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Dynamic Trading of FX Carry and Momentum Portfolios Lorenzo Bertolini Cass Business School, City University, London
June 6, 2009
1
Introduction
2
Methodology
3
Data G10 FX and Yield Data G10 FX Carry and Momentum Indices Risk-Factors & Risk Indicator
4
Benchmark Market Timing Rules Moving-Average Crossover Rule Risk-Indicator Filter Rule Moving Average Crossover/Risk-Indicator Combination
5
Conclusion
6
References
Outline
1
Introduction
2
Methodology
3
Data
4
Benchmark Market Timing Rules
5
Conclusion
6
References
What is Carry and Momentum Trading?
Definition: Carry Trading A strategy in which an investor sells a certain currency with a relatively low interest rate and uses the funds to purchase a different currency yielding a higher interest rate. A trader using this strategy attempts to capture the difference between the rates, which can often be substantial, depending on the amount of leverage the investor chooses to use. source: http://www.investopedia.com/terms/c/currencycarrytrade.asp
Definition: Momentum Trading An investment strategy that aims to capitalize on the continuance of existing trends in the market. The momentum investor believes that large increases in the price of a security will be followed by additional gains and vice versa for declining values. source: http://www.investopedia.com/terms/m/momentum investing.asp
Carry and Momentum are popular FX Trading Styles
Carry and Momentum trading styles in FX markets are amongst the most popular trading strategies applied in the management of FX portfolios (see e.g. Acar [7], BIS-Survey 2007 [5]). There is evidence for positive returns from trading these two investment styles (see e.g. Acar [7], Dunis [8], [4] and Hochradl and Wagner et.al [6]). Carry and Momentum strategies can incur periods of severe drawdowns (see e.g. Dunis [8]).
Factors driving FX Carry and Momentum Returns
Our research builds on three main directions in literature, which study the relationship between FX Carry and Momentum strategy returns and risk-factors: Timing FX Carry/Momentum with RiskMetrics Volatility Estimates Dunis [4] ,[8] finds that during periods of low FX market volatility FX Carry and Momentum trading strategies perform better than they do during periods of high FX market volatility.
Relationship of FX Carry portfolios with risk-factors and monetary variables Burnside et al. [1] examined the relationship between FX Carry trading returns and risk-related and monetary timeseries. They found no evidence for a linear relationship on a monthly timeframe.
Risk-Factors as Inputs for Market Timing Indicators Coudert [3] calculates logistic-regression based early warning indicators with risk-factors as inputs. He achieved good results when predicting equity market crises and poor results when predicting currency crises.
Addressed Research Questions
Question 1
Do risk-factors allow to forecast periods of profitable FX Carry and/or Momentum trading? Question 2
Do more advanced statistical models outperform simple market timing rules? Question 3
Do nonlinear neural network based modeling techniques add value to the market timing process, thereby indicating nonlinear relationships between FX Carry/Momentum Indices and risk-factors?
Outline
1
Introduction
2
Methodology
3
Data
4
Benchmark Market Timing Rules
5
Conclusion
6
References
Simple Market Timing Benchmarks
We will test three simple market timing models and use them as benchmarks for the more advanced statistical techniques: Benchmark Market Timing Models
Simple Moving-Average Crossover Rule Risk-Indicator Filter Rule Combined Moving-Average Crossover/Risk-Indicator Rule
Statistical Classification Techniques
Several studies have reported enhanced predictability of signs of returns versus magnitudes of returns (see e.g. Christoffersen and Diebold [2]). Building on these results we will attempt to classify periods with positive FX Carry/Momentum returns and periods with negative FX Carry/Momentum returns. Adopted Classification Methods
k-Nearest Neighbors Logistic Regression Multi Layer Perceptron Neural Networks Recurrent Neural Networks
Outline
1
Introduction
2
Methodology
3
Data G10 FX and Yield Data G10 FX Carry and Momentum Indices Risk-Factors & Risk Indicator
4
Benchmark Market Timing Rules
5
Conclusion
6
References
Data Overview
We collected data at a weekly frequency from Bloomberg and Datastream. The categories of our data series are: G10 FX and Yield Data This data is used for the FX portfolio backtesting routines needed to test dynamic portfolio strategies with timing indicators.
G10 FX Carry and Momentum Indices For the construction of the FX portfolio timing models, we need to construct FX Carry and FX Momentum indices and transform their total returns timeseries into binary timeseries.
Risk-Factors & Risk Indicator Financial risk-factors will serve as inputs to the FX portfolio timing models.
G10 1-Week Yields
G10 1-Week Yield Data
6 5 4 3 2 7 6 5 6
NZ0001W_INDEX
4 150 100 4 3 2 1
SK0001W_INDEX
5
60
50
NIBOR1W_INDEX
8
103
4
AU0001W_INDEX
8
1
CD0001W_INDEX
5 4 3 2
EU0001W_INDEX
8 1 6 4 2
US0001W_INDEX JY0001W_INDEX
80 1 2 3 4 5 60 6 4
BP0001W_INDEX
2 4 3 2 1
Table: G10 1-Week Yield Data Overview (source: Bloomberg)
1W Yield Data
SF0001W_INDEX
Description EUR 1 WEEK YIELDS USD 1 WEEK YIELDS JPY 1 WEEK YIELDS GBP 1 WEEK YIELDS CHF 1 WEEK YIELDS CAD 1 WEEK YIELDS AUD 1 WEEK YIELDS NZD 1 WEEK YIELDS NOK 1 WEEK YIELDS SEK 1 WEEK YIELDS
0
Series EU0001W INDEX US0001W INDEX JY0001W INDEX BP0001W INDEX SF0001W INDEX CD0001W INDEX AU0001W INDEX NZ0001W INDEX NIBOR1W INDEX SK0001W INDEX
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
G10 1-Month Yields
G10 1-Month Yield Data
8 6 4 2 15 10
BBSW1M_CURNCY CDOR01_CURNCY
5 12 10 8 6
NFIX1M_CURNCY
50 4 30
NIBOR1M_CURNCY
10 600 40
STIB1M_CURNCY
0
20
5 4 3 2 10 1 8 6 4 2 8 0 6 4 2 150 10 5 10 8 6 4 2
Table: G10 1-Month Yield Data Overview (source: Bloomberg)
1M Yield Data SF0001M_CURNCY BP0001M_CURNCY JY0001M_CURNCY US0001M_CURNCY EUR001M_CURNCY
Description EUR 1 MTH YIELDS USD 1 MTH YIELDS JPY 1 MTH YIELDS GBP 1 MTH YIELDS CHF 1 MTH YIELDS CAD 1 MTH YIELDS AUD 1 MTH YIELDS NZD 1 MTH YIELDS NOK 1 MTH YIELDS SEK 1 MTH YIELDS
0
Series EUR001M CURNCY US0001M CURNCY JY0001M CURNCY BP0001M CURNCY SF0001M CURNCY CDOR01 CURNCY BBSW1M CURNCY NFIX1M CURNCY NIBOR1M CURNCY STIB1M CURNCY
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
G10 FX Rates
G10 Foreign Exchange Rate Data
1.1 0.9 0.7 0.5 0.4 0.5 0.6 0.7 0.14 0.12 0.10 0.14 0.10
SEKEUR_CURNCY NOKEUR_CURNCY NZDEUR_CURNCY AUDEUR_CURNCY
1.4 1.0 0.6 0.008
JPYEUR_CURNCY
1.7 0.004 1.5 1.3 0.65 1.1 0.50 0.35 0.9
1980
0.7
CADEUR_CURNCY CHFEUR_CURNCY GBPEUR_CURNCY
Table: G10 FX Rates Overview (source: Bloomberg, Datastream)
0.5
Description USDEUR FX RATE JPYEUR FX RATE GBPEUR FX RATE CHFEUR FX RATE CADEUR FX RATE AUDEUR FX RATE NZDEUR FX RATE NOKEUR FX RATE SEKEUR FX RATE
USDEUR_CURNCY
EUR FX RATES
Series USDEUR CURNCY JPYEUR CURNCY GBPEUR CURNCY CHFEUR CURNCY CADEUR CURNCY AUDEUR CURNCY NZDEUR CURNCY NOKEUR CURNCY SEKEUR CURNCY
1980
1985
1990
1995
2000
2005
2010
1985
1990
1995
2000
2005
2010
Calculating the G10 FX Carry and Momentum Return Indices We build weekly carry and momentum return indices by constructing FX portfolios following the ranking procedure adopted by e.g. Vesilind [10] and Hochradl and Wagner [6]: Asset Allocation Procedure 1
Rank the G10 currencies according to their yield (Carry) or 52-period z-Score (Momentum).
2
Buy the 30% highest ranking currencies and fund these positions by selling the 30% lowest ranking currencies.
3
Hold the FX portfolio for one period.
We apply a spread of 10 basis points on fixed income positions, a spread of 0.03% on FX trades and slippage costs of 0.02% on FX trades.
