A Decomposition Of Portfolio Mom Returns

ISSN 1744-6783

A DECOMPOSITION OF PORTFOLIO MOMENTUM RETURNS

J. SEFTON, A. SCOWCROFT

Tanaka Business School Discussion Papers: TBS/DP04/9 London: Tanaka Business School, 2004

A Decomposition of Portfolio Momentum Returns James Sefton1 and Alan Scowcroft 30 September 2004

Abstract The extensive literature on price momentum effects is a potential source of confusion for portfolio managers as conflicting explanations give rise to different implications for portfolio strategy. Is momentum a stock level phenomenon or is it subsumed by industry or style effects? What are the performance implications of imposing sector or style neutrality? How does price momentum impact estimates of tracking errors or Sharpe ratios? In a value weighted large cap universe, such as the Global MSCI, we found that price return momentum is driven largely by industry momentum; it does not appear to be explained by individual stock momentum. Further, this return continuation is not a result of either cross-sectional dispersion in industry mean returns, or by varying industry exposure to systematic risk. In small cap universes stock specific effects assume greater importance. Over both our sample periods, 1992-01 to 2003-03 and 1980-01 to 2003-03, value investors would have reduced risk by imposing sector neutrality whilst growth managers could have profited from both a growth strategy and a momentum strategy by relaxing sector constraints; though the effects are stronger over the more recent past. In practice, any group of companies sharing a common characteristic has the potential to exhibit price momentum effects. Such a characteristic could be as simple as industry or country or more generally any characteristic that investors expect to impact performance. Controlling the risk in any portfolio therefore requires monitoring style exposure.

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Corresponding Author: Tanaka Business School, Imperial College, South Kensington Campus, London SW7 2AZ, UK.

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Understanding Momentum The literature on price momentum is currently one of the most extensive and potentially most confusing in finance. Though there is a very broad consensus over the size and duration of any pricing momentum effects, there is no consensus over what is driving them. Whether these violations of market efficiency can be given a behavioral explanation or whether they are due to the rational response of investors to real market constraints is far from clear. There is also no consensus on whether these momentum effects can be found only at the stock level or whether they are pervasive at the industry, country or style levels. For practitioners, the academic debate over the causes of momentum effects appears somewhat arcane. The key issues for portfolio strategy are the implications for both alpha generation and risk control. Risk The implications for risk control are potentially far reaching. The presence of short-term price momentum violates the assumption that each period is independent. As a consequence, the true annual variance and tracking variance of returns would be potentially far greater than twelve times the monthly variance. Scowcroft and Sefton (1999), showed that the presence of short term price momentum could lead to annual tracking error forecasts being understated by as much as 50%; Gardner, Bowie, Brooks and Cumberworth (2000) make a similar point. If, as appears to be the case in our study, momentum is largely an industry phenomenon then exposure to additional momentum risk can be limited by running an industry neutral fund. If this is not desirable for investment reasons, at least exposure can be monitored easily from the size of any industry tilts. More generally, any style could exhibit strong momentum if the desired characteristic is currently being "priced" in the market. Such a characteristic could be due to industry momentum but it could be due to any characteristic that investors expect to impact performance. Controlling the risk in any portfolio therefore requires monitoring style exposure too. Return Momentum has obvious implications for alpha generation. If momentum is largely an industry phenomenon then sector rotation strategies could potentially be designed to capture this alpha at the industry level, see for example O'Neal (2000). However, risk models will underestimate the true risk of these types of strategies and so care must be taken in assessing their performance with risk based measures such as Sharpe ratios. Further, if momentum is generally an industry phenomenon and inversely correlated to value, value strategies can reduce their risk by constraining the weights to be industry neutral, Asness (1997). More generally, value managers could improve their risk-adjusted performance by constraining their portfolios to be neutral to non-value factors. Similarly, growth is likely to be positively correlated with momentum, and so the imposition of industry neutrality would have a detrimental impact on the performance of growth managers. 2

A Short History of Momentum in Stock Returns Researchers have identified many pricing anomalies in stock returns. Of these, the one that has received the most attention, after perhaps the value premium, is the finding of a pervasive momentum in stock returns. De Bondt and Thaler (1985, 1987) were the first to document the long-term over-reaction in stock returns. They found stocks that had performed poorly over the previous 3 to 5 years, were more likely to be one of the better performers over the next 3 to 5 years. On stock return data from different years and markets, studies such as Lakonishok, Shleifer, Vishny (1995, 1997) and Schiereck, De Bondt, and Weber (1999) found consistently that the contrarian strategy of buying the long term poor performers and holding for 3 to 5 years earned excess returns of 8% annually. However, Fama and French (1996) have since argued that this pricing anomaly is just a disguised version of their value premium; previous poor performers are more likely to do well over the next 3 to 5 years because they are more likely to have become value stocks and hence earn higher returns due to the value premium. Jegadeesh (1990) and Lehmann (1990) also found reversals in stock returns, but this time over the very short term. The best performing stocks over the previous week, or month, were more likely to be one of the poor performers over the following week, or month. Though this finding has been found to be relatively robust, Lo and MacKinlay (1990) have argued that this anomaly is just an artifact of how the prices are recorded. If a stock is traded fairly infrequently, there is likely to be a ‘bid-ask’ bounce. In one week the ‘ask’ price will be recorded, whereas in the next the ‘bid’ price is recorded, or visa versa. If the spread is sufficiently large, this could induce short-term return reversals. Jegadeesh and Titman (1993, 2001), Chan, Jegadeesh and Lakonishok (1996) discovered return continuation over the medium term (3-12 months). Here the better performing stocks from the previous 6 months are more likely to be one of the better performing stocks of the next 6 months. It is this medium term pricing anomaly that is the most intriguing of the momentum anomalies. It is at the center of a great deal of current academic debate on market efficiency as well as being the main focus of this article. What is the reason for this level of interest? Of all the momentum pricing anomalies, it is this medium term return momentum that is the hardest to explain away using rational pricing models; in the words of the ‘gurus’ of modern finance theory, the ‘main embarrassment’ of their three-factor risk model is its ‘failure to capture the continuation of short-term returns’ (Fama and French (1996), p. 81). Table 1 records the evidence for these different price momentum anomalies from our principal data set, all stocks in the MSCI developed global index over the period January 1992 to March 2003. Later we shall present similar results for the longer period of January 1980 to March 2003. The methodology is described in detail in Appendix A: Building Momentum Portfolios. However, in short, we build market cap weighted portfolios every period of the best and worst performing 20% of stocks by market cap in the previous J months. We then hold the self-financing portfolio, that is long the best and short the worst performers, for the following K months. The table then records the average percentage monthly return to these self-financing portfolios over our sample period. 3

Table 1. Monthly Percentage Returns to Long - Short Momentum Strategies for varying Portfolio Formation and Holding Periods, 199201-200303 (all returns shown in $US, standard errors in parenthesis, no gap between formation and holding period) Holding Period in Months, K 1 3 6 Formation Period in Months, J 12 24 36

1

3

6

12

24

36

-0.78

0.11

0.31

0.38

0.18

0.04

(0.48)

(0.34)

(0.27)

(0.20)

(0.16)

(0.12)

0.04

0.42

0.71

0.65

0.32

0.10

(0.57)

(0.50)

(0.43)

(0.33)

(0.27)

(0.21)

0.59

0.87

1.00

0.86

0.38

0.14

(0.63)

(0.59)

(0.51)

(0.42)

(0.36)

(0.28)

0.92

1.05

0.93

0.79

0.25

-0.02

(0.64)

(0.60)

(0.56)

(0.53)

(0.46)

(0.36)

0.67

0.75

0.66

0.36

-0.34

-0.53

(0.67)

(0.65)

(0.63)

(0.61)

(0.50)

(0.43)

0.35

0.48

0.37

-0.23

-0.75

-1.02

(0.67)

(0.66)

(0.64)

(0.59)

(0.53)

(0.49)

Table 1 provides evidence for all three momentum phenomena. In the top left hand corner, for formation and holding periods of 1 month, there is a short term average return reversal to the self-financing portfolios of –0.78% per month (nearly -10% annually). Over the medium term, return continuation is most significant for formation periods of 6 to 12 months and holding periods of a similar length; the average return is about 1% per month or 12% annually. Over the longer term, for formation and holding periods of 36 months, there is a return reversal of -1.02% per month, or -12% annually.

