selection procedure.

neighbours, which dominate the trade-weighted CHF. This kind of reverse causality suggests that the Swiss Franc is driven by other factors, not necessarily linked to BBoP components, but may be more dependent on short rate differentials and carry flows.

Our empirical results underline the relevance of the aforementioned complications through a comparatively poor fit, in particular since the petroleum fund started to play a more important role in the early 2000s. However, it is interesting that non-oil exports, goods imports and FDI abroad are still all selected. They are also the least oil-affected components of the Norwegian BBoP, although the relatively low level of significance compared with other countries is a further reminder that the NOK may be subject to substantial policy intervention.

Extending the BBoP mining exercise to the other major currencies has increased our confidence in the concept of the BBoP to determine currency movements. In most cases the model provides sensible results, reaffirming our views that BBoP flows are important drivers of currencies. Where the model provided weak results, this was for currencies where the balance of payments flows are complicated by either the dominance of a financial centre (GBP and CHF), oil flows (NOK) and the carry trade for the Yen. In many cases we suspect there may be reverse causalities, which may need further investigation, in particular with regard to non-BBoP factors in the balance of payments that may be a driver of FX. Carryrelated shifts in the Other Investment Account may deserve particular examination in those cases where the standard BBoP analysis looks less appropriate.

Increased Confidence in BBoP Model

Switzerland. Switzerland’s balance of payments suffers from the same problems as that of the UK, namely, that the capital account flows are complicated by the dominance of the financial sector in Switzerland. That said, our model for the Real Swiss TWI selects equity liabilities with the correct sign. The negative sign on both sides of the income balance potentially indicates similar reverse causalities, as seen for a number of other countries above. Even goods imports may be affected by the same problem, with imports rising when the Swiss Franc is particularly strong relative to its Euro-zone

Fiona Lake and Thomas Stolper

CHF Real TWI: Model Results* NOK Real TWI: Model Results* Variable Constant Non-oil exports

Coefficient

Std. Error

t-Statistic

Prob.

95.384 0.000

1.010 0.000

94.433 3.746

0.000 0.000

Variable

Coefficient

Std. Error

t-Statistic

Prob.

Constant

91.7299

0.7563

121.2873

0.0000

Goods Imports

-0.0001

0.0000

-4.4010

0.0001

Income receipts

-0.0002

0.0000

-4.9631

0.0000

Goods imports

0.000

0.000

3.620

0.001

Income expenditure

-0.0001

0.0000

-3.6960

0.0007

FDI Abroad

0.000

0.000

2.474

0.016

equity liabilities

0.0002

0.0000

4.1728

0.0002

R-squared

0.2817

S.D. dependent var

3.6858

R-squared

0.8301

Akaike info criterion

3.8227

Adjusted R-squared

0.2439

Akaike info criterion

5.2306

Adjusted R-squared

0.8112

Schwarz criterion

4.0317

*Quarterly data starting 1994. Source: Haver Analytics, GS Global ECS Research

Chapter 6

*Quarterly data starting 1999. Source: Haver Analytics, GS Global ECS Research

36

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The Foreign Exchange Market

Chapter 7: Over-fitting in Cross-Asset Proxy Baskets In recent years, FX investors have increasingly looked at cross-asset correlations and have also attempted to express fundamental views on other asset classes through customised FX baskets. Using copper prices as a concrete example, we discuss the implications of this approach by pushing it to the extreme in terms of overfitting. We observe the expected parameter instability and a surprisingly weak fit in general. But we also find clusters of stable and relatively high correlation. These clusters tend to appear when the target asset is ‘on the move’. In practical terms, highly optimised proxy baskets are therefore likely to be more useful than basic statistical analysis would suggest. will discuss the periods during which we think a proxy FX basket is likely to have more success.

The Pros and Cons of Cross-Asset Proxy Baskets Expressing views on other asset classes through FX markets is an attractive proposition for many investors, for a variety of reasons.

Despite the expected out-of-sample instability introduced through the short optimisation window, some currencies show very stable coefficients and appear much more frequently in optimised baskets than others. These also tend to be the currencies with the strongest fundamental links to the target asset class.

Some investors may not be able to express a fundamental view directly in the desired asset class, such as commodities or equities, but do have access to the FX market, and therefore will be able to construct a proxy basket of currencies to replicate the off-limit asset class.

Overall, it appears the risks of over-fitting can be reduced substantially by:

Liquidity and depth are a key feature of FX markets; hence, even if institutional access restrictions are not in place, it may still be attractive to consider a substitute FX portfolio. Slippage may be much smaller for larger positions relative to the underlying target market. Moreover, 24-hour liquidity in most currencies may present considerable risk management advantages relative to other asset classes, which may be restricted to a few trading hours per day.

reducing the range of possible basket constituents to those with strong fundamental links, and focusing only on those periods when the target asset class is ‘in play’.

Basket Estimation Strategies In very general terms, there are a number of key choices to make when constructing FX portfolios as proxies for other assets.

FX markets may theoretically provide a way to obtain specific exposure to the long-term outlook of other asset classes, to the extent that exchange rates pick up related changes in the economy. This may be particularly attractive for certain commodities, where storage is costly or virtually impossible.