Asset Allocation Procedure: G10 Carry Portfolio
G10 Yields
Ranked G10 Yields
1985
1990
1995
2000
2005
2010
10 8 6 4 2 100 8 6 4 2
BBSW1M_CURNCY CDOR01_CURNCY
100 8 6 4
NFIX1M_CURNCY
2 100 8 6 4 2
NIBOR1M_CURNCY
100 8 6 4
STIB1M_CURNCY
0 1980
1980
2
10 8 6 4 2 100 8 6 4 2 100 8 6 4 2 100 8 6 4 2 100 8 6 4 2
SF0001M_CURNCY BP0001M_CURNCY JY0001M_CURNCY US0001M_CURNCY EUR001M_CURNCY
50 40 30 20 10 0
as.zoo(x)
Ranked G10 Yields
0
60
G10 Yields EUR001M_CURNCY US0001M_CURNCY JY0001M_CURNCY BP0001M_CURNCY SF0001M_CURNCY CDOR01_CURNCY BBSW1M_CURNCY NFIX1M_CURNCY NIBOR1M_CURNCY STIB1M_CURNCY
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Asset Allocation Procedure: G10 Carry Portfolio
G10 Yields
G10 Carry Portfolio Positions
1985
1990
1995
2000
2005
2010
2000
2005
2010
0.0 0.5 1.0 0.0 0.5 1.0 −1.0
BBSW1M_CURNCY CDOR01_CURNCY 1995
0.0 0.5 1.0 −1.0
NFIX1M_CURNCY 1990
0.0 0.5 1.0 −1.0
NIBOR1M_CURNCY 1985
0.0 0.5 1.0 −1.0
STIB1M_CURNCY 1980
1980
−1.0
0.0 0.5 1.0 0.0 0.5 1.0 −1.0 0.0 0.5 1.0 −1.0 0.0 0.5 1.0 −1.0 0.0 0.5 1.0 −1.0
SF0001M_CURNCY BP0001M_CURNCY JY0001M_CURNCY US0001M_CURNCY EUR001M_CURNCY
50 40 30 20 10 0
as.zoo(x)
Portfolio Positions:G10 Carry Ranker
−1.0
60
G10 Yields EUR001M_CURNCY US0001M_CURNCY JY0001M_CURNCY BP0001M_CURNCY SF0001M_CURNCY CDOR01_CURNCY BBSW1M_CURNCY NFIX1M_CURNCY NIBOR1M_CURNCY STIB1M_CURNCY
1980
1985
1990
1995
2000
2005
2010
Returns to the Long-Only G10 Carry Portfolio
G10 Carry Portfolio Performance
G10 Carry Portfolio Components 1.0
Components Positions: G10 Carry Portfolio
Strategy RoI Index
100
−1.0
−0.5
150
0.0
200
0.5
250
RoI Index of: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
Portfolio Components StrategyReturns: G10 Carry Portfolio
as.zoo(x)
−1.0
−0.2
0.0
0.0 −0.5
0.2
0.4
market position Long market position Short
0.5
1.0
TradingStrategy: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
1985
1990
1995
2000
2005
Index 0.5 0.3 0.1 −0.1
0.5
1.0
Performance Attribution: G10 Carry Portfolio @ 2009−05−15
0.0
as.zoo(x)
1.5
StrategyReturns: G10 Carry Portfolio fx yield transactions slippage total
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Asset Allocation Procedure: G10 Momentum Portfolio
USD Cash Returns
USD Momentum
10
0.8
4
3
1.0
6
USD Momentum (left axis) USD Returns (right axis)
1985
1990
1995
2000
2005
2010
2005
2010
2005
2010
0.6
1980
2
0
0.6
2
0.8
as.zoo(x)
USD Total Returns and USD Momentum
8
USDEUR_CURNCY (left axis) US0001M_CURNCY (right axis)
1.2
1.4
Asset: Cash USD 1M
Index
0.2
0
as.zoo(x)
0.0
1985
1990
1995
2000
0.0
1980
−1
−1.0
−0.5
0.4
1
market position Long market position Short
0.5
1.0
TradingStrategy: CASH USD
−2
−0.2
0.5
−3
0.0 −0.5
as.zoo(x)
1.0
StrategyReturns: CASH USD fx yield transactions slippage total
1980
1985
1990
1995
2000
1980
1985
1990
1995
2000
2005
2010
Asset Allocation Procedure: G10 Momentum Portfolio
G10 Momentum
Ranked G10 Momentum G10 Momentum
1985
1990
1995
2000
2005
2010
10 8 6 4
CASH CAD
100 8 6 4
CASH AUD
2 100 8 6 4
CASH NZD
2 100 8 6 4
CASH NOK
2 100 8 6 4
CASH SEK
2 0
1980
1980
2
6 4
CASH EUR
2 100 8 6 4
CASH USD
8 6
CASH JPY
4 8 6 4 8 6 4 0
2
CASH CHF
100
2
CASH GBP
100
2
0 −2 −4
as.zoo(x)
100
2
4 2
8
10
Ranked G10 Momentum
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Asset Allocation Procedure: G10 Momentum Portfolio
G10 Momentum
G10 Momentum Portfolio Positions G10 Momentum
1985
1990
1995
2000
2005
2010
CASH CAD
0.0 0.5 1.0 0.0 0.5 1.0 −1.0
CASH AUD CASH NZD
0.0 0.5 1.0 −1.0 0.0 0.5 1.0 −1.0
CASH NOK 1980
1980
0.0 0.5 1.0 −1.0
CASH SEK
−1.0
−1.0
CASH EUR
0.0 0.5 1.0 0.0 0.5 1.0 −1.0
CASH USD CASH JPY
0.0 0.5 1.0 −1.0 0.0 0.5 1.0 −1.0
CASH GBP CASH CHF
0.0 0.5 1.0 −1.0
4 2 0 −2 −4
as.zoo(x)
Portfolio Positions:G10 Momentum Ranker
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Returns to the Long-Only G10 Momentum Portfolio
G10 Momentum Portfolio Performance
G10 Momentum Portfolio Components Components Positions: G10 Momentum Portfolio 1.0
RoI Index of: G10 Momentum Portfolio
−1.0
100
−0.5
120
0.0
0.5
140
Strategy RoI Index
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
0.2
Portfolio Components StrategyReturns: G10 Momentum Portfolio
market position Long market position Short
−1.0
0.0 −0.2
−0.5
0.0
as.zoo(x)
0.1
0.5
1.0
TradingStrategy: G10 Momentum Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
1985
1990
1995
2000
2005
Index 0.2 0.1 0.0 −0.2 −0.1
0.0
0.2
Performance Attribution: G10 Momentum Portfolio @ 2009−05−15
−0.2
as.zoo(x)
0.4
StrategyReturns: G10 Momentum Portfolio fx yield transactions slippage total
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Carry and Momentum Returns
FX Carry and Momentum Indices
FX Carry and Momentum Correlation Scatterplot: FX Carry Total Returns vs. FX Momentum Total Returns Correlation: 0.03 0.10
FX Carry Index FX Momentum Index
200
250
FX Carry Index Perfromance vs. FX Momentum Index Perfromance
●
100
150
●
●
1985
1990
1995
2000
2005
●
0.05
1980
2010
●
●
0.00
Carry Returns
●
●
●
1985
1990
1995
2000
2005
●
● ●● ●● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●●●● ● ●● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● ● ●● ●● ●● ● ●● ●● ● ●● ● ●● ● ● ● ●● ● ● ● ● ●●●●●● ● ●● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ●● ●● ● ●● ● ● ● ●● ●●● ●● ● ●●● ● ● ●● ● ● ●● ●● ●● ●●● ● ●● ● ● ● ● ●● ● ● ● ● ●●● ●● ● ● ● ● ● ● ●●● ● ● ● ● ● ●● ● ● ●● ●● ● ● ● ● ● ● ● ●● ● ●●●● ● ● ● ● ● ● ● ●● ●●●● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ●●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ● ●● ●●●● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ●● ● ●● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●●●● ● ● ● ●● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● ●● ● ● ● ●●●●●● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●●●●● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ●●●●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ●● ● ● ● ●●● ●● ● ● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●●● ● ●● ● ● ●● ●● ●● ● ● ●● ●●● ● ● ● ● ●● ● ● ● ● ●●● ● ●●● ●● ● ●●● ● ● ● ●● ●●● ●●● ● ●●● ●● ●●● ● ● ●● ● ● ●●● ●● ●● ●● ●●● ● ● ● ● ●● ● ● ●●● ● ●● ●●●●● ● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ●●●●●● ●●●● ●● ● ● ●●● ● ●● ● ● ● ● ●●● ● ● ● ●●● ●●● ●● ● ●● ● ●● ● ●● ● ●● ● ● ● ●● ●● ●●● ● ●● ●● ● ●● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●
●
−0.10
−0.05
0.00
0.05
Carry Returns
1980
●
●
FX Carry Total Returns
●
2010
●
−0.05
●
Momentum Returns
●
●
● ●
0.00
0.05
0.10
FX Momentum Total Returns
−0.05
●
−0.10 1980
1985
1990
1995
2000
2005
2010
−0.05
0.00
Momentum Returns
0.05
Risk Indicator: Equity Volatility Component
Equity Risk Timeseries
Normalized Equity Volatility Timeseries
2 2 −2
0
z−score: VDAX_INDEX
4
−2
0
z−score: VIX_INDEX
50
VIX_INDEX
30 10 60 50 40 30 20 10
VDAX_INDEX
4
Normalized Risk Factors: Equity Volatility
70
Risk Factors: Equity Volatility
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Equity Volatility Component
Equity Volatility Timeseries
Equity Volatility Risk Indicator Component Normalized Risk Factors: Equity Volatility
Risk Factors: Equity Volatility
4
50
2
as.zoo(x)
30 50
0
40 30 20
−2
10
VDAX_INDEX
60
10
VIX_INDEX
70
z−score: VIX_INDEX z−score: VDAX_INDEX Risk Indicator: Equity Vola Component
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Equity Positioning Component
Equity Positioning Timeseries
Normalized Equity Positioning Timeseries
1985
1990
1995
2000
2005
2010
4 3 2 1 0 −1 −3 4 2 0 −2
−0.2
MSCI Growth/Value Index
−0.4 1.5−0.6 1.0 0.5
MSCI Defensives/Cyclicals Index
0.0 1980
z−score: MSCI Defensives/Cyclicalsz−score: Index MSCI Growth/Value Index