Do Industries drive momentum? Whilst there is a very broad consensus over the size and duration of these momentum pricing anomalies, there is no such consensus over what is driving these excess returns. In particular, whether these momentum effects can only be found at the stock level or whether they can be found at the industry or country level too; are the causes specific to the firm or are they common across the industry or country? The answer is not just of esoteric interest, but has a profound importance for portfolio construction. If momentum is an industry phenomenon, then fund managers trying to play momentum will need only to take small industry tilts in their portfolios. It does not make sense to run a sector neutral momentum strategy. Further, they will probably give more weight to strategist views on the likely future industry prospects. For value fund managers it means that by running sector neutral portfolios they can reduce their exposure to risk from being inevitably underweight momentum.

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Alternatively, if price momentum can only be found at the stock level, these recommendations are almost reversed. Momentum managers must pay more attention to news from the analysts on future individual stock prospects and will be able to run lower risk sector neutral portfolios. Value managers will need to pay more attention to exposure to momentum, so as not to be caught by these medium term market movements. There is no overall consensus in the literature on whether momentum is an industry or stock story. However, careful reading of the literature, allowed us to split the research into two distinct groups; those that did their research using equally weighted portfolios in broad universes and those that did their research using market cap portfolios in larger cap universes. The former group found momentum only at the stock level, whereas the latter found, without exception, momentum to be pervasive at the industry level. Table 2. A summary of the findings of the recent literature on returns to momentum strategies Year

Data

Portfolio Weighting

Summary of Principle Findings

Jegadeesh and Titman

1993

US CRSP Data

Equally

A ‘delayed price reaction to firm specific information’.

Jegadeesh and Titman

2001

US CRSP Data

Equally

Found evidence consistent with their earlier study.

Grundy and Martin

2001

US CRSP Data

Equally

Industry effects are not the primary cause of momentum profits.

Moskowitz and Grinblatt

1999

US CRSP Data

Market Cap

Industry momentum strategies are significantly more profitable than industry neutral momentum strategies.

O’Neal

2000

31 US Sector Fidelity Funds

Market Cap

Found significant profits to industry momentum strategies

Swinkels

2002

Datastream Global Industry Indices

Market Cap

Found significant profits to global industry momentum strategies.

Rouwenhorst

1999

2190 European Firms

Equally

Finds momentum profits in all 12 European markets. Little evidence for a country momentum factor but suggests momentum profits are driven by common component across markets.

Richards

1997

16 MSCI Market Indices

Market Cap

Found evidence of some profitability to country momentum Strategies

Chan, Hameed and Tong

2001

23 Market Datastream Indices

Market Cap

Find evidence of profit to country momentum trading strategies over the short term

Authors

Table 2 gives a summary of the findings of these two groups of studies. It also includes a third group, which investigated whether there were excess profits to country momentum strategies. The first group of studies, all use the US CRSP (Center for Research in Security Prices, University of Chicago) database, which currently includes almost 7000 stocks listed on the AMEX, NYSE and NASDAQ exchanges and construct their momentum portfolios using equal weights. The findings of these studies are all consistent with price momentum being driven by a ‘delayed price reaction to firm specific information’. In contrast, the second group all use value weighted portfolios on larger cap universes and find significant profits to industry momentum strategies. The final group find some evidence of a small profit to country momentum strategies. Recent theoretical papers, that have tried to model the medium term return continuation, have all focused on the mechanism by which ‘news’ on stock performance is slowly 5

incorporated into prices. We will discuss these papers in more detail later. However, it is likely that this process is subtly different for small and large cap stocks. If a large company such as Shell announce better than expected earnings, then it is more than likely that this could be interpreted as ‘news’ that the industry’s prospects are improving and not just Shell’s. Thus the price of BP shares could rise along with those of Shell. Should BP also announce increased earnings later in the year, this could lead to further price rises across the industry, as it becomes more likely that these improvements are industry wide. Thus we observe some momentum in the price of BP shares. It is the difficulty investors have in interpreting how much of a change in a company’s performance is due to industry wide improvements and how much is due to company specific improvements that induces the price momentum. Therefore a possible testable implication of this story is that there are positive cross-correlations between earnings news in one stock and future returns in another stock. However, if we take a smaller producer, then positive news about a change in its earnings are much less likely to be interpreted as a change in the industry’s fortunes. The momentum in its price is far more likely to be induced by the slow diffusion across the investment community of the change in this firm’s prospects. Thus the induced correlation between earnings news and future expected returns is not now across stocks, but within a stock. Thus it is very possible that we could observe very different momentum phenomena in large and small cap universes. Support for this view that large and small companies incorporate ‘news’ differently into prices is supported by recent research on the decomposition of individual stock returns into changes in cash-flow news and changes in discount rate expectations. Vuolteenaho (2002, Table IV) finds that for small companies cash-flow news is positively correlated with changes in discount rate expectations. This evidence supports the notion that small companies’ prices under-react to cash flow news, which results in medium term return momentum at the stock level. However, Vuolteenaho finds very little evidence for this positive correlation in the data for large companies. This suggests that return momentum at the large cap level is not induced by the slow diffusion of cash flow news into prices. A different process, therefore, must induce it. We suggest that an interesting area is to investigate is cross-correlation between cash flow news in one stock and return expectations in another stock. Unfortunately Vuolteenaho did not look for these effects. Yet in a different framework, Lo and MacKinlay (1999) did find that these ‘cross correlations’ could account for the majority of the momentum effect. In the empirical work presented in the next section, we use a new approach to decompose momentum profits. We use it to break down profits to market cap weighted momentum portfolios in a large cap MSCI global universe of around 1300 stocks. We do this for the period January 1992 to March 2003 and for a longer period of January 1980 to March 2003. We also perform a similar break down of momentum profits to equally weighted portfolios in the much broader Dow Jones universe of almost 5500 stocks. However the data on this broader universe is only available for the shorter period of January 1992 to March 2003. Our results are consistent with the above interpretation of the literature. Momentum profits at the large cap level are industry driven, particularly over the more recent period,

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whereas at the smaller cap level it appears to be driven more by reactions to firm specific information.

Decomposing Momentum Returns The evidence for industry momentum Moskowitz and Grinblatt (1999) argued that medium term momentum profits are driven mainly by an implicit sector rotation strategy. To demonstrate this, they, O’Neal (2000) and Swinkels (2002) show that a sector rotation or sector momentum strategy generates very similar profits to a momentum strategy at the stock level. In Table 3: we present similar results for the MSCI global universe. For every period, we rank the 10 MSCI sectors on their performance in the previous J months. The winner portfolio is then the market cap weighted portfolio of all stocks in the best 2 performing sectors, and the loser portfolio is a market cap weighted portfolio of all stocks in the worst 2. As earlier, we hold the self-financing portfolio, that is long the winners and short the losers for the following K months. The table then records the average percentage monthly return to these self-financing portfolios over our sample period. Again the precise methodology is described in Appendix A: Building Momentum Portfolios. For formation and holding periods of 6 to 12 months, we are able to generate profits to these sector rotation strategies that, if anything, are slightly larger than those reported in Table 1. Our shorter data sample, 1992 – 2003, includes the period of the ‘Tech Bubble’, its start being approximately in mid 1998 to its crash in mid 2000. An obvious question, is how much of our profits are generated by a momentum play on this ‘Tech Bubble’? In the second panel of Table 3, we repeat the same exercise but this time we omit all stocks from the Information Technology Sector from our sample. This omission does reduce profits by about 25-50%. However, this also implies that more than 50% of the profits, amounting to an excess return of over 6% annually, comes from rotation in and out of other sectors. For comparison, in the bottom panel we record the profits to these sector rotation strategies over the longer period 1980 – 2003. These profits are of very similar magnitude to those in the second panel. Therefore, though present, the profits to these sector rotation strategies were lower over the 1980s than over the 1990s. However, as we shall show later in Table 9, momentum profits were also on average lower over this longer period; in fact, profits to the sector rotation strategy are of the same order as the profits to the portfolio momentum strategies over this period.