Sample size. The choice of the sample size depends on the trade-off between fit versus robustness. Over very short samples, it is possible to create almost perfectly correlated cross-asset relationships, but these may well be spurious and immediately break down out of sample. Over longer horizons the robustness increases but the fit typically deteriorates. In this piece, our aim is to find baskets with rather high correlations and we are specifically interested in the implications for robustness. The idea is also to look at sample sizes that correspond to the average holding period of a typical discretionary macro trade, which is not more than a few weeks or months. We chose a three-month (60 business days) rolling window.

However, these advantages come at a cost. For example, considerable leverage may be needed in the FX portfolio to obtain the degree of return volatility that the underlying target asset displays. And, most importantly, the correlations between exchange rates and the target asset class may change over time. After all, currencies are driven by a very wide range of fundamental factors and not just those relevant for the target asset. With too short a sample period, there is a substantial risk of over-fitting currency baskets, with negative implications for out-of-sample stability.

Levels versus changes. This is probably the most important choice to make. Standard regression models are based on the assumption that the dependent and explanatory variables are stationary. However, when estimating daily changes, the risk is that a regression model gives too much weight to those observations where a large temporary divergence occurs. In those cases, estimations in levels may be more appropriate but only under specific conditions. All variables have to be integrated and the residuals stationary to satisfy standard

Our main focus here is on the stability of baskets optimised over very short windows. To illustrate the implications of such a deliberate over-fitting exercise, we use copper prices as a practical example. We show that, even with the best optimisation procedures and over a short sample, it is often not possible to build well-fitting proxy FX baskets for other asset classes. We Chapter 7

37

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Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

assumptions in a so-called co-integration relationship. It is not uncommon for financial data to display cointegration relationships even over relatively short samples. However, over the short three-month sample chosen above, it is probably safer to stick to changes.

Number of Baskets

Fit of Proxy Baskets Often Disappoints

800 Distribution of R-squared

700 600

Variable selection. There are many variable selection strategies and by adding more currencies to the FX basket it is always possible to improve the fit relative to the target asset. That said, insignificant variables will deteriorate the out-of-sample performance. A number of test statistics help with the variable selection. We combined the use of the AIC test statistic with an iterative procedure that literally runs through all possible currency baskets until the one with the best AIC score has been found. Specifically, we first limit our currency universe to the 17 most liquid Dollar crosses (AUD, BRL, CAD, CHF, CLP, EUR, GBP, JPY, KRW, MXN, NOK, NZD, PLN, RUB, SEK, TRY, ZAR). We then regress our target asset on each of the 17 variables individually, on all two-variable combinations, threevariable combination, and so on. Once we find an nvariable combination with an AIC criterion that cannot be improved by any (n+1)-variable combinations, we retain the n-variable results as the best possible basket over the sample window. After shifting the sample window by one observation, we repeat the whole variable selection procedure. Iterating through 10 years of data frequently implies estimating several million regressions in this ‘brute force’ approach. However, we can be confident that if there were any well-fitting FX basket, our routine would find it.

500 400 300 200 100

R-squared

0 < 0.1 < 0.2 < 0.3 < 0.4 < 0.5 < 0.6 < 0.7 < 0.8 < 0.9 Source: GS Global ECS Research

<= 1.0

target asset through a proxy FX basket. The average Rsquared over our 2,710 optimal FX baskets is only 23%. A more detailed look at the distribution of R-squared shows that a relatively large part of the distribution has an extremely weak fit of less than 10%. This is rather surprising given our deliberate over-fitting strategy. Cross-asset proxy baskets should therefore be used very selectively and with great precaution, as there is always a risk that a tight relationship breaks down out of sample and to a degree that many may not expect. However, there are also periods when the R-squared is very high, in particular when taking into account that the model is estimated in changes. We find peak R-squared readings of almost 80%. Even more interesting, the FX baskets show a particularly high R-squared when volatility in copper, also measured over a three-month horizon, is particularly high (see chart).

Other factors influencing basket selection. We have deliberately discounted a number of factors for this analysis, such as transaction costs or bid-offer spreads, which may be quite different for the currencies mentioned above. Moreover, we also did not rebalance our portfolio. Of course, the estimated regression coefficients are proportional to the constant weights over the sample period of the respective currency. However, if one currency on the long side continues to appreciate steadily over the sample period, its weight will likely increase. Theoretically, one would have to rebalance the basket but we assume our sample is short enough not to worry about this issue.

The second factor that seems to affect the fit of the currency baskets is the level of the target asset price. The next chart shows that when copper prices are high the Rsquared values of the FX models appear to be higher, whereas at lower price levels the R-squared also appears to be low. This factor seems to have been particularly Proxy Baskets Fit Improves on High Target Asset Volatility

%

0.9

Vol (%)

80

0.8

Rolling R-squared of optimised baskets (LHS)

Following the discussion above, our aim was to find optimised FX baskets to proxy copper as the target asset. Starting in early 1999, we calculated the optimal FX baskets for 2,710 different 60-day windows. In total our optimiser ran through more than 5 million individual regressions.