Normalized Risk Factors: Equity Market Positioning
0.0
Risk Factors: Equity Market Positioning
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Equity Positioning Component
Equity Positioning Timeseries
Equity Positioning Risk Indicator Component Normalized Risk Factors: Equity Market Positioning
0 −2
0.5
1.0
1.5−0.6
as.zoo(x)
−0.4
2
−0.2
4
z−score: MSCI Growth/Value Index z−score: MSCI Defensives/Cyclicals Index Risk Indicator: Equity Posi Component
0.0
MSCI Defensives/Cyclicals Index
MSCI Growth/Value Index
0.0
Risk Factors: Equity Market Positioning
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: FX Volatility Component
FX Volatility Timeseries
Normalized FX Volatility Timeseries
1985
1990
1995
2000
2005
2010
4 2 0 −2 6 4 2 0
25 20 15
JPMVXYEM_INDEX
10 1980
−2
z−score: JPMVXYEM_INDEX
10
15
20
z−score: JPMVXYG7_INDEX
Normalized Risk Factors: FX Volatility
30
JPMVXYG7_INDEX
Risk Factors: FX Volatility
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: FX Volatility Component
FX Volatility Timeseries
FX Volatility Risk Indicator Component Normalized Risk Factors: FX Volatility
Risk Factors: FX Volatility
20
4
15
2
as.zoo(x)
10
0
25 20
−2
15 10
JPMVXYEM_INDEX
30
JPMVXYG7_INDEX
6
z−score: JPMVXYG7_INDEX z−score: JPMVXYEM_INDEX Risk Indicator: FX Vola Component
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Yield and Credit Component
Yield and Credit Timeseries
Normalized Yield and Credit Timeseries
1985
1990
1995
2000
2005
2010
4 2 0 −2 4 2 0 −2 −4 4 2 0 −2 4 2 0
3 2
.TEDSP_INDEX
1 60 5 4 3
usa credit spread
2 1 1980
−2
20
60
100
20
60
100
140
z−score: usa credit spread z−score: .TEDSP_INDEX z−score: USSP10_CMPL_CURNCY z−score: USSP2_CMPL_CURNCY
Normalized Risk Factors: Yield and Credit Conditions
4
USSP10_CMPL_CURNCY USSP2_CMPL_CURNCY
Risk Factors: Yield and Credit Conditions
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Yield and Credit Component
Yield and Credit Timeseries
Yield and Credit Risk Indicator Component Normalized Risk Factors: Yield and Credit Conditions
140 20
as.zoo(x)
60
2
100
20
4
60
100
z−score: USSP2_CMPL_CURNCY z−score: USSP10_CMPL_CURNCY z−score: .TEDSP_INDEX z−score: usa credit spread Risk Indicator: Yield and Credit Component
0
3 2 1
−2
5 4 3 2 1980
1985
1990
1995
2000
2005
2010
−4
1
usa credit spread
60
.TEDSP_INDEX
4
USSP10_CMPL_CURNCY USSP2_CMPL_CURNCY
Risk Factors: Yield and Credit Conditions
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Safe Haven Component
Safe Haven Timeseries
Normalized Safe Haven Timeseries
Normalized Risk Factors: Safe Haven Assets
1995
2000
2005
2010
2
3
−2
0
2
4 1990
1
z−score: GOLDS_INDEX 1985
0
z−score: CHFUSD_CURNCY 1980
−3 −2 −1
800 600 400 0.8 0.6 0.4
CHFUSD_CURNCY
1.0
GOLDS_INDEX
1000
Risk Factors: Safe Haven Assets
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Safe Haven Component
Safe Haven Timeseries
Safe Haven Risk Indicator Component Normalized Risk Factors: Safe Haven Assets
as.zoo(x)
−2
0.6
0.8
0
400
2
600
800
4
z−score: GOLDS_INDEX z−score: CHFUSD_CURNCY Risk Indicator: Safe Haven Component
0.4
CHFUSD_CURNCY
1.0
GOLDS_INDEX
1000
Risk Factors: Safe Haven Assets
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Aggregated Risk Indicator
Risk Indicator Timeseries
We calculate the aggregated Risk Indicator by equally weighting the 5 sub-components:
6
Risk Indicator & Subcomponents
4
Risk Indicator: Equity Vola Component Risk Indicator: Equity Vola Component Risk Indicator: Equity Posi Component Risk Indicator: FX Vola Component Risk Indicator: Yield and Credit Component Risk Indicator: Safe Haven Component risk indicator value
as.zoo(x)
2
Equity Volatility Equity Positioning 0
FX Volatility
−2
Yield and Credit Safe Haven 1980
1985
1990
1995
2000
2005
2010
Aggregated Risk Indicator
The Aggregated Risk Indicator Aggregated Risk Indicator 3
risk indicator value
−3
−2
−1
0
1
2
We will use the aggregated Risk Indicator as a measure for risk-appetite (low indicator values) and risk-aversion (high indicator values) in the markets.
1980
1985
1990
1995
2000
2005
2010
Outline
1
Introduction
2
Methodology
3
Data
4
Benchmark Market Timing Rules Moving-Average Crossover Rule Risk-Indicator Filter Rule Moving Average Crossover/Risk-Indicator Combination
5
Conclusion
6
References
Timing the Carry Trade with a Moving Average Crossover Rule
Moving Average Crossover Signal
We create a simple Carry timing indicator, following standard moving average crossover trading rules:
200 150 100
as.zoo(x)
250
TradRule1: Moving Average Crossover (1,52) FX Carry Index tsRollMean(FX Carry Index,1) tsRollMean(FX Carry Index,52)
1980
1985
1990
1995
2000
2005
2010
Entry Long when the FX Carry Index crosses over the 52-period moving average.
Index
−1.0
−0.5
0.0
0.5
1.0
Trading Signal SignalPositions_EntriesExits Long SignalPositions_EntriesExits Short
1980
1985
1990
1995
2000
2005
2010
2000
2005
2010
0.6 0.2
0.4
entry long exit long entry short exit short
0.0
as.zoo(x)
0.8
1.0
Market Entry/Exit Signals
1980
1985
1990
1995
Entry Short when the FX Carry Index crosses under the 52-period moving average.
Timing the FX Carry Trade with a Moving Average Crossover Rule
Timed FX Carry Portfolio Components
Timed FX Carry Portfolio
Components Positions: G10 Carry Portfolio 1.0
Strategy RoI Index
100
−1.0
−0.5
150
0.0
200
0.5
250
RoI Index of: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Carry Portfolio 0.4 0.2 0.0
−1.0
−0.2
−0.5
0.0
as.zoo(x)
0.5
1.0
TradingStrategy: G10 Carry Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Carry Portfolio @ 2009−05−15
0.0
0.1
0.4
0.2
0.3
fx yield transactions slippage total
0.0
as.zoo(x)
0.8
StrategyReturns: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Timing the FX Momentum Trade with a Moving Average Crossover Rule We create a simple Momentum timing indicator, following standard moving average crossover trading rules:
Moving Average Crossover Signal
120 100
as.zoo(x)
140
TradRule1: Moving Average Crossover (1,52) FX Momentum Index tsRollMean(FX Momentum Index,1) tsRollMean(FX Momentum Index,52)
1980
1985
1990
1995
2000
2005
2010
2000
2005
2010
Index
−1.0
−0.5
0.0
0.5
1.0
Trading Signal SignalPositions_EntriesExits Long SignalPositions_EntriesExits Short
1980
1985
1990
1995
0.6 0.2
0.4
entry long exit long entry short exit short
0.0
as.zoo(x)
0.8
1.0
Market Entry/Exit Signals
1980
1985
1990
1995
2000
2005
2010
Entry Long when the FX Momentum Index crosses over the 52-period moving average. Entry Short when the FX Momentum Index crosses under the 52-period moving average.
Timing the FX Momentum Trade with a Moving Average Crossover Rule
Timed FX Momentum Portfolio Components
Timed FX Momentum Portfolio
Components Positions: G10 Momentum Portfolio 1.0
RoI Index of: G10 Momentum Portfolio
−1.0
100
−0.5
120
0.0
0.5
140
Strategy RoI Index
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Momentum Portfolio 0.2 −0.2
−1.0
−0.4
−0.5
0.0
as.zoo(x)
0.0
0.5
1.0
TradingStrategy: G10 Momentum Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Momentum Portfolio @ 2009−05−15 0.1 −0.1 −0.3 −0.5
−0.4
−0.2
fx yield transactions slippage total
−0.6
as.zoo(x)
0.0
StrategyReturns: G10 Momentum Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Timing the FX Carry Trade with a Risk Indicator Filter Rule
Risk Indicator Signal
We create a Risk-Indicator based Carry timing indicator, following the following trading rules:
0 −1 −3
−2
as.zoo(x)
1
2
3
TradRule1: Risk Indicator Filter Risk−Appetite Indicator threshold line: 0
1980
1985
1990
1995
2000
2005
2010
Index
Entry Long when the Risk-Appetite Indicator crosses over the zero-line.