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Table 3: Monthly Excess Returns of Long/Short Sector Momentum Strategies for varying Portfolio Formation and Holding Periods – Market Cap Weights Monthly % Average Returns to (J, K, 1) Sector Rotation Strategies in a Market Cap Weighted MSCI Universe, January 1992 – March 2003.

1

Formation Period in Months, J

3 6 12

1 0.69 (0.59) 0.62 (0.55) 1.36 (0.63) 1.37 (0.69)

Holding Period in Months, K 3 6 0.47 0.61 (0.37) (0.31) 0.83 0.73 (0.52) (0.46) 1.18 1.09 (0.61) (0.56) 1.18 1.09 (0.62) (0.62)

12 0.51 (0.23) 0.61 (0.37) 0.80 (0.49) 0.78 (0.62)

24 0.42 (0.19) 0.39 (0.35) 0.36 (0.46) 0.15 (0.57)

Monthly % Average Returns to (J, K, 1) Sector Rotation Strategies in a Market Cap Weighted MSCI Universe ex Information Technology Sector, January 1992 – March 2003.

1

Formation Period in Months, J

3 6 12

1 0.11 (0.42) 0.02 (0.38) 0.54 (0.43) 1.17 (0.45)

Holding Period in Months, K 3 6 0.18 0.33 (0.24) (0.20) 0.24 0.22 (0.33) (0.30) 0.35 0.55 (0.42) (0.37) 0.89 0.75 (0.43) (0.41)

12 0.42 (0.15) 0.39 (0.22) 0.51 (0.30) 0.52 (0.38)

24 0.32 (0.11) 0.23 (0.18) 0.16 (0.27) 0.00 (0.34)

Monthly % Average Returns to (J, K, 1) Sector Rotation Strategies in a Market Cap Weighted MSCI Universe, January 1980 – March 2003. 1 1

Formation Period in Months, J

3 6 12

0.11 (0.25) 0.34 (0.24) 0.39 (0.26) 0.66 (0.28)

Holding Period in Months, K 3 6 0.18 (0.15) 0.44 (0.20) 0.47 (0.24) 0.69 (0.26)

0.22 (0.12) 0.34 (0.18) 0.57 (0.22) 0.54 (0.24)

12

24

0.26 (0.09) 0.40 (0.14) 0.39 (0.18) 0.30 (0.22)

0.13 (0.07) 0.16 (0.12) 0.16 (0.16) 0.07 (0.19)

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Figure 1 to Figure 4 visually compare the sector makeup of the momentum portfolios constructed for a (6,6,1) stock level momentum strategy with the comparable sector rotation portfolios constructed for Table 3. Figure 1 and Figure 2 focus on the loser or short portfolios Figure 3 and Figure 4 on the winner or long portfolios. Figure 1 gives the percentage of stocks in each MSCI sector for the loser momentum portfolio over time. Figure 2 shows which sectors are held in the loser portfolio in the sector rotation strategy. Similarly, Figure 3 presents the same decomposition as Figure 1 for the winner momentum portfolio, and Figure 4 shows the sectors held in the winner portfolio in the sector rotation strategy. There are several observations worth highlighting from these charts. 1. When there is an above average number of stocks held in a given sector in the loser or winner portfolios, then, almost without exception, that sector is held in the corresponding sector rotation portfolio. Similarly when there is a below average number of stocks held in a given sector in the loser or winner portfolios, then that sector is not held in the corresponding sector rotation portfolio. Thus, from Figure 1, we can see that around August 1998 and August 2001, there are very few utility stocks in the loser momentum portfolio. These are the very same periods when, from Figure 2, we can see the Utility Sector does not belong to loser portfolio in the sector rotation strategy. 2. We can easily observe the effects of the ‘Tech Bubble’. In the momentum portfolios, more than an average number of Information Technology stocks are held in the winner portfolio during the boom years of 1998 to early 2000, and more than average number are held in the loser portfolio during the crash of 2000 and 2001. We can observe the same sector rotation in the breakdown of sector rotation strategies in Figure 2 and Figure 4. 3. There is strong evidence for rotation in and out of other sectors, other than Information Technology, over this period. It is particularly marked in the Utilities Sector, the Consumer Non-Cyclical Sector after 1999 and Telecommunications, Energy, Basic Materials and Financials between 1995-1998. Figure 1 to Figure 4 and Table 3 provide compelling evidence that the simple sector rotation strategies capture most of the information on medium term momentum in the momentum strategy portfolios. We observe in Figure 1 to Figure 4 that within the momentum portfolios there is the same implicit sector rotation and in Table 3 we observe that the sector rotation strategy can generate the same level of profits.

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Figure 1 - Short portfolio sector weights for (6, 6, 1) stock momentum strategy

Utilities

Telecommunications

Technology

Consumer Non Cyclical

Industrial

Healthcare

Financial

Energy

Consumer Cyclical

Basic Materials

AUG93

AUG94

AUG95

AUG96

AUG97

AUG98

AUG99

AUG00

AUG01

AUG02

Figure 2 Sector composition of (6, 6, 1) sector rotation strategy short portfolio

Utilities

Telecommunications

Technology

Consumer Non Cyclical

Industrial

Healthcare

Financial

Energy

Consumer Cyclical

Basic Materials

AUG93

AUG94

AUG95

AUG96

AUG97

AUG98

AUG99

AUG00

AUG01

AUG02

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Figure 3 - Long portfolio sector weights for (6, 6, 1) stock momentum strategy

Utilities

Telecommunications

Technology

Consumer Non Cyclical

Industrial

Healthcare

Financial

Energy

Consumer Cyclical

Basic Materials

AUG93

AUG94

AUG95

AUG96

AUG97

AUG98

AUG99

AUG00

AUG01

AUG02

Figure 4 - Long portfolio sector composition of (6, 6, 1) sector rotation strategy

Utilities

Telecommunications

Technology

Consumer Non Cyclical

Industrial

Healthcare

Financial

Energy

Consumer Cyclical

Basic Materials

AUG93

AUG94

AUG95

AUG96

AUG97

AUG98

AUG99

AUG00

AUG01

AUG02

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Table 4: Monthly Excess Returns to Long-Short Momentum Strategies for each MSCI Global Sector over the period January 1992 to March 2003.