0.7

Copper: 3mth realised volatility

Regression fit. Given that our variable selection procedure has been designed to maximise the in-sample fit, it is interesting that the fit is often quite poor. The Rsquared appears to be quite variable over time, and for lengthy periods it is virtually impossible to replicate the

0.2

20

0.1

10

Results Show Clusters of Stability

Chapter 7

70 60

0.6

50

0.5

40

0.4

30

0.3

0

0 99

00

01

02

03

04

05

06

07

08

09

10

Source: GS Global ECS Research

38

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Improved Fit in Proxy Baskets on High Target Asset Volatility

%

0.9

$

basket returns

10000

Rolling R-squared of optimised baskets (LHS)

0.8

200%

9000

Copper Spot

Copper, 1st nearby future

7000

0.6

100%

6000

0.5

5000

0.4

Optimised Proxy FX Basket (01/06/2009)

150%

8000

0.7

Poor Long-term Performance of Proxy Basket

50%

4000

0.3

0%

3000

0.2

2000

0.1

1000

0

-50% Optimisation w indow

-100%

0 99

00

01 02

03

04

05

06

07 08

09

99

10

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

Source: GS Global ECS Research

important in 2007 and 2008, when realised copper volatility wasn’t that high but the consistently good fit of the FX models appeared to be linked to the high levels of copper prices.

with a good fit (R2 = 44.4%) and plotted it against the target asset. As was to be expected, both track each other quite closely but then diverge very rapidly within days of leaving the estimation window.

To explain this pattern, it may be useful to think in terms of signal-to-noise ratios. With many factors affecting FX markets simultaneously, it may just be that for most of the time commodities do not really play a major role. Other factors such as capital flows or rate differentials may matter more. However, when the ‘signal’ becomes really strong, meaning that copper prices become really volatile or reach new highs, rapid adjustments in macroeconomic expectations may follow—and hence copper (or other assets highly correlated with copper) starts to become a dominating factor in FX markets.

And when looking over a much longer horizon, it becomes clear that the proxy basket is anything but a proxy basket outside the optimisation sample. Another way to illustrate this is by looking at the correlation in returns, which by construction is very high at +50% for the in-sample period (60 days to 1/6/2009) but, overall, the rolling 60-day correlation between this specific basket and copper prices only averages about +14% since 1999. This instability is a standard result of over-fitted models and very much expected given our approach. One reason why this occurs is the instability of coefficient estimates, which we will discuss in the next section.

Out-of-Sample Robustness. Despite some regularities of R-squared, it is important to highlight that the in-sample fit has no strong bearing on the out-of-sample fit. In other words, it is quite likely that after extensive optimisation an investor will find that the ideal basket of the last three months has very little value going forward. To illustrate this, we have chosen one of the baskets in recent months basket returns

80%

Basket composition. When looking at the composition of the optimal baskets through time, individual currencies frequently enter and drop out of the baskets, and also appear frequently on either the short or the long side of the baskets. This instability of the basket composition can

Poor Out-Of-Sample Performance of the Proxy Basket

Estimated EUR Coefficients in All FX Proxy Baskets

10 8

60%

6 4

40%

2 0

20% Optimisation w indow

0% -20% -40% Jan-09

-2 -4 -6

Optimised Proxy FX Basket (01/06/2009)

-8

Copper, 1st nearby future Mar-09

May-09

-10 Jul-09

99

Sep-09

Chapter 7

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

Source: GS Global ECS Research

39

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

include all optimisation results with an R-squared of at least 40%, which corresponds to about 423 baskets. These are the best 16% windows, with each basket also representing the best possible variable combination for its period as discussed above.

Estimated AUD Coefficients in All FX Proxy Baskets

10 8 6 4

The table summarises how often a currency appears on the long or short side of these well-fitting proxy baskets. While the AUD, CLP and BRL are among the most frequently appearing variables on the long side of the basket, they do not appear a single time on the short side, as we would expect from these globally dominating industrial metals producers. On the other hand, the CHF appears to be the most frequently shorted currency apart from the Dollar. Given that we use the Dollar as numeraire for all crosses, it implicitly appears in all regressions and its basket weight is the difference between estimated long and short positions in the basket.

2 0 -2 -4 -6 -8 -10 99

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

be illustrated by plotting the changing coefficients through time. As one example, the chart shows the estimated coefficient of the EUR, indicating that there is essentially no regularity in the relationship—something we would expect in an over-fitting exercise.

Interestingly, we find that even in the selected baskets with an R-squared above 40%, most currencies display unstable signs. For example, the MXN appears in 34 baskets on the short side but in 42 baskets on the long side. This is a further indication of likely out-of-sample instability, as discussed above.

But some currencies also appear very systematically with the same sign in the different proxy baskets, such as the AUD (see above). Moreover, the coefficient for the AUD also appears to remain typically within a fairly narrow range. This suggests that there is more than just a spurious relationship between the AUD and copper.

Turning back to the robust basket components, such as the AUD or CLP, it is interesting that the coefficients still change significantly—even though they remain consistently on one side of the basket. For example, the CLP coefficients in our best-fitting baskets vary between 5.2 and 0.3. This means that the basket composition likely needs frequent adjustment—even when focusing on those components that in the past have reliably occurred on one side of the basket only.