−1.0
−0.5
0.0
0.5
1.0
Trading Signal SignalPositions_EntriesExits Long SignalPositions_EntriesExits Short
1980
1985
1990
1995
2000
2005
2010
Entry Short when the Risk-Appetite Indicator crosses under the zero-line.
0.6 0.2
0.4
entry long exit long entry short exit short
0.0
as.zoo(x)
0.8
1.0
Market Entry/Exit Signals
1980
1985
1990
1995
2000
2005
2010
Timing the FX Carry Trade with a Risk Indicator Filter Rule
Timed FX Carry Portfolio Components
Timed FX Carry Portfolio
Components Positions: G10 Carry Portfolio 1.0
Strategy RoI Index
100
−1.0
−0.5
150
0.0
200
0.5
250
RoI Index of: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Carry Portfolio 0.2 0.0 −0.2
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
−0.4
−1.0
−0.5
0.0
as.zoo(x)
0.5
1.0
TradingStrategy: G10 Carry Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Carry Portfolio @ 2009−05−15 0.2 0.1 0.0 −0.1
0.0
0.2
fx yield transactions slippage total
−0.2
−0.4 −0.2
as.zoo(x)
0.4
StrategyReturns: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Timing the FX Momentum Trade with a Risk Indicator Filter Rule
Risk Indicator Signal
0 −1 −3
−2
as.zoo(x)
1
2
3
TradRule1: Risk Indicator Filter Risk−Appetite Indicator threshold line: 0
1980
1985
1990
1995
2000
2005
2010
We create a Risk-Indicator based Momentum timing indicator, following the following trading rules:
Index
−1.0
−0.5
0.0
0.5
1.0
Trading Signal SignalPositions_EntriesExits Long SignalPositions_EntriesExits Short
1980
1985
1990
1995
2000
2005
2010
0.2
0.4
0.6
Entry Short when the Risk-Appetite Indicator crosses under the zero-line.
entry long exit long entry short exit short
0.0
as.zoo(x)
0.8
1.0
Market Entry/Exit Signals
1980
1985
1990
1995
Entry Long when the Risk-Appetite Indicator crosses over the zero-line.
2000
2005
2010
Timing the FX Momentum Trade with a Risk Indicator Filter Rule
Timed FX Momentum Portfolio Components
Timed FX Momentum Portfolio
Components Positions: G10 Momentum Portfolio 1.0
RoI Index of: G10 Momentum Portfolio
−1.0
100
−0.5
120
0.0
0.5
140
Strategy RoI Index
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Momentum Portfolio 0.1 0.2 as.zoo(x)
0.0 −1.0
−0.3
−0.5
−0.1
0.5
1.0
TradingStrategy: G10 Momentum Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Momentum Portfolio @ 2009−05−15 0.2 0.1 0.0 −0.2
0.0 0.2 0.4 0.6
fx yield transactions slippage total
−0.4
as.zoo(x)
StrategyReturns: G10 Momentum Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Timing the FX Carry Trade with a combined Moving Average/Risk Appetite Signal
Combined Moving Average/Risk Appetite Signal
0.6
1.0
1.4
Position Signal: Aggregated Strategy Signal position
1980
1985
1990
1995
2000
2005
2010
2005
2010
2000
2005
2010
2000
2005
2010
2000
2005
2010
Trading Rules:
position
−1.0 0.0
1.0
Position Signal: Moving Average Crossover (1,52)
1980
1985
1990
1995
2000
−1.0 0.0
1.0
Filter Signal: Risk Indicator Filter filter
1980
1985
1990
1995
market position
−1.0 0.0
1.0
Aggregated Strategy Signal
1980
1985
1990
1995
buy sell
−2
0
2
Strategy Trades
1980
1985
1990
1995
Long When the Moving Average Rule AND the Risk-Indicator rule are long. Short When the Moving Average Rule AND the Risk-Indicator rule are short.
Timing the FX Carry Trade with a combined Moving Average/Risk Appetite Signal
Timed FX Carry Portfolio Components
Timed FX Carry Portfolio
Components Positions: G10 Carry Portfolio 1.0
Strategy RoI Index
100
−1.0
−0.5
150
0.0
200
0.5
250
RoI Index of: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Carry Portfolio 0.2 0.1 as.zoo(x)
0.0 −0.5
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
−0.3
−1.0
−0.1 0.0
0.5
1.0
TradingStrategy: G10 Carry Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Carry Portfolio @ 2009−05−15 0.15 0.05
0.2
0.4
fx yield transactions slippage total
−0.05
0.0
as.zoo(x)
0.6
StrategyReturns: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Timing the FX Momentum Trade with a combined Moving Average/Risk Appetite Signal
Combined Moving Average/Risk Appetite Signal
0.6
1.0
1.4
Position Signal: Aggregated Strategy Signal position
1980
1985
1990
1995
2000
2005
2010
2005
2010
2000
2005
2010
2000
2005
2010
2000
2005
2010
Trading Rules:
position
−1.0 0.0
1.0
Position Signal: Moving Average Crossover (1,52)
1980
1985
1990
1995
2000
−1.0 0.0
1.0
Filter Signal: Risk Indicator Filter filter
1980
1985
1990
1995
market position
−1.0 0.0
1.0
Aggregated Strategy Signal
1980
1985
1990
1995
buy sell
−2
0
2
Strategy Trades
1980
1985
1990
1995
Long When the Moving Average Rule AND the Risk-Indicator rule are long. Short When the Moving Average Rule AND the Risk-Indicator rule are short.
Timing the FX Momentum Trade with a combined Moving Average/Risk Appetite Signal
Timed FX Momentum Portfolio Components
Timed FX Momentum Portfolio
Components Positions: G10 Momentum Portfolio 1.0
RoI Index of: G10 Momentum Portfolio
−1.0
100
−0.5
120
0.0
0.5
140
Strategy RoI Index
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Momentum Portfolio 0.1
−1.0
−0.1 −0.3
−0.5
0.0
as.zoo(x)
0.5
1.0
TradingStrategy: G10 Momentum Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Momentum Portfolio @ 2009−05−15 0.1 0.0 −0.2
−0.1
0.1
fx yield transactions slippage total
−0.4
−0.3
as.zoo(x)
0.3
StrategyReturns: G10 Momentum Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Outline
1
Introduction
2
Methodology
3
Data
4
Benchmark Market Timing Rules
5
Conclusion
6
References
Dynamic FX Portfolio Trading: Status-Quo
We built a software for backtesting portfolios of trading systems. We tested benchmark FX Carry and Momentum portfolio timing strategies with mixed results. The approach of combining different types of market timing rules looks promising. Next steps: Calculation of the statistical market timing indicators based on risk-factors.
Outline
1
Introduction
2
Methodology
3
Data
4
Benchmark Market Timing Rules
5
Conclusion
6
References
Craig Burnside, Martin Eichenbaum, Isaac Kleshchelski, and Sergio Tavares Rebelo. The returns to currency speculation. SSRN eLibrary, 2006. Peter F. Christoffersen and Francis X. Diebold. Financial asset returns, direction-of-change forecasting, and volatility dynamics. Technical Report 10009, October 2003. Virginie Coudert and Mathieu Gex. Can risk aversion indicators anticipate financial crises? Technical Report 9, Banque de France, December 2006. Christian L. Dunis and Jia Miao. Trading foreign exchange portfolios with volatility filters: the carry model revisited. Applied Financial Economics, 17(3):249–255, 2007. Alex Heath, Christian Upper, Paola Gallardo, Philippe Mesny, and Carlos Mallo.
Triennial Central Bank Survey. Bank for International Settlements, 2007. Markus Hochradl and Christian Wagner. Trading the forward bias: Are there limits to speculation? SSRN eLibrary, 2007. P. Lequeux and E. Acar. A dynamic index for managed currencies funds using cme currency contracts. European Journal of Finance, 4(4):311–330, 1998. Jia Miao and Christian L. Dunis. Volatility filters for fx portfolios trading: the impact of alternative volatility models. Applied Financial Economics Letters, 2(6):389–394, 2006. Darren Read, William Darwin, and Pauline O’Neill. Measuring equity market risk. Technical report, UBS Investment Research, Global Equity Strategy, June 2006.
Andres Vesilind. Profitability of simple trading strategies exploiting the forward premium bias in foreign exchange markets and the time premium in yield curves. Technical Report 2006-04, Oct 2006.
June 6, 2009
1
Introduction
2
Methodology
3
Data G10 FX and Yield Data G10 FX Carry and Momentum Indices Risk-Factors & Risk Indicator
4
Benchmark Market Timing Rules Moving-Average Crossover Rule Risk-Indicator Filter Rule Moving Average Crossover/Risk-Indicator Combination
5
Conclusion
6
References
Outline
1
Introduction
2
Methodology
3
Data
4
Benchmark Market Timing Rules
5
Conclusion
6
References
What is Carry and Momentum Trading?