(% Monthly Average Returns to (6,6,1) Momentum Strategies in different Markets, standard errors in parentheses)

Energy Basic Materials Industrial Consumer Cyclical Cons Non Cyclical Healthcare Financial Technology Telecommunications Utilities

Large Cap Universes Small Cap Universe MSCI Large Cap Dow Jones Dow Jones Equally Market Equally Market Equally Market Weighted Weighted Weighted Weighted Weighted Weighted 0.32 0.30 0.58 0.37 0.57 0.33 (0.49) (0.29) (0.48) (0.31) (0.53) (0.36) -0.11 0.00 -0.10 0.10 0.34 0.02 (0.43) (0.39) (0.40) (0.40) (0.48) (0.37) 0.29 1.00 0.98 0.90 0.87 0.85 (0.55) (0.50) (0.58) (0.41) (0.53) (0.45) 0.60 0.65 0.37 0.60 1.24 0.85 (0.46) (0.44) (0.44) (0.45) (0.45) (0.46) 0.83 -0.11 0.30 -0.09 1.02 0.17 (0.44) (0.37) (0.41) (0.44) (0.44) (0.37) 0.87 0.12 0.43 0.01 0.85 0.43 (0.45) (0.33) (0.45) (0.33) (0.60) (0.37) 0.91 1.00 0.78 0.75 0.97 0.77 (0.59) (0.54) (0.58) (0.52) (0.49) (0.48) 0.47 0.75 0.19 0.65 0.26 0.89 (0.88) (0.63) (0.88) (0.62) (0.71) (0.62) 0.95 -0.40 0.73 -0.16 1.19 -0.10 (0.94) (0.69) (0.75) (0.65) (0.95) (0.64) 0.21 0.81 0.27 0.96 0.50 0.73 (0.47) (0.44) (0.51) (0.48) (0.33) (0.38)

If the majority of profits to medium term momentum are mainly generated by an implicit sector rotation strategy, then if we limit our universe to a particular global sector we should observe much reduced profits to momentum strategies. Table 4 reports the results from just this exercise, where we have limited ourselves to reporting the monthly profits to the 6-month formation and holding strategy. It is clear from the 2nd and 4th columns that when we limit ourselves to a market cap weighted large cap universe, this is largely what we find. The only exceptions are the Industrial and Financial Sectors, which are relatively heterogeneous groups of stocks. It may therefore be necessary to further disaggregate these sectors into a more homogeneous grouping to remove the momentum profits. In the other columns in Table 4, we report the results when we equally weight our portfolios and expand the universe to include many more small-cap stocks. In the 5th

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column, corresponding to equally weighted portfolios constructed using the entire Dow Jones universe of around 5500 stocks (and hence the set of experiments giving the greatest weight to small cap stocks), we find momentum profits return in nearly all the sectors. It therefore appears at this small cap level, that industry momentum is not the whole story and that a firm specific story might be more appropriate. We shall return to this later. The evidence for country momentum Richards (1997) found some evidence that country rotation momentum strategies can deliver a small excess profit over the medium term. In the previous section, we estimated the returns to sector rotation strategies. In this section we repeat the experiment but for countries instead. Thus in every month, we rank the 20 countries in our universe on their performance in the previous J months. The winner portfolio is then the market cap weighted portfolio of all stocks in the best 4 performing countries, and the loser portfolio is a market cap weighted portfolio of all stocks in the worst 4. The construction process then proceeds as before. Table 5 records the results to these experiments. Over the shorter period of 1992-2003 and for formation and holding periods of 6 to 12 months, the excess return to these country rotation strategies are of the order 0.65% per month or about 7.5% annually. In the second panel of Table 5 we investigate the proportion of this profit that can attributed to a play on the three smallest countries in our sample, Singapore, Hong Kong and South Korea, during the Asian Crisis of mid 1997 to early 1999. We rerun the experiment having removed all stocks from these countries from our sample. This reduces profits by around 50%. In the bottom panel, we record the profits to country rotation strategies over the longer period 1980 – 2003. These profits are of very similar magnitude to those in the second panel, suggesting that profits to country rotation strategies were lower over the 1980s than over the 1990s. This is consistent with the results, to be shown later in Table 9, that momentum profits were on average lower over the longer period than over the shorter.

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Table 5: Monthly Excess Returns of Long-Short Regional Momentum Strategies (Monthly % Average Returns to (J, K, 1) Country Rotation Strategies in a Market Cap Weighted MSCI Universe between January 1992 and March 2003)

1

Formation Period in Months, J

3 6 12

1 0.53 (0.46) 0.86 (0.49) 0.60 (0.51) 0.79 (0.47)

Holding Period in Months, K 3 6 12 0.15 0.27 0.04 (0.27) (0.23) (0.16) 0.85 0.68 0.37 (0.41) (0.33) (0.26) 0.71 0.65 0.34 (0.43) (0.37) (0.34) 0.42 0.46 0.37 (0.45) (0.43) (0.43)

24 -0.01 (0.13) 0.11 (0.23) 0.15 (0.28) -0.05 (0.36)

(Monthly % Average Returns to (J, K, 1) Country Rotation Strategies in a Market Cap Weighted MSCI Universe excluding Asia between January 1992 and March 2003)

1

Formation Period in Months, J

3 6 12

1 0.51 (0.35) 0.36 (0.37) 0.67 (0.39) 0.51 (0.38)

Holding Period in Months, K 3 6 12 0.40 0.33 0.11 (0.20) (0.18) (0.13) 0.50 0.46 0.11 (0.29) (0.25) (0.19) 0.37 0.38 0.03 (0.33) (0.31) (0.25) 0.16 0.04 -0.26 (0.37) (0.35) (0.32)

24 0.04 (0.09) -0.08 (0.15) -0.17 (0.19) -0.33 (0.24)

(Monthly % Average Returns to (J, K, 1) Country Rotation Strategies in a Market Cap Weighted MSCI Universe January 1980 and March 2003)

1

Formation Period in Months, J

3 6 12

1 0.03 (0.28) 0.41 (0.34) 0.44 (0.31) 0.40 (0.32)

Holding Period in Months, K 3 6 12 0.38 0.12 0.06 (0.19) (0.14) (0.10) 0.38 0.37 0.25 (0.25) (0.20) (0.16) 0.51 0.37 0.16 (0.27) (0.23) (0.19) 0.34 0.27 0.19 (0.29) (0.27) (0.24)

24 0.02 (0.07) 0.11 (0.11) 0.13 (0.14) 0.10 (0.19)

14

Table 6: Monthly Excess Returns of Long-Short Country or Region Momentum Strategies (% Monthly Average Returns to (6,6,1) Momentum Strategies in different Markets, standard errors in parentheses)

United Kingdom United States Europe EMU France Germany Far East ex Japan Japan

Large Cap Universes MSCI Large Cap Dow Jones Equally Market Equally Market Weighted Weighted Weighted Weighted 0.42 0.55 0.77 0.52 (0.53) (0.47) (0.59) (0.49) 0.47 0.76 0.69 0.67 (0.64) (0.57) (0.68) (0.57) 0.62 0.61 0.48 0.53 (0.48) (0.56) (0.60) (0.58) 0.55 0.43 0.49 0.38 (0.47) (0.52) (0.55) (0.52) 0.25 0.32 0.17 0.23 (0.68) (0.69) (0.74) (0.65) 1.06 0.53 0.40 0.57 (0.70) (0.67) (0.61) (0.64) 0.60 0.44 0.51 0.57 (0.62) (0.63) (0.73) (0.67) 0.09 0.36 0.33 0.43 (0.66) (0.67) (0.60) (0.68)

Small Cap Universe Dow Jones Equally Market Weighted Weighted 0.93 0.62 (0.59) (0.47) 0.89 0.87 (0.67) (0.57) 1.02 0.78 (0.51) (0.52) 0.96 0.58 (0.51) (0.49) 0.70 0.51 (0.64) (0.60) 1.48 0.76 (0.68) (0.61) 1.76 0.92 (0.60) (0.64) 0.08 0.45 (0.55) (0.67)

If some of the profits to momentum strategies are generated by an implicit country rotation strategy, then if we limit our universe to a particular country or region we should observe reduced profits. In Table 6 we report the profits to a 6-month formation and holding momentum strategy limited to the main economic regions or countries in our sample. Focusing first on the 2nd and 4th columns as before, and so limiting ourselves to a market cap weighted large cap universe within these regions, we find in all cases, except Japan, a return of the order of 0.5% - 0.6% monthly. This is roughly half the level of our basic stock level momentum strategy. The 5th column of reports the corresponding results in the broader Dow Jones universe when the portfolios are equally weighted. Again we find in this smaller cap world, profits are restored to similar levels as found for basic global momentum strategies. This is the Rouwenhorst (1999) result that in a broad universe, momentum strategies deliver similar profits in different markets. However, we also find that in a large cap world, limiting ourselves to specific markets does reduce profits, and therefore some of the profits to our global momentum strategies are generated by an implicit country rotation strategy. 15

