Original Article

Style investing and momentum investing: A case study Received (in revised form): 13th April 2011

Sandrine de Moerloose holds a Master in Economics, and recently completed a Master in Finance, at the Universite´ Catholique de Louvain (UCL) in Belgium. She is now working for a private bank in Belgium as equity analyst.

Pierre Giot is full professor of finance at the University of Namur (member of LSM group) in Belgium, and a member of CORE (UCL). He has widely published in academic journals such as the Journal of Banking and Finance, the Journal of Empirical Finance or the Journal of Portfolio Management. His current research interests focus on venture capital economics, asset management and market microstructure. Correspondence: Pierre Giot, University of Namur; CORE, Universite´ catholique de Louvain, Belgium E-mail: [email protected]

ABSTRACT We examine whether an investor should choose a style rotation strategy (that is style investing) rather than a buy-and-hold strategy or a momentum strategy. We run outof-sample forecasting/investing horse races between style rotation strategies (based on logit models), simple momentum strategies and buy-and-hold strategies. Regarding style rotation strategies, we consider switches between value and growth indexes, and small-cap and large-cap indexes. To gain a long-term perspective, we use the freely available Fama– French data set, which segments US stocks into value and growth stocks, and small-cap and large-cap stocks. Although the choice of variables to include in the logit models and the investment outcomes depend on the indexes (style switches) under review, our study shows that style switching gives interesting investment results. Journal of Asset Management (2011) 12, 407–417. doi:10.1057/jam.2011.28; published online 19 May 2011 Keywords: style switching; momentum investing; value and growth stocks; small-cap and large-cap stocks

INTRODUCTION Style investing (for example, investing at specific times in value or growth stocks, in small-cap or large-cap stocks)1 has become an important topic in empirical portfolio management. Indeed, if an investor can identify the cycle of styles over time, he can allocate his assets optimally and thus obtain returns considerably larger than those of a buy-and-hold strategy. Arnott et al (1989), Fisher et al (1995), Kao and Shumaker (1999), Levis and Liodakis (1999), Lucas et al (2002) or Arshanapalli, Switzer and Panju

(2007) use historical data to demonstrate the potential benefits of style rotation. In these studies, the authors mainly use logit models with variables such as inflation, industrial production, P/E ratio, term spread, yield spread to identify when to best change the investment style. According to these studies, forecasting models of style rotation deliver statistically significant results (at least before transaction costs). In the same vein, Jegadeesh and Titman (1993) and Rouwenhorst (1996) demonstrate the profitability of simple strategies such as momentum strategies. With

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these strategies, the profitability comes from the fact that investors overreact or underreact to news or specific events, causing the momentum effect. Securities that have registered a good (bad) performance in the recent past will tend to have a good (bad) performance in the future. Capual et al (1993) or Chan and Lakonishok (2004) have investigated style effects on an international basis and have shown that the US evidence also extends to many other countries. Our study involves two different analyses related to the style switching and momentum literature. The first will analyze investment strategies in value and growth indexes. The second analysis will focus on small-cap and large-cap indexes. Four different styles of stocks will therefore be addressed in this study: value, growth, small-cap and large-cap stocks. In contrast to other studies that usually focus solely on style switching, our goal is to compare the performances of styleswitching models with the performances obtained using simpler momentum rules, which are still favored by many traders. We run these tests on a rather long historical sample as we use the publicly available Fama– French style databases that conveniently allocate US stocks into small-cap, large-cap, value and growth returns (hence indexes can be built). Although these indexes are, strictly speaking, not tradable, they do provide a long-term perspective into the potential benefits of style switching and momentum investing. Although we provide many empirical results in the article, some key issues can be highlighted. We show that, if our investment decision involves two styles of indexes (value and growth indexes or small-cap and largecap indexes), the logit model with five variables leads to a superior performance of our portfolio relative to a buy-and-hold strategy or a momentum strategy. The five variables are economic growth, the yield spread, an indicator of investor confidence in the market, inflation and the term spread in the case of style rotation in value and growth

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indexes. This last variable is replaced by the P/E ratio for the S&P500 index for the style rotation in small-cap and large-cap indexes. The economic strategy with five variables is, in the case of the value/growth indexes and the small-cap/large-cap indexes, statistically significant and it is also the least risky strategy among all tested strategies (buy-and-hold, momentum and logit strategies).