Basket Composition for Baskets with a Good Fit There is very little value in analysing FX baskets that do not offer a decent fit to the target asset. We will therefore look more specifically at the composition of well-fitting baskets. We use a cut-off point in R-squared terms to decide whether or not we are interested in the individual optimised currency basket composition. After eyeballing the R-squared distribution shown above, we decided to

To assess the coefficient stability, we have plotted the estimated coefficients for every cross through time in the Appendix. Clusters of coefficient stability. Despite these overwhelming signs of instability, there seem to be clusters of coefficient stability as well. For example, when zooming in on the AUD coefficients for the best

Selection Frequency for Copper Proxy Basket* AUD CLP CAD ZAR NZD BRL PLN SEK NOK KRW GBP TRY MXN EUR JPY RUR CHF USD

Short

Long

Net

Total

0 0 12 1 4 0 3 21 9 31 3 40 34 41 48 58 87 375

205 105 81 59 52 47 45 48 32 47 18 50 42 31 31 27 16 48

205 105 69 58 48 47 42 27 23 16 15 10 8 -10 -17 -31 -71 -327

205 105 93 60 56 47 48 69 41 78 21 90 76 72 79 85 103 423

1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3 Jan-09

* Baskets w ith an R2 of at least 40% Source: GS Calculations

Chapter 7

Estimated AUD Coefficients in FX Proxy Baskets with R2>40%

Long postion in the proxy basket

Mar-09

May-09

Jul-09

Source: GS Global ECS Research

40

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Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

baskets, we can identify a period in 2008 when the coefficient barely changed. In this and in a number of other cases, these clusters have lasted several months. We also note that these clusters correspond to the periods when copper prices either reached record highs or displayed a lot of volatility, as discussed above.

All told, when using FX proxy baskets, the quality of the fit and the stability of coefficients has to be checked continuously and basket weights may have to be adjusted frequently. Yet even with the best precautions, out-ofsample performance may be very poor. That said, there are periods when highly optimised FX proxy baskets do make sense, in particular when the target assets display high degrees of volatility or breaks above established price ranges. Moreover, fundamentally related currencies display the best coefficient stability and appear most frequently in the best-fitting proxy baskets.

Conclusion: FX Proxy Baskets Do Occasionally Work Having pursued a deliberate over-fitting strategy to replicate copper prices with FX proxy baskets, we conclude the following: Even with the very best over-fitting procedure, short sample sizes and when willingly sacrificing out-ofsample stability, it often appears impossible to construct well-fitting FX proxy baskets.

In practical terms, over-fitted cross-asset proxy baskets probably work better than statistical analysis would suggest. This is because investors will be most inclined to use them when the target asset is ‘on the move’—and this is precisely when proxy FX baskets tend to perform best.

However, the chances of finding a useful proxy FX basket grow substantially when the target asset is ‘on the move’, as indicated by increased volatility in the target asset or relatively high price levels compared with the past.

Most of the results in this piece depend on the choice of the proxy assets, which in this case were spot copper prices. Any conclusions therefore may not hold for other target assets. That said, preliminary tests for other target assets suggest most of the results are comparable.

The degree of coefficient instability is very high, as expected, and yet some currencies display a lot more regularity, in particular in terms of the coefficient signs.

Thomas Stolper

Those currencies that show the best coefficient stability are also those that have the strongest fundamental links to the target assets. Despite all the expected instability, there are clusters of coefficient stability lasting several months at a time.

Chapter 7

41

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Appendix Estimated AUD Coefficients in All FX Proxy Baskets

10

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

Estimated CHF Coefficients in All FX Proxy Baskets

10

Estimated AUD Coefficients in FX Proxy Baskets with R2>40%

Estimated CHF Coefficients in FX Proxy Baskets with R2>40%

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

Estimated GBP Coefficients in All FX Proxy Baskets

10

00

01

02

03

04

05

06

07

08

09

08

09

Source: GS Global ECS Research

Estimated GBP Coefficients in FX Proxy Baskets with R2>40%

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

Chapter 7

00

01

02

03

04

05

06

07

Source: GS Global ECS Research

42

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Estimated MXN Coefficients in All FX Proxy Baskets

10

Estimated MXN Coefficients in FX Proxy Baskets with R2>40%

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

Estimated PLN Coefficients in All FX Proxy Baskets

10

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

02

03

04

05

06

07

08

09

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

Estimated TRY Coefficients in All FX Proxy Baskets

10

01

Estimated PLN Coefficients in FX Proxy Baskets with R2>40%

10

8

99

00

Source: GS Global ECS Research

Estimated TRY Coefficients in FX Proxy Baskets with R2>40%

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

Chapter 7

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

43

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Estimated BRL Coefficients in All FX Proxy Baskets

10

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

00

01

02

03

04

05

06

07

08

09

08

09

08

09

Source: GS Global ECS Research

Estimated CLP Coefficients in All FX Proxy Baskets

10

Estimated BRL Coefficients in FX Proxy Baskets with R2>40%

Estimated CLP Coefficients in FX Proxy Baskets with R2>40%

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

Long postion in the proxy basket

-10

-10 99

00

01

02

03

04

05

06

07

08

99

09

Source: GS Global ECS Research

Estimated JPY Coefficients in All FX Proxy Baskets

10

00

01

02

03

04

05

06

07

Source: GS Global ECS Research

Estimated JPY Coefficients in FX Proxy Baskets with R2>40%

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

Chapter 7

00

01

02

03

04

05

06

07

Source: GS Global ECS Research

44

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Estimated NOK Coefficients in All FX Proxy Baskets