A decomposition of momentum returns In this section, we present an approach to decomposing the returns to momentum strategies into the proportion that can be attributed to a sector rotation strategy, the proportion that can be attributed to a country rotation strategy and the proportion that can be attributed to a momentum play on firm specific returns. The idea is straightforward. We estimate a linear factor model (LFM) for stock returns, where both sets of sector and country factors are included in the set of factors. The estimation procedure is described in detail in Appendix B: Decomposing Momentum Returns, but it is based on the Heston and Rowuwenhorst (1995) random coefficient model. In this model, stocks are assumed to have a beta of 1 with respect to the market, their own country and sector factors and a beta of 0 with respect to all other country and sector factors. A time series of country and sector factor returns can then be estimated by performing cross sectional least squares regressions of stock returns on these betas in every month. This model therefore enables us to decompose the returns to every stock into a component due to sector factors, a component due to the set of country factors and a residual or firm specific component. We can now use this decomposition of stock returns into sector, country and firm specific components, to decompose the profits to momentum strategies. We construct our momentum portfolios as before, by ranking all the stocks on their performance in the previous J months, and building market cap portfolios of the top 20% and bottom 20% of performers. However, at this point, when calculating the return to these portfolios over the next K months, instead of using the total return to the constituent stocks, we repeat the procedure three times using first the sector component of returns, then the country component and finally the firm specific component. The sum of these three components, by construction, must equal the earlier total return calculation. As before, we record the percentage monthly return to the self-financing portfolios, portfolios that are long the best and short the worst performers, over our sample period but now we do it three times using each time a different component of the stock returns. Our decomposition of the profits to the momentum strategies is then simply the decomposition of the average returns to these three different components. Table 7 records this decomposition of the returns to the different momentum strategies. The first panel gives the total return to the strategies, the second panel records the component attributable to the firm specific component of returns, the third panel the component attributable to the global sector factors and the fourth the component attributable to the country factors.

16

Table 7: Decomposition of the Monthly Excess Returns to (J, K, 1) Momentum Strategies in a Market Cap Weighted MSCI Global Universe, , January 1992 – March 2003 Total % Monthly Average Returns 1 1 3 Formation Period in Months, J

6 12

Holding Period in Months, K 3 6

12

24

0.16

0.41

0.48

0.40

0.21

(0.49)

(0.34)

(0.27)

(0.20)

(0.15)

0.71

0.63

0.74

0.59

0.31

(0.55)

(0.49)

(0.40)

(0.31)

(0.27)

0.98

0.96

1.06

0.78

0.35

(0.61)

(0.55)

(0.48)

(0.41)

(0.36)

1.13

0.98

0.89

0.67

0.21

(0.60)

(0.56)

(0.55)

(0.53)

(0.45)

% monthly average firm specific returns 1 1 3 Formation Period in Months, J

6 12

Holding Period in Months, K 3 6

12

24

-0.19

-0.06

0.04

0.09

0.02

(0.25)

(0.18)

(0.14)

(0.11)

(0.09)

-0.07

0.04

0.10

0.03

0.00

(0.31)

(0.28)

(0.22)

(0.19)

(0.15)

0.03

0.15

0.24

0.09

-0.03

(0.33)

(0.29)

(0.26)

(0.24)

(0.21)

0.13

0.04

0.04

-0.03

-0.13

(0.33)

(0.32)

(0.31)

(0.30)

(0.27)

% Monthly Average Returns to the Global Sector Factors 1 1 3 Formation Period in Months, J

6 12

Holding Period in Months, K 3 6

12

24

0.28

0.28

0.29

0.21

0.08

(0.38)

(0.27)

(0.22)

(0.15)

(0.11)

0.38

0.36

0.38

0.34

0.11

(0.43)

(0.38)

(0.32)

(0.23)

(0.20)

0.61

0.53

0.51

0.43

0.11

(0.47)

(0.43)

(0.37)

(0.31)

(0.27)

0.78

0.65

0.56

0.36

0.00

(0.47)

(0.43)

(0.42)

(0.40)

(0.34)

% Monthly Average Returns to the Country Factors 1 1 3 Formation Period in Months, J

6 12

Holding Period in Months, K 3 6

12

24

0.05

0.19

0.13

0.10

0.11

(0.31)

(0.23)

(0.18)

(0.14)

(0.10)

0.39

0.21

0.25

0.21

0.20

(0.38)

(0.34)

(0.27)

(0.22)

(0.18)

0.32

0.28

0.29

0.26

0.27

(0.41)

(0.37)

(0.33)

(0.29)

(0.24)

0.20

0.28

0.28

0.33

0.34

(0.42)

(0.39)

(0.38)

(0.37)

(0.31)

17

Table 8: Decomposition of the Monthly Excess Returns to Momentum Strategies in an Equally Weighted Dow Jones Global Universe, January 1992 – March 2003 Total % Monthly Average Returns 1 1 3 Formation Period in Months, J

6 12

Holding Period in Months, K 3 6

12

24

0.02

0.25

0.34

0.41

0.20

(0.52)

(0.39)

(0.31)

(0.23)

(0.17)

0.41

0.43

0.77

0.67

0.28

(0.62)

(0.55)

(0.46)

(0.35)

(0.26)

0.88

1.03

1.12

0.72

0.24

(0.67)

(0.61)

(0.53)

(0.45)

(0.32)

1.06

1.00

0.79

0.32

-0.04

(0.64)

(0.60)

(0.58)

(0.52)

(0.39)

% Monthly Average Returns to firm specific returns 1 1

Formation Period in Months, J

3 6 12

Holding Period in Months, K 3 6

12

24

0.03

0.23

0.29

0.29

0.16

(0.23)

(0.19)

(0.16)

(0.12)

(0.08)

0.41

0.47

0.55

0.46

0.24

(0.31)

(0.28)

(0.24)

(0.18)

(0.13)

0.70

0.74

0.73

0.48

0.23

(0.35)

(0.32)

(0.28)

(0.22)

(0.16)

0.66

0.60

0.47

0.22

0.06

(0.34)

(0.31)

(0.29)

(0.24)

(0.18)

Total Monthly Excess Returns from only the Global Sector Returns 1 1

Formation Period in Months

3 6 12

Holding Period in Months 3 6

12

24

0.13

0.18

0.18

0.11

0.05

(0.46)

(0.33)

(0.27)

(0.19)

(0.14)

0.30

0.15

0.19

0.13

0.07

(0.53)

(0.48)

(0.39)

(0.30)

(0.22)

0.28

0.22

0.33

0.30

0.11

(0.58)

(0.52)

(0.44)

(0.39)

(0.28)

0.47

0.38

0.41

0.45

0.15

(0.54)

(0.52)

(0.51)

(0.46)

(0.34)

Total Monthly Excess Returns from only the Country Returns 1 1

Formation Period in Months

3 6 12

Holding Period in Months 3 6

12

24

0.07

0.11

0.08

0.01

0.00

(0.28)

(0.23)

(0.18)

(0.13)

(0.09)

0.16

0.03

0.05

-0.01

0.01

(0.36)

(0.32)

(0.27)

(0.20)

(0.14)

0.03

0.02

0.12

0.14

0.08

(0.39)

(0.36)

(0.31)

(0.25)

(0.18)

0.24

0.17

0.25

0.38

0.19

(0.38)

(0.35)

(0.32)

(0.28)

(0.20)