Definition: Carry Trading A strategy in which an investor sells a certain currency with a relatively low interest rate and uses the funds to purchase a different currency yielding a higher interest rate. A trader using this strategy attempts to capture the difference between the rates, which can often be substantial, depending on the amount of leverage the investor chooses to use. source: http://www.investopedia.com/terms/c/currencycarrytrade.asp
Definition: Momentum Trading An investment strategy that aims to capitalize on the continuance of existing trends in the market. The momentum investor believes that large increases in the price of a security will be followed by additional gains and vice versa for declining values. source: http://www.investopedia.com/terms/m/momentum investing.asp
Carry and Momentum are popular FX Trading Styles
Carry and Momentum trading styles in FX markets are amongst the most popular trading strategies applied in the management of FX portfolios (see e.g. Acar [7], BIS-Survey 2007 [5]). There is evidence for positive returns from trading these two investment styles (see e.g. Acar [7], Dunis [8], [4] and Hochradl and Wagner et.al [6]). Carry and Momentum strategies can incur periods of severe drawdowns (see e.g. Dunis [8]).
Factors driving FX Carry and Momentum Returns
Our research builds on three main directions in literature, which study the relationship between FX Carry and Momentum strategy returns and risk-factors: Timing FX Carry/Momentum with RiskMetrics Volatility Estimates Dunis [4] ,[8] finds that during periods of low FX market volatility FX Carry and Momentum trading strategies perform better than they do during periods of high FX market volatility.
Relationship of FX Carry portfolios with risk-factors and monetary variables Burnside et al. [1] examined the relationship between FX Carry trading returns and risk-related and monetary timeseries. They found no evidence for a linear relationship on a monthly timeframe.
Risk-Factors as Inputs for Market Timing Indicators Coudert [3] calculates logistic-regression based early warning indicators with risk-factors as inputs. He achieved good results when predicting equity market crises and poor results when predicting currency crises.
Addressed Research Questions
Question 1
Do risk-factors allow to forecast periods of profitable FX Carry and/or Momentum trading? Question 2
Do more advanced statistical models outperform simple market timing rules? Question 3
Do nonlinear neural network based modeling techniques add value to the market timing process, thereby indicating nonlinear relationships between FX Carry/Momentum Indices and risk-factors?
Outline
1
Introduction
2
Methodology
3
Data
4
Benchmark Market Timing Rules
5
Conclusion
6
References
Simple Market Timing Benchmarks
We will test three simple market timing models and use them as benchmarks for the more advanced statistical techniques: Benchmark Market Timing Models
Simple Moving-Average Crossover Rule Risk-Indicator Filter Rule Combined Moving-Average Crossover/Risk-Indicator Rule
Statistical Classification Techniques
Several studies have reported enhanced predictability of signs of returns versus magnitudes of returns (see e.g. Christoffersen and Diebold [2]). Building on these results we will attempt to classify periods with positive FX Carry/Momentum returns and periods with negative FX Carry/Momentum returns. Adopted Classification Methods
k-Nearest Neighbors Logistic Regression Multi Layer Perceptron Neural Networks Recurrent Neural Networks
Outline
1
Introduction
2
Methodology
3
Data G10 FX and Yield Data G10 FX Carry and Momentum Indices Risk-Factors & Risk Indicator
4
Benchmark Market Timing Rules
5
Conclusion
6
References
Data Overview
We collected data at a weekly frequency from Bloomberg and Datastream. The categories of our data series are: G10 FX and Yield Data This data is used for the FX portfolio backtesting routines needed to test dynamic portfolio strategies with timing indicators.
G10 FX Carry and Momentum Indices For the construction of the FX portfolio timing models, we need to construct FX Carry and FX Momentum indices and transform their total returns timeseries into binary timeseries.
Risk-Factors & Risk Indicator Financial risk-factors will serve as inputs to the FX portfolio timing models.
G10 1-Week Yields
G10 1-Week Yield Data
6 5 4 3 2 7 6 5 6
NZ0001W_INDEX
4 150 100 4 3 2 1
SK0001W_INDEX
5
60
50
NIBOR1W_INDEX
8
103
4
AU0001W_INDEX
8
1
CD0001W_INDEX
5 4 3 2
EU0001W_INDEX
8 1 6 4 2
US0001W_INDEX JY0001W_INDEX
80 1 2 3 4 5 60 6 4
BP0001W_INDEX
2 4 3 2 1
Table: G10 1-Week Yield Data Overview (source: Bloomberg)
1W Yield Data
SF0001W_INDEX
Description EUR 1 WEEK YIELDS USD 1 WEEK YIELDS JPY 1 WEEK YIELDS GBP 1 WEEK YIELDS CHF 1 WEEK YIELDS CAD 1 WEEK YIELDS AUD 1 WEEK YIELDS NZD 1 WEEK YIELDS NOK 1 WEEK YIELDS SEK 1 WEEK YIELDS
0
Series EU0001W INDEX US0001W INDEX JY0001W INDEX BP0001W INDEX SF0001W INDEX CD0001W INDEX AU0001W INDEX NZ0001W INDEX NIBOR1W INDEX SK0001W INDEX
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
G10 1-Month Yields
G10 1-Month Yield Data
8 6 4 2 15 10
BBSW1M_CURNCY CDOR01_CURNCY
5 12 10 8 6
NFIX1M_CURNCY
50 4 30
NIBOR1M_CURNCY
10 600 40
STIB1M_CURNCY
0
20
5 4 3 2 10 1 8 6 4 2 8 0 6 4 2 150 10 5 10 8 6 4 2
Table: G10 1-Month Yield Data Overview (source: Bloomberg)
1M Yield Data SF0001M_CURNCY BP0001M_CURNCY JY0001M_CURNCY US0001M_CURNCY EUR001M_CURNCY
Description EUR 1 MTH YIELDS USD 1 MTH YIELDS JPY 1 MTH YIELDS GBP 1 MTH YIELDS CHF 1 MTH YIELDS CAD 1 MTH YIELDS AUD 1 MTH YIELDS NZD 1 MTH YIELDS NOK 1 MTH YIELDS SEK 1 MTH YIELDS
0
Series EUR001M CURNCY US0001M CURNCY JY0001M CURNCY BP0001M CURNCY SF0001M CURNCY CDOR01 CURNCY BBSW1M CURNCY NFIX1M CURNCY NIBOR1M CURNCY STIB1M CURNCY
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
G10 FX Rates
G10 Foreign Exchange Rate Data
1.1 0.9 0.7 0.5 0.4 0.5 0.6 0.7 0.14 0.12 0.10 0.14 0.10
SEKEUR_CURNCY NOKEUR_CURNCY NZDEUR_CURNCY AUDEUR_CURNCY
1.4 1.0 0.6 0.008
JPYEUR_CURNCY
1.7 0.004 1.5 1.3 0.65 1.1 0.50 0.35 0.9
1980
0.7
CADEUR_CURNCY CHFEUR_CURNCY GBPEUR_CURNCY
Table: G10 FX Rates Overview (source: Bloomberg, Datastream)
0.5
Description USDEUR FX RATE JPYEUR FX RATE GBPEUR FX RATE CHFEUR FX RATE CADEUR FX RATE AUDEUR FX RATE NZDEUR FX RATE NOKEUR FX RATE SEKEUR FX RATE
USDEUR_CURNCY
EUR FX RATES
Series USDEUR CURNCY JPYEUR CURNCY GBPEUR CURNCY CHFEUR CURNCY CADEUR CURNCY AUDEUR CURNCY NZDEUR CURNCY NOKEUR CURNCY SEKEUR CURNCY
1980
1985
1990
1995
2000
2005
2010
1985
1990
1995
2000
2005
2010
Calculating the G10 FX Carry and Momentum Return Indices We build weekly carry and momentum return indices by constructing FX portfolios following the ranking procedure adopted by e.g. Vesilind [10] and Hochradl and Wagner [6]: Asset Allocation Procedure 1
Rank the G10 currencies according to their yield (Carry) or 52-period z-Score (Momentum).
2
Buy the 30% highest ranking currencies and fund these positions by selling the 30% lowest ranking currencies.
3
Hold the FX portfolio for one period.
We apply a spread of 10 basis points on fixed income positions, a spread of 0.03% on FX trades and slippage costs of 0.02% on FX trades.