LITERATURE REVIEW Many papers in the literature on investment styles suggest that systematic investment in value and/or small-cap stocks yields larger returns, even when adjusted for risk, than investing in growth and/or large-cap stocks, especially in the medium and long term.2 In practice, investing systematically in the same style over time may, however, not be the optimal strategy. Indeed, the performance of each style varies over time. A style can outperform relative to another style at a time, and vice versa at another moment. Researchers have tested whether smallcap and large-cap stock returns, and value and growth stocks returns, were somewhat predictable. According to Coggin (1998), style changes could be predicted based on macroeconomic information, as well as information on the economic cycle. Regarding the factors that give the best signals when to change the style of investment, there is no consensus in the different studies. Arnott et al (1989) use an index of leading indicators, the producer price index and the money supply. Sorensen and Lazzara (1995) argue that the industrial production and the interest rates positively influence the gap between the yields of value and growth stocks. Anderson (1996) finds a positive relationship between the yield curve and the yield spread between small-cap and large-cap stocks. Kao and Shumaker (1999) advocate the use of the term structure of interest rates, the real bond yield, the difference between the rate of corporate bonds and the risk-free rate, the estimated

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growth of GDP, the production price index and the P/E ratio for the S&P500 to identify when to change the investment style. Asness et al (2000) make predictions about future returns on value and growth strategies using the gaps of long-term predictions of earnings growth for the value and growth stocks. Lucas et al (2002) use the differences between short-term and long-term interest rates. Coggin (1998) and Kao and Schumaker (1999) confirm the usefulness of models based on economic factors as signals for the style rotation. Levis and Tessaromatis (2004) also find that style rotation strategies are profitable. Although the various studies mentioned above indicate the profitability of style rotation strategies thanks to quantitative forecasting models such as the logit model, other studies show that a simpler approach, such as the momentum strategy, can also be used to obtain similar results. Momentum strategies are based on the idea that markets tend to continue moving in the same direction as they did in the recent past. The securities having thus registered a good (bad) performance in the past will tend to have a good (bad) performance in the future. Jegadeesh and Titman (1993) highlight the profitability of momentum strategies. In their view, investors overreact or under-react to news or events specific to the company, causing the momentum effect. Rouwenhorst (1996) shows that momentum effects are present internationally. In his study, he documents the existence of momentum effects in 12 European countries and in the United States from 1978 to 1995. The key to take advantage of the profitability of the momentum effect is to identify the trends in the market early and to react quickly.

METHODOLOGY Database and sample The returns database used in this study comes from the public online data library of Fama

and French.3 The returns are those of the indexes of the different styles analyzed. In the first analysis, the returns of the growth and value indexes are used. The growth index includes the top 20 per cent of stocks having the highest market value relative to their book value on the three biggest US markets: the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX) and the National Association of Securities Dealers Automated Quotations (NASDAQ). The value index includes the bottom 20 per cent of stocks that have the lowest market value relative to their book value on the NYSE, AMEX and NASDAQ. In the second analysis, the returns of two other indexes are used: a small-cap and a large-cap index. The small-cap index used here includes the bottom 20 per cent of stocks representing the smallest capitalization on the NASDAQ, NYSE and AMEX markets. The large-cap index includes the top 20 per cent of stocks representing the largest capitalizations on the NYSE, NASDAQ and AMEX markets. The data sample begins in the first quarter of 1960 and ends in the fourth quarter of 2008. The data are quarterly, and we have a sample of 196 observations.

The strategies Momentum strategies In the first phase of the analysis, two momentum strategies are tested. The first strategy is the ‘Momentum 1’ strategy: the investment is made today, at time t, in the style that has achieved the best returns in the previous period, at time t1. The second momentum strategy is the ‘Momentum 2’ strategy. In this strategy, the analysis focuses on what happened at times t1 and t2 to decide in what style to invest. If the same style has generated the best returns during the two periods in a row, the investment will be in this style today. If during these two periods, the same style did not get the best returns, the investment choice will be the

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same as the one in which we have invested in the previous period.