18

Table 9: Decomposition of the Monthly Excess Returns to (J, K, 1) Momentum Strategies in a Market Cap Weighted MSCI Global Universe, January 1980 – March 2003 Total % Monthly Average Returns 1 1 3 Formation Period in Months, J

6 12

Holding Period in Months, K 3 6

12

24

-0.36

0.07

0.11

0.21

0.09

(0.25)

(0.17)

(0.13)

(0.09)

(0.07)

0.01

0.11

0.30

0.30

0.14

(0.28)

(0.24)

(0.19)

(0.14)

(0.11)

0.30

0.44

0.68

0.36

0.19

(0.31)

(0.27)

(0.24)

(0.20)

(0.16)

0.65

0.61

0.45

0.22

0.07

(0.30)

(0.29)

(0.27)

(0.24)

(0.20)

% Monthly Average Returns to firm specific returns 1 1

Formation Period in Months, J

3 6 12

Holding Period in Months, K 3 6

12

24

-0.46

-0.11

0.00

0.06

0.01

(0.23)

(0.15)

(0.11)

(0.08)

(0.06)

-0.24

-0.09

0.08

0.08

0.00

(0.26)

(0.22)

(0.17)

(0.13)

(0.10)

-0.02

0.08

0.14

0.08

-0.01

(0.28)

(0.25)

(0.21)

(0.18)

(0.14)

0.07

0.11

0.08

-0.05

-0.09

(0.28)

(0.26)

(0.25)

(0.22)

(0.19)

Total Monthly Excess Returns from only the Global Sector Returns

1

Formation Period in Months

3 6 12

1 0.07

Holding Period in Months 3 6 0.09 0.08

12 0.08

24 0.02 (0.04)

(0.16)

(0.10)

(0.08)

(0.06)

0.11

0.09

0.10

0.11

0.02

(0.17)

(0.14)

(0.11)

(0.09)

(0.08)

0.14

0.12

0.29

0.12

0.00

(0.18)

(0.16)

(0.14)

(0.13)

(0.11)

0.33

0.24

0.17

0.03

-0.08

(0.19)

(0.18)

(0.18)

(0.17)

(0.15)

Total Monthly Excess Returns from only the Country Returns

1

1 0.03 (0.18)

Formation Period in Months

3 6 12

Holding Period in Months 3 6 0.09 0.03 (0.11)

(0.08)

12 0.06

24 0.06

(0.07)

(0.05)

0.14

0.11

0.12

0.11

0.12

(0.20)

(0.16)

(0.14)

(0.11)

(0.09)

0.17

0.24

0.25

0.16

0.19

(0.21)

(0.21)

(0.19)

(0.16)

(0.13)

0.26

0.25

0.20

0.24

0.24

(0.23)

(0.22)

(0.22)

(0.20)

(0.17)

19

For holding periods of up to 6 months, it appears that between 50-65% of the momentum returns can be attributed to an implicit sector rotation strategy; around 20-25% to an implicit country rotation strategy and between 15-25% to a play on firm specific momentum. In all our analysis so far, we have found that a small cap universe behaves differently. Therefore in Table 8 we have repeated our decomposition analysis but for equally weighted portfolios in the broader Dow Jones Universe. Indeed we do find that in a universe dominated by the behavior of small firms, the amount of the return that can be attributed to firm specific effects is now nearly 75%. The amount that can be attributed to implicit industry and country rotation strategies falls to 30% and 10% respectively. Table 9 records the decomposition for the MSCI large cap universe over the longer period 1980-2003. From the top panel, it is clear that momentum profits over the longer period are on average 35% less than over the shorter period. This fall in profits can be attributed almost entirely to the sub-period 1980 –1985 rather than the period 1985-1992. For example profits to the (6,6,1) momentum strategy was on average only 0.19% per month between 1980-1985, whereas it was 0.86% per month over the period 1985-1992. As per the results in Table 7 for the shorter period, the majority of the profits to the momentum strategies can be attributed to either the implicit sector or country rotation strategies and not to the idiosyncratic stock returns. What does change over the two periods is the proportion that can be attributed to the country rotation strategy. Over the longer period the magnitude of the profits attributable to the country rotation strategy is almost as large as that attributable to the sector rotation strategy. This result is consistent with the work of Cavaglia, Brightman and Aked (2000), Phylaktis and Xia (2003) and Rouwenhorst (1999), who all find that that sector factor returns have become a far more important determinant of stock returns over the 1990s. Summary of Findings We have suggested, and verified, a consistent interpretation of the multitude of research articles on momentum that has important implications for fund management. In a value weighted large cap universe, such as the Global MSCI, we found that price return momentum is driven largely by industry momentum; it does not appear to be explained by individual stock momentum. Further this return continuation is not a result of either cross-section dispersion in industry mean returns, or by differing industry exposure to systematic risk. As Fama and French (1996, p. 81) note, the linear factor model of returns ‘cannot capture the continuation of short-term returns’. In addition, unlike the momentum returns in equal-weighted portfolios where the return is typically generated by shorting losers, in value weighted portfolios the greater part of return accrues from being long the winners. Practitioners are often critical of the equally weighted returns reported in many papers because of the costs of implementing the short portfolio. In Table 10 and Table 11 we report the quintile breakdown of the returns to the value weighted momentum strategies where it is clear that the statistically significant returns are largely generated by long positions in the winning quintiles.

20

Table 10: % Monthly Average returns to the Quintile Portfolios formed for a (6, 6,1) Momentum Strategy in a Market Cap Weighted MSCI Universe (standard errors in parentheses) Mean Std. Err.

Losers -0.27 (0.53)

Quintile 2 0.18 (0.40)

Quintile 3 0.33 (0.37)

Quintile 4 0.54 (0.37)

Winners 0.80 (0.48)

Table 11: % Monthly Average returns to the Quintile Portfolios formed for a (6, 6,1) Sector Rotation Momentum Strategy in a Market Cap Weighted MSCI Universe (standard errors in parentheses) Mean Std. Err.

Losers -0.16 (0.55)

Quintile 2 0.23 (0.39)

Quintile 3 0.35 (0.40)

Quintile 4 0.59 (0.37)

Winners 0.92 (0.45)

It therefore appears that fund managers could add alpha to their portfolios by building in sector tilts based on past return performance. However, this increase in performance will come at the cost of slightly increased risk; firstly from the tilts and secondly from the increased exposure to momentum. Taking this into account, O’Neal (2000) in his work using US sector mutual funds, calculates that such strategies, even after costs, do improve portfolio Sharpe ratios and other measures of performance. In a small cap universe, the evidence is that the majority of momentum profits are attributable to individual stock momentum effects. Though this result is probably of less interest to all but small cap fund managers, it does have interesting implications for understanding these pricing anomalies. What is causing return momentum? Explaining the momentum pricing anomaly has become one of the principal ‘battlefields’ in finance between the behaviorists and the rationalists. In this section, we discuss how their models of price momentum might be adapted to explain why momentum in a large cap world is industry driven but in a small cap world is more stock specific. The behaviorists almost exclusively focus on the mechanism by which new information or ‘news’ diffuses into prices, if investors are prone to exhibiting various psychological biases. Daniel, Hirshleifer, and Subrahmanyam (1998) consider the asymmetries induced by self-attribution bias; the tendency of investors to attribute positive outcomes to ‘skill’, and dismiss negative outcomes as ‘bad luck’. Self-attribution bias can induce both medium term momentum, and long term price overreaction. For following a decision to buy, an investor exhibiting this bias is far more likely to later buy more of the stock should he receive further good news than he is likely to sell if he receives bad news. This asymmetry causes prices to rise too far in the short term, and correct themselves later. In contrast, Barberis, Shleifer and Vishny’s investors exhibit conservatism. This makes them slow to update their priors in the event of good (bad) news. Therefore, prices do not adjust completely to any new information. Given this, it is more likely that further news will also be positive (negative) and prices will then adjust some more later. This induces short-term return continuation too. 21