Asset Allocation Procedure: G10 Carry Portfolio
G10 Yields
Ranked G10 Yields
1985
1990
1995
2000
2005
2010
10 8 6 4 2 100 8 6 4 2
BBSW1M_CURNCY CDOR01_CURNCY
100 8 6 4
NFIX1M_CURNCY
2 100 8 6 4 2
NIBOR1M_CURNCY
100 8 6 4
STIB1M_CURNCY
0 1980
1980
2
10 8 6 4 2 100 8 6 4 2 100 8 6 4 2 100 8 6 4 2 100 8 6 4 2
SF0001M_CURNCY BP0001M_CURNCY JY0001M_CURNCY US0001M_CURNCY EUR001M_CURNCY
50 40 30 20 10 0
as.zoo(x)
Ranked G10 Yields
0
60
G10 Yields EUR001M_CURNCY US0001M_CURNCY JY0001M_CURNCY BP0001M_CURNCY SF0001M_CURNCY CDOR01_CURNCY BBSW1M_CURNCY NFIX1M_CURNCY NIBOR1M_CURNCY STIB1M_CURNCY
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Asset Allocation Procedure: G10 Carry Portfolio
G10 Yields
G10 Carry Portfolio Positions
1985
1990
1995
2000
2005
2010
2000
2005
2010
0.0 0.5 1.0 0.0 0.5 1.0 −1.0
BBSW1M_CURNCY CDOR01_CURNCY 1995
0.0 0.5 1.0 −1.0
NFIX1M_CURNCY 1990
0.0 0.5 1.0 −1.0
NIBOR1M_CURNCY 1985
0.0 0.5 1.0 −1.0
STIB1M_CURNCY 1980
1980
−1.0
0.0 0.5 1.0 0.0 0.5 1.0 −1.0 0.0 0.5 1.0 −1.0 0.0 0.5 1.0 −1.0 0.0 0.5 1.0 −1.0
SF0001M_CURNCY BP0001M_CURNCY JY0001M_CURNCY US0001M_CURNCY EUR001M_CURNCY
50 40 30 20 10 0
as.zoo(x)
Portfolio Positions:G10 Carry Ranker
−1.0
60
G10 Yields EUR001M_CURNCY US0001M_CURNCY JY0001M_CURNCY BP0001M_CURNCY SF0001M_CURNCY CDOR01_CURNCY BBSW1M_CURNCY NFIX1M_CURNCY NIBOR1M_CURNCY STIB1M_CURNCY
1980
1985
1990
1995
2000
2005
2010
Returns to the Long-Only G10 Carry Portfolio
G10 Carry Portfolio Performance
G10 Carry Portfolio Components 1.0
Components Positions: G10 Carry Portfolio
Strategy RoI Index
100
−1.0
−0.5
150
0.0
200
0.5
250
RoI Index of: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
Portfolio Components StrategyReturns: G10 Carry Portfolio
as.zoo(x)
−1.0
−0.2
0.0
0.0 −0.5
0.2
0.4
market position Long market position Short
0.5
1.0
TradingStrategy: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
1985
1990
1995
2000
2005
Index 0.5 0.3 0.1 −0.1
0.5
1.0
Performance Attribution: G10 Carry Portfolio @ 2009−05−15
0.0
as.zoo(x)
1.5
StrategyReturns: G10 Carry Portfolio fx yield transactions slippage total
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Asset Allocation Procedure: G10 Momentum Portfolio
USD Cash Returns
USD Momentum
10
0.8
4
3
1.0
6
USD Momentum (left axis) USD Returns (right axis)
1985
1990
1995
2000
2005
2010
2005
2010
2005
2010
0.6
1980
2
0
0.6
2
0.8
as.zoo(x)
USD Total Returns and USD Momentum
8
USDEUR_CURNCY (left axis) US0001M_CURNCY (right axis)
1.2
1.4
Asset: Cash USD 1M
Index
0.2
0
as.zoo(x)
0.0
1985
1990
1995
2000
0.0
1980
−1
−1.0
−0.5
0.4
1
market position Long market position Short
0.5
1.0
TradingStrategy: CASH USD
−2
−0.2
0.5
−3
0.0 −0.5
as.zoo(x)
1.0
StrategyReturns: CASH USD fx yield transactions slippage total
1980
1985
1990
1995
2000
1980
1985
1990
1995
2000
2005
2010
Asset Allocation Procedure: G10 Momentum Portfolio
G10 Momentum
Ranked G10 Momentum G10 Momentum
1985
1990
1995
2000
2005
2010
10 8 6 4
CASH CAD
100 8 6 4
CASH AUD
2 100 8 6 4
CASH NZD
2 100 8 6 4
CASH NOK
2 100 8 6 4
CASH SEK
2 0
1980
1980
2
6 4
CASH EUR
2 100 8 6 4
CASH USD
8 6
CASH JPY
4 8 6 4 8 6 4 0
2
CASH CHF
100
2
CASH GBP
100
2
0 −2 −4
as.zoo(x)
100
2
4 2
8
10
Ranked G10 Momentum
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Asset Allocation Procedure: G10 Momentum Portfolio
G10 Momentum
G10 Momentum Portfolio Positions G10 Momentum
1985
1990
1995
2000
2005
2010
CASH CAD
0.0 0.5 1.0 0.0 0.5 1.0 −1.0
CASH AUD CASH NZD
0.0 0.5 1.0 −1.0 0.0 0.5 1.0 −1.0
CASH NOK 1980
1980
0.0 0.5 1.0 −1.0
CASH SEK
−1.0
−1.0
CASH EUR
0.0 0.5 1.0 0.0 0.5 1.0 −1.0
CASH USD CASH JPY
0.0 0.5 1.0 −1.0 0.0 0.5 1.0 −1.0
CASH GBP CASH CHF
0.0 0.5 1.0 −1.0
4 2 0 −2 −4
as.zoo(x)
Portfolio Positions:G10 Momentum Ranker
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Returns to the Long-Only G10 Momentum Portfolio
G10 Momentum Portfolio Performance
G10 Momentum Portfolio Components Components Positions: G10 Momentum Portfolio 1.0
RoI Index of: G10 Momentum Portfolio
−1.0
100
−0.5
120
0.0
0.5
140
Strategy RoI Index
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
0.2
Portfolio Components StrategyReturns: G10 Momentum Portfolio
market position Long market position Short
−1.0
0.0 −0.2
−0.5
0.0
as.zoo(x)
0.1
0.5
1.0
TradingStrategy: G10 Momentum Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
1985
1990
1995
2000
2005
Index 0.2 0.1 0.0 −0.2 −0.1
0.0
0.2
Performance Attribution: G10 Momentum Portfolio @ 2009−05−15
−0.2
as.zoo(x)
0.4
StrategyReturns: G10 Momentum Portfolio fx yield transactions slippage total
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Carry and Momentum Returns
FX Carry and Momentum Indices
FX Carry and Momentum Correlation Scatterplot: FX Carry Total Returns vs. FX Momentum Total Returns Correlation: 0.03 0.10
FX Carry Index FX Momentum Index
200
250
FX Carry Index Perfromance vs. FX Momentum Index Perfromance
●
100
150
●
●
1985
1990
1995
2000
2005
●
0.05
1980
2010
●
●
0.00
Carry Returns
●
●
●
1985
1990
1995
2000
2005
●
● ●● ●● ● ● ● ● ●● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ●● ● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ●●●● ● ●● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● ● ●● ●● ●● ● ●● ●● ● ●● ● ●● ● ● ● ●● ● ● ● ● ●●●●●● ● ●● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ●● ●● ●● ● ●● ● ● ● ●● ●●● ●● ● ●●● ● ● ●● ● ● ●● ●● ●● ●●● ● ●● ● ● ● ● ●● ● ● ● ● ●●● ●● ● ● ● ● ● ● ●●● ● ● ● ● ● ●● ● ● ●● ●● ● ● ● ● ● ● ● ●● ● ●●●● ● ● ● ● ● ● ● ●● ●●●● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ●● ●●● ● ● ● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●● ● ● ● ●● ●●●● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ●● ● ●● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●●●●● ● ● ● ●● ● ●●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ●● ● ● ● ●● ● ● ● ● ● ● ● ●●● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●● ● ● ● ●● ●● ● ● ● ●●●●●● ●● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●●●●● ● ●● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ●●●●● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ●● ● ● ● ●●● ●● ● ● ● ●● ● ● ● ● ●● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ●● ● ●● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ●●● ● ●● ● ● ●● ●● ●● ● ● ●● ●●● ● ● ● ● ●● ● ● ● ● ●●● ● ●●● ●● ● ●●● ● ● ● ●● ●●● ●●● ● ●●● ●● ●●● ● ● ●● ● ● ●●● ●● ●● ●● ●●● ● ● ● ● ●● ● ● ●●● ● ●● ●●●●● ● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ●● ● ● ● ● ● ●● ● ●●●●●● ●●●● ●● ● ● ●●● ● ●● ● ● ● ● ●●● ● ● ● ●●● ●●● ●● ● ●● ● ●● ● ●● ● ●● ● ● ● ●● ●● ●●● ● ●● ●● ● ●● ● ● ● ●● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ●
●
−0.10
−0.05
0.00
0.05
Carry Returns
1980
●
●
FX Carry Total Returns
●
2010
●
−0.05
●
Momentum Returns
●
●
● ●
0.00
0.05
0.10
FX Momentum Total Returns
−0.05
●
−0.10 1980
1985
1990
1995
2000
2005
2010
−0.05
0.00
Momentum Returns
0.05
Risk Indicator: Equity Volatility Component
Equity Risk Timeseries
Normalized Equity Volatility Timeseries
2 2 −2
0
z−score: VDAX_INDEX
4
−2
0
z−score: VIX_INDEX
50
VIX_INDEX
30 10 60 50 40 30 20 10
VDAX_INDEX
4
Normalized Risk Factors: Equity Volatility
70
Risk Factors: Equity Volatility
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Equity Volatility Component
Equity Volatility Timeseries
Equity Volatility Risk Indicator Component Normalized Risk Factors: Equity Volatility
Risk Factors: Equity Volatility
4
50
2
as.zoo(x)
30 50
0
40 30 20
−2
10
VDAX_INDEX
60
10
VIX_INDEX
70
z−score: VIX_INDEX z−score: VDAX_INDEX Risk Indicator: Equity Vola Component
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Equity Positioning Component
Equity Positioning Timeseries
Normalized Equity Positioning Timeseries
1985
1990
1995
2000
2005
2010
4 3 2 1 0 −1 −3 4 2 0 −2
−0.2
MSCI Growth/Value Index