10

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

Estimated RUB Coefficients in All FX Proxy Baskets

10

Estimated NOK Coefficients in FX Proxy Baskets with R2>40%

Estimated RUB Coefficients in FX Proxy Baskets with R2>40%

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

Estimated ZAR Coefficients in All FX Proxy Baskets

10

00

01

02

03

04

05

06

07

08

09

08

09

Source: GS Global ECS Research

Estimated ZAR Coefficients in FX Proxy Baskets with R2>40%

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

Chapter 7

00

01

02

03

04

05

06

07

Source: GS Global ECS Research

45

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Estimated CAD Coefficients in All FX Proxy Baskets

10

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10 00

01

02

03

04

05

06

07

08

02

03

04

05

06

07

08

09

08

09

-10

09

99

Source: GS Global ECS Research

00

01

02

03

04

05

06

07

Source: GS Global ECS Research

Estimated KRW Coefficients in All FX Proxy Baskets

10

01

Estimated EUR Coefficients in FX Proxy Baskets with R2>40%

10

8

99

00

Source: GS Global ECS Research

Estimated EUR Coefficients in All FX Proxy Baskets

10

Estimated CAD Coefficients in FX Proxy Baskets with R2>40%

Estimated KRW Coefficients in FX Proxy Baskets with R2>40%

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

Chapter 7

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

46

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Estimated NZD Coefficients in All FX Proxy Baskets

10

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

Estimated SEK Coefficients in All FX Proxy Baskets

10

Estimated NZD Coefficients in FX Proxy Baskets with R2>40%

Estimated SEK Coefficients in FX Proxy Baskets with R2>40%

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

Estimated USD Coefficients in All FX Proxy Baskets

10

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

Estimated USD Coefficients in FX Proxy Baskets with R2>40%

10

8

8

6

6

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10 99

00

01

02

03

04

05

06

07

08

09

99

Source: GS Global ECS Research

Chapter 7

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

47

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Chapter 8: FX Volatility Still Looks Expensive Relative to Cyclical Factors FX volatility still looks high when taking into account current cyclical factors. As the economic slowdown gives way to a modest expansion, cyclical forces should support further downside in realised FX volatility. Implied 1yr FX volatility has declined only moderately and is still at high levels. As realised volatility starts to converge towards its cyclical norms, 1yr implied volatilities are likely to follow suit. Lastly, Dollar weakness has correlated strongly with risky asset outperformance. In other words, both EUR/$ and $/EM crosses have co-moved heavily with the SPX on average, with strong SPX performance coinciding with broad Dollar weakness. The net result of this correlation structure has been the compression of EUR/EM volatility relative to broader volatility trends.

FX Volatility Still Looks Expensive FX volatility has peaked. Ever since the extreme FX shifts of late 2008, moves in FX markets have been more orderly and incremental. We think the fact that this shift in volatility has coincided with the bottoming of the cycle is no coincidence. We have long held the view that there is a cyclical element to FX volatility. In December 2008 we carried out a simple benchmarking of realised volatility relative to cyclical factors. We argued back then that FX volatility levels were too high. We also argued that a moderation in the pace of economic decline would support an even more marked decline in volatility.

FX Volatility Has Overshot Cyclical Norms Volatility has picked up substantially relative to early 2007. Chart 1 displays monthly average 1yr realised volatility for the EUR and JPY. This G3 FX volatility metric has picked up from a bottom of about 6.4% in July 2007 to a current level of 16.6%, the highest in the data history. Faster-moving measures of realised volatility have started to decline, indicating that 1yr realised volatility should also moderate in the months to come.

Since then, 1yr realised volatility coefficients have remained high—partly because they include data from Q4 2008. But implied volatilities have also remained at very high levels of close to 14%. This raises the question of how these levels fare relative to current cyclical dynamics.

As we discussed in our 2006 work on the subject, there is a cyclical element to volatility shifts. In Global Economics Weekly 06/31, we noted that FX volatility tends to be higher as growth declines and the output gap shifts from positive to negative. However, as growth recovers, volatility tends to decline significantly.

We have applied the same framework used in December to current fundamentals. Relative to the current cyclical backdrop, an average of EUR/$ and $/JPY 1yr volatilities should trade lower. Our analysis also suggests that cyclical forces should continue to support declining volatility until much later in the cycle.

Although the cyclical environment has supported higher volatility, realised volatility has significantly overshot the levels that current cyclical dynamics would imply are fair, as illustrated in Chart 1. The fitted value of a simple framework that adjusts volatility to cyclical factors has picked up to levels not seen since the early 1980s. However, realised volatility has increased to unprecedentedly high levels. As a result, the deviation between the two is the largest on file.