Both these mechanisms could induce momentum at the industry level or the stock level. For if investors focus on industry signals for large cap firms and firm specific news for small cap firms (a form of representativeness bias), then return continuation will be at the industry level for large cap and at the stock level for small cap. The rationalists focus, not on psychological biases, but on how ‘minimally rational’ investors reacting to unpredictable changes in market conditions could induce these pricing anomalies. Though there is no single paper that has managed to satisfactorily model the medium term momentum effect, there are some promising avenues of research. Empirically, O’Neal (2000) found the ‘winner’ industries performed well when the default risk premium on high-yield bonds fell. A fall in this premium is suggestive of improving market conditions. Lo and MacKinlay (1999, Chapter 5) found that the majority of the momentum effect can be attributed to positive ‘cross auto-covariances’ and not to simple cross-correlations. By this they mean, that when one stock does well, it is the tendency for similar stocks to do well later, rather than that specific stock, that causes the above average return to these momentum portfolios. These empirical observations are therefore suggestive that as market conditions improve news slowly diffuses into the prices of similar stocks, or stocks in the same industry; after all, industrial classification is just a way of grouping similar stocks. These empirical observations therefore link well with Berk, Green and Naik (1999) who show theoretically that changes in a firm’s growth opportunities, that are related to their systematic risk, can generate medium term momentum in returns. As growth opportunities are most likely to be correlated across industries, this mechanism will induce an industry momentum effect. Also linking with the above empirical observations, Lewellyn and Shanken (2002) start their paper by stating that investors do not know the true distribution of stock returns. They must, therefore, estimate this distribution based on observed past data, and update these distributions, as new data becomes available. This implies that even though the investors make entirely rational investment decisions based on their subjective distribution of returns, ex-post returns may exhibit some correlation. Though their model has more success at explaining over-reaction, it can explain return continuation if investors place too much confidence in their priors.

22

Figure 5: Recent performance of (6, 6, 1) momentum strategy 15.00 10.00 5.00 0.00 -5.00 -10.00 -15.00 OCT94

OCT95

OCT96

OCT97

Winners Minus Losers

OCT98

OCT99

Mean Return

OCT00

OCT01

OCT02

Mean over past Year

It is however important to raise one note of caution, Figure 5 illustrates the recent performance of a (6, 6, 1) momentum strategy. Whilst the average monthly return has been a healthy 106 basis points the month to month variation can be large and the 12 month rolling return was negative through 2000. It seems clear that strategies should not be pursued in isolation, but rather used as an indication of which factors are being priced in the market in a multi-factor stock selection framework. Implications for Portfolio Management In this final section, we draw out the implications of this research for the principal portfolio management styles. Value Managers: Asness (1996) reports that measures of momentum and value have historically been negatively correlated across stocks. This relationship has been, though, less pronounced over the last ten years due to the long value rally over the previous two to three years. This negative correlation implies that it is difficult for value managers to simultaneously play the momentum game, for generally value managers find themselves underweight momentum. This research suggests that value managers could reduce the possibility of underperformance due to being underweight momentum, by holding a sector neutral portfolio. This would also have the added advantage of reducing their long run portfolio risk due to transitory momentum effects, Scowcroft and Sefton (2001). Growth Managers: Given that momentum appears to be industry driven at the large cap level, then growth managers could augment their portfolio alpha by pursuing simultaneously a sector momentum strategy. Their portfolio would incorporate a gentle tilt to sectors that had performed well over the previous six to 12 months. However, they would need to accept that standard risk models might underestimate their portfolio risk, and therefore would be advised to remain cautious with respect to their risk mandate.

23

Momentum Investors: Momentum managers benchmarked to any of the standard value weighted indices, should concentrate on spotting trends at the industry level and not at the stock level. This is likely to have the added advantage of simultaneously reducing their transaction costs. In contrast, investors working in a small cap universe would need to continue to focus on individual stock stories. All investors: Exposure to the additional risk from transitory momentum effects needs to be continuously monitored by measuring both portfolio momentum style exposures and portfolio industry tilts. If we define a ‘style’ to be a group of companies that share some common characteristic that have the potential to co-vary then any such style could exhibit strong momentum if the desired characteristic is currently being ‘priced’ in the market, causing the prices of a group of related companies to move together. Such a characteristic could be as simple as industry or country or more generally any characteristic that investors expect to impact performance. Controlling the risk in any portfolio therefore requires monitoring style exposure. The clear implication is that momentum should not be regarded as a simple stock level phenomenon. Portfolio managers have typically used momentum as a sentiment indicator largely used to complement a valuation metric affecting timing decisions. However, when one stock does well, it is the tendency for similar stocks to do well later, rather than that specific stock, that causes the above average return to these momentum portfolios. At different points in the business cycle momentum could be either an industry or a style phenomenon.

24

References Asness (1997). “The Interaction of Value and Momentum”, FAJ March Barberis, Shleifer and Visney (1998). “A Model of Investor Sentiment” Journal of Financial Economics 49 Berk, Green and Naik (1999). “Optimal Investment, Growth Options, and Security Returns”, Journal of Finance 54(5) Cavaglia, Stefano, C. Brightman and M. Aked (2000). ‘On the increasing importance of Industry Factors: implications for Global Portfolio Management’, Financial Analyst Journal, September 2000, pp41-53. Chan, Hameed and Tong (2000). “Profitability of Momentum Strategies in the International Equity Markets”, Journal of Financial and Quantitative Analysis 35 Chan, Jegadeesh and Lakonishok (1996). “Momentum Strategies”, Journal of Finance 51(5) Fama, Eugene F. and Kenneth R French (1996). “Multifactor Explanations of Asset Pricing Anomalies”, Journal Of Finance, 51(1) Gardner, Bowie, Brooks and Cumberworth (2000). “Predicted Tracking Errors – Fact or Fantasy?” Faculty and Institute of Actuaries Grundy and Martin (2001). “Understanding the Nature of the Risks and the Source of the Rewards to Momentum Investing”, The Review of Financial Studies, 14(1) Heston, Steven and K. Geert Rouwenhorst (1995), ‘Does Industrial Structure explain the benefits of International Diversification’. Journal of Financial Economics, Vol 36, 3-27. Jegadeesh (1990). “Evidence of Predictable Behavior of Security Returns”, Journal of Finance, 45(3) Jegasheesh and Titman (1993). “Returns to Buying Winners and Selling Losers; Implications for Stock Market Efficiency”, Journal of Finance 48(1) Jegadeesh and Titman (2001). “Profitability of Momentum Strategies - An Evaluation of Alternative Explanations”, Journal of Finance 56(2) Lakonishok, Shleifer and Vishny “Contrarian Investment, Extrapolation, and Risk”, Journal of Finance, 49(5) Lehmann (1990). “Fads, Martingales and Market Efficiency”, Quarterly Journal of Economics 105 Lo and MacKinlay (1990). “When are Contrarian profits due to stock market overreaction?” Review of Financial Studies, 3 Lo and MacKinlay (1999). A non random walk down Wall Street. Princeton University Press. Moskowitz and Grinblatt (1999). “Do Industries Explain Momentum?”, Journal of Finance, 54(4) Nijman, Swinkels and Verbeek (2003). “Do Countries or Industries Explain Momentum in Europe?”, Journal of Empirical Finance, Forthcoming O'Neal (2000). “Industry Momentum and Sector Mutual Funds”, FAJ June Phylaktis, K. and Xia, L. (2003). 'The Changing Role of Industry and Country Effects in the Global Equity Markets' Discussion Paper, Emerging Markets Group, Cass Business School. Porta, Lakonishok, Shleifer and Vishny (1997). “Good News for Value Stocks: Further Evidence on Market Efficiency”, Journal of Finance, 52(2)