−0.4 1.5−0.6 1.0 0.5
MSCI Defensives/Cyclicals Index
0.0 1980
z−score: MSCI Defensives/Cyclicalsz−score: Index MSCI Growth/Value Index
Normalized Risk Factors: Equity Market Positioning
0.0
Risk Factors: Equity Market Positioning
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Equity Positioning Component
Equity Positioning Timeseries
Equity Positioning Risk Indicator Component Normalized Risk Factors: Equity Market Positioning
0 −2
0.5
1.0
1.5−0.6
as.zoo(x)
−0.4
2
−0.2
4
z−score: MSCI Growth/Value Index z−score: MSCI Defensives/Cyclicals Index Risk Indicator: Equity Posi Component
0.0
MSCI Defensives/Cyclicals Index
MSCI Growth/Value Index
0.0
Risk Factors: Equity Market Positioning
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: FX Volatility Component
FX Volatility Timeseries
Normalized FX Volatility Timeseries
1985
1990
1995
2000
2005
2010
4 2 0 −2 6 4 2 0
25 20 15
JPMVXYEM_INDEX
10 1980
−2
z−score: JPMVXYEM_INDEX
10
15
20
z−score: JPMVXYG7_INDEX
Normalized Risk Factors: FX Volatility
30
JPMVXYG7_INDEX
Risk Factors: FX Volatility
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: FX Volatility Component
FX Volatility Timeseries
FX Volatility Risk Indicator Component Normalized Risk Factors: FX Volatility
Risk Factors: FX Volatility
20
4
15
2
as.zoo(x)
10
0
25 20
−2
15 10
JPMVXYEM_INDEX
30
JPMVXYG7_INDEX
6
z−score: JPMVXYG7_INDEX z−score: JPMVXYEM_INDEX Risk Indicator: FX Vola Component
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Yield and Credit Component
Yield and Credit Timeseries
Normalized Yield and Credit Timeseries
1985
1990
1995
2000
2005
2010
4 2 0 −2 4 2 0 −2 −4 4 2 0 −2 4 2 0
3 2
.TEDSP_INDEX
1 60 5 4 3
usa credit spread
2 1 1980
−2
20
60
100
20
60
100
140
z−score: usa credit spread z−score: .TEDSP_INDEX z−score: USSP10_CMPL_CURNCY z−score: USSP2_CMPL_CURNCY
Normalized Risk Factors: Yield and Credit Conditions
4
USSP10_CMPL_CURNCY USSP2_CMPL_CURNCY
Risk Factors: Yield and Credit Conditions
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Yield and Credit Component
Yield and Credit Timeseries
Yield and Credit Risk Indicator Component Normalized Risk Factors: Yield and Credit Conditions
140 20
as.zoo(x)
60
2
100
20
4
60
100
z−score: USSP2_CMPL_CURNCY z−score: USSP10_CMPL_CURNCY z−score: .TEDSP_INDEX z−score: usa credit spread Risk Indicator: Yield and Credit Component
0
3 2 1
−2
5 4 3 2 1980
1985
1990
1995
2000
2005
2010
−4
1
usa credit spread
60
.TEDSP_INDEX
4
USSP10_CMPL_CURNCY USSP2_CMPL_CURNCY
Risk Factors: Yield and Credit Conditions
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Safe Haven Component
Safe Haven Timeseries
Normalized Safe Haven Timeseries
Normalized Risk Factors: Safe Haven Assets
1995
2000
2005
2010
2
3
−2
0
2
4 1990
1
z−score: GOLDS_INDEX 1985
0
z−score: CHFUSD_CURNCY 1980
−3 −2 −1
800 600 400 0.8 0.6 0.4
CHFUSD_CURNCY
1.0
GOLDS_INDEX
1000
Risk Factors: Safe Haven Assets
1980
1985
1990
1995
2000
2005
2010
Risk Indicator: Safe Haven Component
Safe Haven Timeseries
Safe Haven Risk Indicator Component Normalized Risk Factors: Safe Haven Assets
as.zoo(x)
−2
0.6
0.8
0
400
2
600
800
4
z−score: GOLDS_INDEX z−score: CHFUSD_CURNCY Risk Indicator: Safe Haven Component
0.4
CHFUSD_CURNCY
1.0
GOLDS_INDEX
1000
Risk Factors: Safe Haven Assets
1980
1985
1990
1995
2000
2005
2010
1980
1985
1990
1995
2000
2005
2010
Aggregated Risk Indicator
Risk Indicator Timeseries
We calculate the aggregated Risk Indicator by equally weighting the 5 sub-components:
6
Risk Indicator & Subcomponents
4
Risk Indicator: Equity Vola Component Risk Indicator: Equity Vola Component Risk Indicator: Equity Posi Component Risk Indicator: FX Vola Component Risk Indicator: Yield and Credit Component Risk Indicator: Safe Haven Component risk indicator value
as.zoo(x)
2
Equity Volatility Equity Positioning 0
FX Volatility
−2
Yield and Credit Safe Haven 1980
1985
1990
1995
2000
2005
2010
Aggregated Risk Indicator
The Aggregated Risk Indicator Aggregated Risk Indicator 3
risk indicator value
−3
−2
−1
0
1
2
We will use the aggregated Risk Indicator as a measure for risk-appetite (low indicator values) and risk-aversion (high indicator values) in the markets.
1980
1985
1990
1995
2000
2005
2010
Outline
1
Introduction
2
Methodology
3
Data
4
Benchmark Market Timing Rules Moving-Average Crossover Rule Risk-Indicator Filter Rule Moving Average Crossover/Risk-Indicator Combination
5
Conclusion
6
References
Timing the Carry Trade with a Moving Average Crossover Rule
Moving Average Crossover Signal
We create a simple Carry timing indicator, following standard moving average crossover trading rules:
200 150 100
as.zoo(x)
250
TradRule1: Moving Average Crossover (1,52) FX Carry Index tsRollMean(FX Carry Index,1) tsRollMean(FX Carry Index,52)
1980
1985
1990
1995
2000
2005
2010
Entry Long when the FX Carry Index crosses over the 52-period moving average.
Index
−1.0
−0.5
0.0
0.5
1.0
Trading Signal SignalPositions_EntriesExits Long SignalPositions_EntriesExits Short
1980
1985
1990
1995
2000
2005
2010
2000
2005
2010
0.6 0.2
0.4
entry long exit long entry short exit short
0.0
as.zoo(x)
0.8
1.0
Market Entry/Exit Signals
1980
1985
1990
1995
Entry Short when the FX Carry Index crosses under the 52-period moving average.
Timing the FX Carry Trade with a Moving Average Crossover Rule
Timed FX Carry Portfolio Components
Timed FX Carry Portfolio
Components Positions: G10 Carry Portfolio 1.0
Strategy RoI Index
100
−1.0
−0.5
150
0.0
200
0.5
250
RoI Index of: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Carry Portfolio 0.4 0.2 0.0
−1.0
−0.2
−0.5
0.0
as.zoo(x)
0.5
1.0
TradingStrategy: G10 Carry Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Carry Portfolio @ 2009−05−15
0.0
0.1
0.4
0.2
0.3
fx yield transactions slippage total
0.0
as.zoo(x)
0.8
StrategyReturns: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Timing the FX Momentum Trade with a Moving Average Crossover Rule We create a simple Momentum timing indicator, following standard moving average crossover trading rules:
Moving Average Crossover Signal
120 100
as.zoo(x)
140
TradRule1: Moving Average Crossover (1,52) FX Momentum Index tsRollMean(FX Momentum Index,1) tsRollMean(FX Momentum Index,52)
1980
1985
1990
1995
2000
2005
2010
2000
2005
2010
Index
−1.0
−0.5
0.0
0.5
1.0
Trading Signal SignalPositions_EntriesExits Long SignalPositions_EntriesExits Short
1980
1985
1990
1995
0.6 0.2
0.4
entry long exit long entry short exit short
0.0
as.zoo(x)
0.8
1.0
Market Entry/Exit Signals
1980
1985
1990
1995
2000
2005
2010
Entry Long when the FX Momentum Index crosses over the 52-period moving average. Entry Short when the FX Momentum Index crosses under the 52-period moving average.
Timing the FX Momentum Trade with a Moving Average Crossover Rule
Timed FX Momentum Portfolio Components
Timed FX Momentum Portfolio
Components Positions: G10 Momentum Portfolio 1.0
RoI Index of: G10 Momentum Portfolio
−1.0
100
−0.5
120
0.0
0.5
140
Strategy RoI Index
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Momentum Portfolio 0.2 −0.2
−1.0
−0.4
−0.5
0.0
as.zoo(x)
0.0
0.5
1.0
TradingStrategy: G10 Momentum Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Momentum Portfolio @ 2009−05−15 0.1 −0.1 −0.3 −0.5
−0.4
−0.2
fx yield transactions slippage total
−0.6
as.zoo(x)
0.0
StrategyReturns: G10 Momentum Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Timing the FX Carry Trade with a Risk Indicator Filter Rule
Risk Indicator Signal
We create a Risk-Indicator based Carry timing indicator, following the following trading rules:
0 −1 −3
−2
as.zoo(x)
1
2
3
TradRule1: Risk Indicator Filter Risk−Appetite Indicator threshold line: 0
1980
1985
1990
1995
2000
2005
2010
Index
Entry Long when the Risk-Appetite Indicator crosses over the zero-line.