A weaker Dollar has also supported the reduction in emerging market (EM) FX implied volatility. We expect the Dollar to remain on the weak side for the next six months. Together with the trends in broad FX volatility space, this should also support further declines in EM FX volatility. Chart 1: 1yr Implied Vols Correcting From Extremes But Still High Relative to Cyclical Backdrop 3

Chart 2: FX Volatility Drops At Times of Growth Below Capacity 1.0

18 St.Devs.

16

2

% 3 mth vol during phase - average vol across phases

Avg. EUR+JPY

0.6

14

1

0.2 12

0 -1 -2

Deviation From Cyclical Volatility (lhs)

10

-0.2

8

-0.6

6 -1.0

$/JPY and $/DEM Avg 1y Implied Vol (rhs) -3

4

Positive and Rising

76 78 80 82 84 86 88 90 92 94 96 98 00 02 04 06 08

Positive and Negative and Negative and Falling Falling Rising

Source: GS Global ECS Research

Source: GS Global ECS Research

Chapter 8

Output Gap:

48

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Chart 5: Gap between 1yr Realised and 1yr Implied

Chart 3: Cyclical Forces Should Support a Decline in Volatility

% vol Vol in G3 Reflects Reduction in Short-term Vol

19

7

EUR/$ and $/JPY 1y Realized Vol

17

Cyclical Fitted Value

G3 Implied - Realized 1yr FX Vol

5

15 13

3

11

1

9

-1

7 -3

5

-5

3

98

78 80 82 84 86 88 90 92 94 96 98 00 02 04 06 08 10

99

00

01

02

03

04

05

06

07

08

Source:GS Global ECS Research

How do we account for the cyclical drivers of volatility? We regress an average of 1yr realised volatility in EUR/$ and $/JPY on the following US-based variables: 1) changes in the unemployment rate, 2) real 1yr interest rates, 3) core inflation and inflation volatility, and 4) 3mth rates volatility. We find that increases in the unemployment rate, higher real interest rates and higher inflation / short rates volatility tend to boost FX volatility as well. Our coefficients are statistically significant.

However, comparing G3 implied FX volatility to our own measure of ‘cyclical volatility’, we find there is still room for implied volatilities to decline by about 3 points to align with current cyclical fundamentals. In addition, cyclical fundamentals are likely to improve, compressing implied vols further. It is not as easy to place EM FX volatility in a framework like the one we used for G3, given that there are only a few years of floating exchange rate history for emerging currencies. Up until the late 1990s, most currencies were either pegged or heavily managed, and a number of them were experiencing high inflation.

Our results imply that as the unemployment rate, real interest rate, policy rates volatility and inflation start to fall, so will realised FX volatility. In other words, according to our macro forecasts, cyclical forces should support an outright decline in realised volatility to about 11%, as Chart 3 shows.

Nevertheless, in a comparison between our metric of JPY and EUR realised volatility trends and a similar metric including a wide set of EM currencies, we observe that the two measures have followed similar broad trends over the past 10 years. EM FX realised volatility appears to be more erratic but the cyclical implications we established for G10 FX volatility will likely hold for EM as well, as Chart 6 shows.

That said, 1yr realised volatility measures do not fully reflect the decline that we have already observed in shorter-term volatility and implied volatility measures. As Charts 4 & 5 also show, 1yr implied volatility is trading well below realised volatility measures in both G3 and EM FX space.

Chart 4: Gap between 1yr Realised and 1yr Implied EM Vol Reflects Reduction in Short-term Vol % vol

% vol

Chart 6: Realised Vol in EM has Followed Broadly Similar Trends to G3 Vol over last 10 yrs % vol

18

20

24 G3 Realized 1yr Vol (Mthly Avg - lhs)

EM Implied - Realized 1yr FX Vol

15

16

10

14

5

12

0

10

-5

8

22

EM Realized 1yr Vol (Mthly Avg - rhs)

20 18 16 14 12 10 8

6

-10 98

99

00

01

02

03

04

05

06

07

08

09

6 98

10

99

00

01

02

03

04

05

06

07

08

09

Source: GS Global ECS Research

Source: GS Global ECS Research

Chapter 8

09

Source: GS Global ECS Research

49

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Dollar Direction Key in Driving the Convergence Between EM and G10 Volatility

% vol

12

Beyond cyclical forces, shifts in implied volatility will depend on broader risk premia across markets. Indeed, spikes in risk aversion are much more important drivers of near-term implied volatility moves. The fact that implied volatility is still trading wide relative to where our cyclical benchmarking argues it should trade also reflects to some extent that the come-back in risk appetite among market participants has been gradual. And it is fairly hard to predict how risk appetite will shift in the near term.

8

97

US Dollar Twi 92

4 2

87 0 -2 Dec-06

82 Jun-07

Dec-07

Jun-08

Dec-08

Jun-09

Source: GS Global ECS Research

that we think this will occur with a backdrop of healthy risk appetite and ongoing cyclical improvement, it will be interesting to see whether overall it will help EM volatilities hold their ground relative to G3 vols.

Correlations with EUR/EM Vols

Equities

Have

Suppressed

One of the most striking features of the trading environment of the last few months has been the exceptionally high correlation between the Dollar and global risk appetite, where stronger risk appetite has coincided with Dollar weakness. This market feature has kept EUR/EM volatilities low relative to $/EM vols. The mechanics are simple. Given the intense correlations between 1) EUR/$ and global risk sentiment, and 2) $/EM and global risk sentiment, crossing EUR with EM neutralises a significant source of volatility. Although EM currencies have mostly strengthened relative to the USD, they have either remained range-bound or have weakened relative to the EUR.