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Richards (1997). “Winner-Loser Reversals in National Stock Market Indices: Can They be Explained?”, Journal of Finance, 52(5) Rouwenhorst (1998). “International momentum strategies”. Journal of Finance, 53(1) Rowenhorst, K. Geert (1999). ‘European Equity Markets and the EMU’, Financial Analysts Journal, Vol 55(2), March 1999, pp 35-50. Scowcroft and Sefton (2001). “Do Tracking Errors Reliably Estimate Portfolio Risk?” Journal of Asset Management, December Scowcroft and Sefton (2002). “A New Global Country Sector Model” UBS Warburg Quantitative Research Paper. Lewellen and Shanken (2003). “Learning, asset-pricing tests, and market efficiency”, Journal of Finance Swinkels (2002). “International industry momentum”, Journal of Asset Management 3(2) Vuolteenaho, Tuomo (2002). “What Drives Firm-Level Stock returns?”, Journal of Finance, Vol. LVII, No.1 February Werner, De Bondt and Thaler (1985). “Does the Stock Market Overreact?” Journal of Finance, 40(3) Werner, De Bondt and Thaler (1987). “Further Evidence on Investor Overreaction and Stock Market Seasonality”, Journal of Finance, 42(3)

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Appendix A: Building Momentum Portfolios The approach adopted here is almost identical to the original method of Jagadeesh and Titman (1993). For this reason we keep it brief and present it as a menu. We use data on stock returns over the period January 1992 to March 2003 and limit our universe in any month to either all stocks in the Dow Jones Global Index or all stocks in the MSCI Global Index. The approach is as follows: 1. At every month end, rank all stocks in the universe according to their cumulated price performance over the previous J months, time t-J+1 to t where the index t is in months. 2. Sort the stocks into 5 equal portfolios by either number (equally weighted) or by market cap. Thus the 1st portfolio or ‘Winner’ portfolio contains the top 20%, by number or market cap, of ranked stocks, the 2nd portfolio the next 20% and so on. So the 5th portfolio or ‘Loser’ portfolio consists of the worst 20% of performers. 3. Measure the return to each of these portfolios in every month for the next K months after formation, t+1 to t+K. We also look at the small variant, so as to avoid short term price reversals, where a month’s gap is left between formation and holding and returns are measured instead for months t +2 to t+K+1. 4. The return to Momentum Winners (Losers) in period t+1 is the average of the returns to the top (bottom) quintile portfolios formed at t, t-1, …, t-K+1 in period t+1. Thus the return to the Momentum Winners is the average return to the K winner portfolios formed consecutively over the previous K months. If a month’s gap is left, the return at period t+1 is the average of the returns to the top (bottom) quintile portfolios formed at t-1, t-2, …, t-K. 5. The returns to the Momentum Strategy (J, K, 0) or ((J, K, 1) if a month’s gap is left) is the average return to the self-financing portfolio of Winners - Losers over the data sample. In this article, we also look at the return to momentum strategies based on picking the best performing industries (countries) over the previous J months and holding all stocks in these industries (countries) for the next K months. These portfolios are formed in a similar way to the approach described above except steps (1) and (2) are modified to the following: (1a)

At every month end, rank all the industries (countries) according to their cumulated price performance over the previous J months.

(2a)

Sort the stocks into 5 portfolios. The 1st portfolio or ‘Winner’ portfolio contains all stocks in the top 20% of performing industries (countries) either equally weighted or market cap weighted. The 5th portfolio or ‘Loser’ portfolio contains

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all stocks in the bottom 20% of performing industries (countries), again either equally weighted or market cap weighted. The remaining steps (3)-(5) are identical. Appendix B: Decomposing Momentum Returns We shall assume a Linear Factor Model (LFM) describes stock returns. More specifically, we shall assume stock returns are related to the returns of a given set of factors; specifically, a market index, a set of sector indices and a set of country indices. Thus if rit denotes the return to stock i at time t, fMt, fSj,t and fCk,t denote the global market, global sector, and local country factor returns respectively, then we can write rit

E iM f Mt 

¦

jSectors

f Sj ,t E i , Sj 

¦

fCk ,t E i ,Ck  H it

(1)

k Countries

Where E iM , E i , Sj , E i ,Ck , are the corresponding sensitivities of the stock’s return to these

factors and H it ҏis the idiosyncratic or stock specific return. The stock specific return is assumed to be normally distributed and uncorrelated with the factors and the stock specific return of any other stock. Scowcroft and Sefton (2002) detail the approaches used to estimate this LFM. In this paper we use the random coefficient approach of Heston and Rouwenhorst (1995). It is the simplest approach that attempts to unravel country and sector returns. Scowcroft and Sefton (2001) discuss refinements to this model that relax some of their strong assumptions. Heston and Rouwenhorst assume all the sensitivities are either 1 or 0. Each stock has a sensitivity of 1 with respect to the market, its own sector and country factors and sensitivities of 0 otherwise. Therefore we can rewrite equation (1) in matrix notation as

ª r1t º « r » « 2t » « # » « » « rnt » « r( n 1)t » « » «¬ # »¼

ª1 «1 « «# « «1 «1 « «¬#

1 0 " 0 1 0 " 1 0 " 0 0 1 " # # % # # # % 0 1 " 0 1 0 " 0 1 " 0 0 1 " # # % # # # %

ª f Mt º « » f S 1,t » « 0º H « f S 1,t » ª« 1t º» » » 0» « H 2t » « # » «« #» « # » » « f SM ,t »»  « » 0» H nt » « f « » 0 » « C1,t » «H ( n 1)t » » « fC 2,t » « » # »¼ « # ¼» ¬ « # » « » ¬« fCN ,t ¼»

(2)

where, for illustration, we have assumed stocks 1 and 2 belong to sector 1 and countries 1 and 2 respectively, and stocks n and n+1 belong to sector 2 and also to countries 1 and 2 respectively. Under this assumption, the factor returns in any period can be estimated by regressing the matrix of sensitivities on the vector of stock returns. This regression could be unweighted, however, we follow Heston and Rouwenhorst and perform a weighted least squares regression (WLS), where the weighting matrix is the diagonal matrix of the respective stock market caps. Finally, there is a co-linearity problem – note that if we sum the sensitivity vectors corresponding to the sector factors or the country factors we get the

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vector of sensitivities to the market factor (the 1st column). To remove this problem we perform the WLS regression subject to the following two constraints

¦ ¦

w jk f Sj ,t

0 and

k Country jSector

¦ ¦

w jk f Ck ,t

0

(3)

k Country jSector

where wkj is the market cap weight of sector j in country k as a percentage of world market cap. Now by performing these constrained WLS regressions for each period of the data sample, we can estimate a time series of country and sector factor returns. We can now describe how we use this LFM to decompose momentum returns. In Appendix A: Building Momentum Portfolios, we detailed the 5 steps to calculating the returns to our momentum strategies. To decompose this return, we construct the portfolios as before – steps (1) and (2). However, in step (3) rather than calculating the total return to these portfolios, we decompose this return into three components; the returns due to the sector factors, the returns due to the country factors and the returns due to the firm specific factors. To describe this more precisely, denote as wit the weight of stock i in the portfolio of interest at time t. Then if we wish to estimate the industry momentum contribution to the momentum strategy, we use (4) ¦ ¦ wit E i, Sj f Sj ,t iStocks jSector

as the return to this portfolio in steps (4) – (5), rather than

¦

wit rit

(5)

iStocks

as before. Similarly, to estimate the country contribution, we use the returns to country factors and to estimate the firm specific returns we use the stock specific idiosyncratic returns ¦ wit H it . iStocks

It follows immediately from equation (1), that the sum of industry, country and stock specific contributions to the momentum strategy must equal the total return to this strategy.

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