−1.0
−0.5
0.0
0.5
1.0
Trading Signal SignalPositions_EntriesExits Long SignalPositions_EntriesExits Short
1980
1985
1990
1995
2000
2005
2010
Entry Short when the Risk-Appetite Indicator crosses under the zero-line.
0.6 0.2
0.4
entry long exit long entry short exit short
0.0
as.zoo(x)
0.8
1.0
Market Entry/Exit Signals
1980
1985
1990
1995
2000
2005
2010
Timing the FX Carry Trade with a Risk Indicator Filter Rule
Timed FX Carry Portfolio Components
Timed FX Carry Portfolio
Components Positions: G10 Carry Portfolio 1.0
Strategy RoI Index
100
−1.0
−0.5
150
0.0
200
0.5
250
RoI Index of: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Carry Portfolio 0.2 0.0 −0.2
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
−0.4
−1.0
−0.5
0.0
as.zoo(x)
0.5
1.0
TradingStrategy: G10 Carry Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Carry Portfolio @ 2009−05−15 0.2 0.1 0.0 −0.1
0.0
0.2
fx yield transactions slippage total
−0.2
−0.4 −0.2
as.zoo(x)
0.4
StrategyReturns: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Timing the FX Momentum Trade with a Risk Indicator Filter Rule
Risk Indicator Signal
0 −1 −3
−2
as.zoo(x)
1
2
3
TradRule1: Risk Indicator Filter Risk−Appetite Indicator threshold line: 0
1980
1985
1990
1995
2000
2005
2010
We create a Risk-Indicator based Momentum timing indicator, following the following trading rules:
Index
−1.0
−0.5
0.0
0.5
1.0
Trading Signal SignalPositions_EntriesExits Long SignalPositions_EntriesExits Short
1980
1985
1990
1995
2000
2005
2010
0.2
0.4
0.6
Entry Short when the Risk-Appetite Indicator crosses under the zero-line.
entry long exit long entry short exit short
0.0
as.zoo(x)
0.8
1.0
Market Entry/Exit Signals
1980
1985
1990
1995
Entry Long when the Risk-Appetite Indicator crosses over the zero-line.
2000
2005
2010
Timing the FX Momentum Trade with a Risk Indicator Filter Rule
Timed FX Momentum Portfolio Components
Timed FX Momentum Portfolio
Components Positions: G10 Momentum Portfolio 1.0
RoI Index of: G10 Momentum Portfolio
−1.0
100
−0.5
120
0.0
0.5
140
Strategy RoI Index
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Momentum Portfolio 0.1 0.2 as.zoo(x)
0.0 −1.0
−0.3
−0.5
−0.1
0.5
1.0
TradingStrategy: G10 Momentum Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Momentum Portfolio @ 2009−05−15 0.2 0.1 0.0 −0.2
0.0 0.2 0.4 0.6
fx yield transactions slippage total
−0.4
as.zoo(x)
StrategyReturns: G10 Momentum Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Timing the FX Carry Trade with a combined Moving Average/Risk Appetite Signal
Combined Moving Average/Risk Appetite Signal
0.6
1.0
1.4
Position Signal: Aggregated Strategy Signal position
1980
1985
1990
1995
2000
2005
2010
2005
2010
2000
2005
2010
2000
2005
2010
2000
2005
2010
Trading Rules:
position
−1.0 0.0
1.0
Position Signal: Moving Average Crossover (1,52)
1980
1985
1990
1995
2000
−1.0 0.0
1.0
Filter Signal: Risk Indicator Filter filter
1980
1985
1990
1995
market position
−1.0 0.0
1.0
Aggregated Strategy Signal
1980
1985
1990
1995
buy sell
−2
0
2
Strategy Trades
1980
1985
1990
1995
Long When the Moving Average Rule AND the Risk-Indicator rule are long. Short When the Moving Average Rule AND the Risk-Indicator rule are short.
Timing the FX Carry Trade with a combined Moving Average/Risk Appetite Signal
Timed FX Carry Portfolio Components
Timed FX Carry Portfolio
Components Positions: G10 Carry Portfolio 1.0
Strategy RoI Index
100
−1.0
−0.5
150
0.0
200
0.5
250
RoI Index of: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Carry Portfolio 0.2 0.1 as.zoo(x)
0.0 −0.5
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
−0.3
−1.0
−0.1 0.0
0.5
1.0
TradingStrategy: G10 Carry Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Carry Portfolio @ 2009−05−15 0.15 0.05
0.2
0.4
fx yield transactions slippage total
−0.05
0.0
as.zoo(x)
0.6
StrategyReturns: G10 Carry Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Timing the FX Momentum Trade with a combined Moving Average/Risk Appetite Signal
Combined Moving Average/Risk Appetite Signal
0.6
1.0
1.4
Position Signal: Aggregated Strategy Signal position
1980
1985
1990
1995
2000
2005
2010
2005
2010
2000
2005
2010
2000
2005
2010
2000
2005
2010
Trading Rules:
position
−1.0 0.0
1.0
Position Signal: Moving Average Crossover (1,52)
1980
1985
1990
1995
2000
−1.0 0.0
1.0
Filter Signal: Risk Indicator Filter filter
1980
1985
1990
1995
market position
−1.0 0.0
1.0
Aggregated Strategy Signal
1980
1985
1990
1995
buy sell
−2
0
2
Strategy Trades
1980
1985
1990
1995
Long When the Moving Average Rule AND the Risk-Indicator rule are long. Short When the Moving Average Rule AND the Risk-Indicator rule are short.
Timing the FX Momentum Trade with a combined Moving Average/Risk Appetite Signal
Timed FX Momentum Portfolio Components
Timed FX Momentum Portfolio
Components Positions: G10 Momentum Portfolio 1.0
RoI Index of: G10 Momentum Portfolio
−1.0
100
−0.5
120
0.0
0.5
140
Strategy RoI Index
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980−01−04 1983−09−09 1987−05−15 1991−01−18 1994−09−23 1998−05−29 2002−02−01 2005−10−07
2010
Portfolio Components StrategyReturns: G10 Momentum Portfolio 0.1
−1.0
−0.1 −0.3
−0.5
0.0
as.zoo(x)
0.5
1.0
TradingStrategy: G10 Momentum Portfolio market position Long market position Short
1980
1985
1990
1995
2000
2005
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
1980
2010
1985
1990
1995
2000
2005
Index
Performance Attribution: G10 Momentum Portfolio @ 2009−05−15 0.1 0.0 −0.2
−0.1
0.1
fx yield transactions slippage total
−0.4
−0.3
as.zoo(x)
0.3
StrategyReturns: G10 Momentum Portfolio
1980
1985
1990
1995
2000
2005
2010
CASH EUR CASH USD CASH JPY CASH GBP CASH CHF CASH CAD CASH AUD CASH NZD CASH NOK CASH SEK
2010
Outline
1
Introduction
2
Methodology
3
Data
4
Benchmark Market Timing Rules
5
Conclusion
6
References
Dynamic FX Portfolio Trading: Status-Quo
We built a software for backtesting portfolios of trading systems. We tested benchmark FX Carry and Momentum portfolio timing strategies with mixed results. The approach of combining different types of market timing rules looks promising. Next steps: Calculation of the statistical market timing indicators based on risk-factors.
Outline
1
Introduction
2
Methodology
3
Data
4
Benchmark Market Timing Rules
5
Conclusion
6
References
Craig Burnside, Martin Eichenbaum, Isaac Kleshchelski, and Sergio Tavares Rebelo. The returns to currency speculation. SSRN eLibrary, 2006. Peter F. Christoffersen and Francis X. Diebold. Financial asset returns, direction-of-change forecasting, and volatility dynamics. Technical Report 10009, October 2003. Virginie Coudert and Mathieu Gex. Can risk aversion indicators anticipate financial crises? Technical Report 9, Banque de France, December 2006. Christian L. Dunis and Jia Miao. Trading foreign exchange portfolios with volatility filters: the carry model revisited. Applied Financial Economics, 17(3):249–255, 2007. Alex Heath, Christian Upper, Paola Gallardo, Philippe Mesny, and Carlos Mallo.
Triennial Central Bank Survey. Bank for International Settlements, 2007. Markus Hochradl and Christian Wagner. Trading the forward bias: Are there limits to speculation? SSRN eLibrary, 2007. P. Lequeux and E. Acar. A dynamic index for managed currencies funds using cme currency contracts. European Journal of Finance, 4(4):311–330, 1998. Jia Miao and Christian L. Dunis. Volatility filters for fx portfolios trading: the impact of alternative volatility models. Applied Financial Economics Letters, 2(6):389–394, 2006. Darren Read, William Darwin, and Pauline O’Neill. Measuring equity market risk. Technical report, UBS Investment Research, Global Equity Strategy, June 2006.
Andres Vesilind. Profitability of simple trading strategies exploiting the forward premium bias in foreign exchange markets and the time premium in yield curves. Technical Report 2006-04, Oct 2006.
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