Our views have not changed recently. We continue to expect Dollar weakness over the next six months. This will mean that EM volatilities are likely to remain close to G10 vols. However, we also expect a modest Dollar rebound beyond the six-month forecasting horizon. Given

The chart below illustrates this point. It shows how the correlation between the SPX and the USD TWI has been

Chart 8: EM Vol Has Converged Towards G10 Vol

26

102

EM Vol - G10 Vol

6

Over the course of 2009 a combination of a weaker Dollar and stronger risk appetite helped EM FX vols converge to G10 FX vols. Of course, given the correlation of the USD and risk sentiment, it is hard to separate the impact of each factor. That said, the intense short-term correlation between the Dollar and the gap between EM and G10 FX volatility supports the argument that there is a strong Dollar component in EM volatilities.

31

USD TWI

EM Vol Rising Relative to G10 Vol, USD Appreciating.

10

However, there is another, more predictable, component to implied volatility (especially in EM space), namely, USD direction. The speed and the strength of the Dollar rally was a bullish development for implied volatilities in late 2008, even beyond the obvious pick-up in realised volatility. This is because the Dollar rally triggered the unwinding in levered hedges and short volatility structures, and created extreme trading constraints in FX volatility markets, with market participants reluctant to sell volatility in uncertain times. In addition, given the typical volatility skew in several EM currencies (especially high yielders), FX depreciation helped to mark EM implied volatilities higher. As a result, EM FX vols spiked well above G10 FX vols.

% vol

Chart 7: Dollar Decline Supported EM Vol Convergence Towards G10 Vol

0.8

G10 1yr Implied Vol

0.6

EM 1yr Implied Vol

0.4

21

16

11

Chart 9: Correlation Between USD and Risk Sentiment Has Kept EUR/EM Vols Low Correlation Spx w ith USD TWI (lhs) EUR/EM 3m Implied Vols vs USD/EM (rhs)

1.3 1.3 1.2

0.2

1.2

0.0

1.1

-0.2

1.1

-0.4

1.0

-0.6

1.0

-0.8

0.9 EM includes BRL, TRY and INR

6 98

99

00

01

02

03

04

05

06

07

08

-1.0 0.9 Aug-06 Feb-07 Aug-07 Feb-08 Aug-08 Feb-09 Aug-09

09

Source: GS Global ECS Research

Chapter 8

Source: GS Global ECS Research

50

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

strongly negative and how that trend has co-existed with EUR/EM underperformance of vols. Our core views for the year ahead imply broader EM FX strength. Long EM positions relative to the EUR potentially enjoy a lower volatility and cost. However, should current correlations persist, crossing the EUR means missing out of significant upside from ongoing risk appetite improvement. Therefore, it is mostly those portfolios that already have significant exposure to risky assets that will likely benefit the most from such a trend. Inversely, if current correlations break, EM volatility relative to the EUR could pick up significantly.

Cyclical Forces Still Support Vol Downside FX volatility has peaked. We think the fact that this shift in volatility has coincided with the bottoming of the cycle is no coincidence. Our analysis shows that cyclical forces continue to support volatility downside. Adjusting current realised volatility levels to cyclical factors, we find that EUR/$ and $/JPY 1yr vols should be trading close to 11%, lower than current levels of about 14%. And as the cyclical backdrop continues to improve, volatility could decline even further. A weaker Dollar has supported the reduction in EM FX implied volatility as well. We expect the Dollar to remain on the weak side for the next six months. Together with the trends in broad FX volatility space, this should also support further declines in EM FX volatility. Lastly, Dollar weakness has correlated strongly with risky asset outperformance. This has resulted in a compression of EUR/EM volatility relative to broader volatility trends. Themistoklis Fiotakis

Chapter 8

51

October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

We, Dominic Wilson, Thomas Stolper, Themistoklis Fiotakis, Fiona Lake, Roman Maranets, Malachy Meechan, Anna Stupnytska, Mark Tan and Swarnali Ahmed, hereby certify that all of the views expressed in this report accurately reflect personal views, which have not been influenced by considerations of the firm's business or client relationships. Global product; distributing entities The Global Investment Research Division of Goldman Sachs produces and distributes research products for clients of Goldman Sachs, and pursuant to certain contractual arrangements, on a global basis. Analysts based in Goldman Sachs offices around the world produce equity research on industries and companies, and research on macroeconomics, currencies, commodities and portfolio strategy. This research is disseminated in Australia by Goldman Sachs JBWere Pty Ltd (ABN 21 006 797 897) on behalf of Goldman Sachs; in Canada by Goldman Sachs Canada Inc. regarding Canadian equities and by Goldman Sachs & Co. (all other research); in Hong Kong by Goldman Sachs (Asia) L.L.C.; in India by Goldman Sachs (India) Securities Private Ltd.; in Japan by Goldman Sachs Japan Co., Ltd.; in the Republic of Korea by Goldman Sachs (Asia) L.L.C., Seoul Branch; in New Zealand by Goldman Sachs JBWere (NZ) Limited on behalf of Goldman Sachs; in Russia by OOO Goldman Sachs; in Singapore by Goldman Sachs (Singapore) Pte. (Company Number: 198602165W); and in the United States of America by Goldman, Sachs & Co. Goldman Sachs International has approved this research in connection with its distribution in the United Kingdom and European Union. European Union: Goldman Sachs International, authorised and regulated by the Financial Services Authority, has approved this research in connection with its distribution in the European Union and United Kingdom; Goldman, Sachs & Co. oHG, regulated by the Bundesanstalt für Finanzdienstleistungsaufsicht, may also distribute research in Germany. 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October 2009

Goldman Sachs Global Economics, Commodities and Strategy Research

The Foreign Exchange Market

Goldman Sachs Global Economics, Commodities and Strategy Research Jim O'Neill~ - Global Head 44(20)7774-2699 Americas Jan Hatzius~ Dominic Wilson~

1(212)902-0394 1(212)902-5924

US Economics Research Edward McKelvey* Alec Phillips* Andrew Tilton* David Kelley^

1(212)902-3393 1(202)637-3746 1(212)357-2619 1(212)902-3053

Latin America Economics Research Paulo Leme~ 1(305)755-1038 Luis Cezario* 55(11)3371-0778 Alberto Ramos* 1(212)357-5768 Malachy Meechan# 1(212)357-5772 US Portfolio Strategy Research David Kostin~ 1(212)902-6781 Nicole Fox# 1(212)357-1744 Caesar Maasry# 1(212)902-9693 Amanda Sneider# 1(212)357-9860 US Credit Strategy Research Charles Himmelberg~ 1(917)343-3218 Alberto Gallo* 1(917)343-3214 Lotfi Karoui# 1(917)343-1548 Annie Chu^ 1(212)357-5522 Asia Kathy Matsui~

81(3)6437-9950

Asia-Pacific Economics Research Michael Buchanan~ 852()2978-1802 Enoch Fung* 852()2978-0784 Goohoon Kwon* 82(2)3788-1775 Tushar Poddar* 91(22)6616-9042 Helen (Hong) Qiao* 852()2978-1630 Pranjul Bhandari# 852()2978-2676 Keun Myung Kim# 82(2)3788-1726 Yu Song# 852()2978-1260 Shirla Sum^ 852()2978-6634 Professor Song Guoqing 86(10)6627-3021 Japan Economics Research Tetsufumi Yamakawa~ 81(3)6437-9960 Chiwoong Lee* 81(3)6437-9984 Yuriko Tanaka* 81(3)6437-9964

~MD

* VP/ED

#Associate

Asia cont'd Asia-Pacific Portfolio Strategy Research Timothy Moe~ 852()2978-1328 Thomas Deng~ 852()2978-1062 Kinger Lau# 852()2978-1224 Stephanie Leung# 852()2978-0106 Richard Tang^ 852()2978-0722 Japan Portfolio Strategy Research Hiromi Suzuki* 81(3)6437-9955 Pan-Asia Strategy Derivatives Research Christopher Eoyang~ 852()2978-0800 Kenneth Kok* 852()2978-0960 Sam Gellman# 852()2978-1631 Jason Lui^ 852()2978-6613

Europe, Middle East and Africa Peter Oppenheimer~ 44(20)7552-5782 Erik F. Nielsen~ 44(20)7774-1749 Economics Research Ben Broadbent~ Rory MacFarquhar~ Ahmet Akarli* Kevin Daly* Javier Perez de Azpillaga* Dirk Schumacher* Natacha Valla* Anna Zadornova# Nick Kojucharov^ Adrian Paul^ Jonathan Pinder^

44(20)7552-1347 7(495)645-4010 44(20)7051-1875 44(20)7774-5908 44(20)7774-5205 49(69)7532-1210 33(1)4212-1343 44(20)7774-1163 44(20)7774-1169 44(20)7552-5748 44(20)7774-1137

Portfolio Strategy Research Sharon Bell* 44(20)7552-1341 Jessica Binder* 44(20)7051-0460 Gerald Moser# 44(20)7774-5725 Christian MuellerGlissmann# 44(20)7774-1714 Anders Nielsen# 44(20)7552-3000 Matthieu Walterspiler^ 44(20)7552-3403

^Research Assistant/Analyst

Global Markets Research Dominic Wilson~ Francesco Garzarelli~

1(212)902-5924 44(20)7774-5078

Global Macro Research Peter Berezin* Anna Stupnytska# Alex Kelston^

1(212)902-8763 44(20)7774-5061 1(212)855-0684

FX Research Themistoklis Fiotakis* Fiona Lake* Thomas Stolper* Mark Tan#

44(20)7552-2901 852()2978-6088 44(20)7774-5183 1(212)357-7621

Fixed Income Research Michael Vaknin* Swarnali Ahmed^

44(20)7774-1386 44(20)7051-4009

Macro Equity Research Noah Weisberger~ Roman Maranets* Aleksandar Timcenko* Kamakshya Trivedi*

1(212)357-6261 1(212)357-6107 1(212)357-7628 44(20)7051-4005

Commodities Research Jeffrey Currie~

44(20)7774-6112

Energy Samantha Dart*

44(20)7552-9350

Non-Energy Janet Kong~ John Baumgartner#

852()2978-6128 1(212)902-3307

Commodity Strategy Allison Nathan~ David Greely* Damien Courvalin# Stefan Wieler#

1(212)357-7504 1(212)902-2850 44(20)7051-4092 44(20)7051-5119

Administration Lewis Segal~ Linda Britten* Paul O'Connell* Loretta Sunnucks*

1(212)357-4322 44(20)7774-1165 44(20)7774-1107 44(20)7774-3223

Advisors Willem Buiter

44(20)7774-2731

Email: [email protected]

October 2009