‘Economic strategies’ using logit models The models Two economic strategies predicting in what style to invest are analyzed. The first strategy uses three economic variables to make the forecasts. The second uses five variables, three of which are the same as in the first strategy. The first three variables that appeared to have the most influence on stock returns and came back the most often in the studies analyzed were selected from a pool of several variables. According to Sorensen and Lazzara (1995), Anderson (1996) and Kao and Schumaker (1999), the three variables that are the best signals to predict when a change of style is needed are economic growth, the yield spread and a confidence indicator. Two choices were sometimes possible for the same variable, and therefore different combinations were tested, keeping only the combination that gave the best value of the investment portfolio at the end of 2008 (and not the best success rate of prediction). With regard to the strategy with five variables, different tests were performed to determine which variables need to be added to the three ‘basic’ variables to get the best portfolio value at the end of 2008. Following the analysis, different variables can have the best forecasting power. In the case of the growth and value styles, it is the term spread and inflation. In the case of the style rotation in small-cap–large-cap indexes, the P/E ratio for the S&P500 index and the consumer price enable to obtain the best forecasts. The use of these variables is also recommended in the studies of Lucas et al (2002), Kao and Shumaker (1999) and Arnott et al (1989), as forecasts in the style rotation. The sample size used to estimate the model is equal to 10 years and remains fixed

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over time (fixed rolling-window forecasting methodology). The data of the 10 years before the forecast made, that is data made up of 40 quarters, are used to predict the style in which to invest. For example, the data from the first quarter of 1960 to the fourth quarter of 1969 are used to predict in which style to invest in the first quarter of 1970. Thereafter, the data from the second quarter of 1960 to the first quarter of 1970 are used to predict in which style to invest in the second quarter of 1970. More precisely, we begin by making a logit regression over a period of 10 years, with a constant and the variables chosen delayed by one period. In the case where there are three variables used in the economic strategy, the equation estimated by the logit method is as follows: Yt ¼aþb1 X1 ; t1 þb2 X2 ; t1 þb3 X3 ; t1 where Yt is the binary dependent variable, a is the constant, b1, b2, b3 are the coefficients of the independant variables, and X1, t1, X2, t1, X3, t1 are the independent variables. In the case of the economic strategy with five variables, the equation, estimated by the logit method, is as follows: Yt ¼aþb1 X1 ; t1 þb2 X2 ; t1 þb3 X3 ; t1 þ b4 X4 ; t1 þ b5 X5 ; t1 where Yt is the binary dependent variable, a is the constant, b1, b2, b3, b4, b5 are the coefficients of the independent variables, and X1, t1, X2, t1, X3, t1, X4, t1, X5, t1 are the independent variables. Once the coefficients of the variables are estimated, they are used to estimate the probability that an index outperforms the other using the logit transformation: Prðyi ¼ jÞ ¼

expðXi bj Þ Pj 1 þ j¼1 expðXi bj Þ

The estimated probabilities are between 0 and 1. Depending on the probability, the strategy consists to invest in one or another style. Next, at the end of the period t þ 1, the

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coefficients of the variables are again estimated, from the data of the 40 quarters preceding the new prediction in t þ 2. Again, the coefficients are used in the above equation with the variable values in t þ 1, to obtain the probability that an index outperforms the other in t þ 2. The estimation procedure, followed by the calculation of the probability of outperformance of an index relative to the other, is repeated each quarter, for each new prediction. The forecasts generated by the logit model indicate the probability that a type of index outperforms another, rather than the magnitude of outperformance. The procedure is to invest in each period in the type of index that was predicted by the model as outperforming from the others. If the model predicts that in the next quarter the value (small-cap) or growth (large-cap) index will give the best returns, the investor will invest in this index and vice versa.

Economic variables used in the logit forecasting model The literature review given above suggests many macroeconomic variables as possible regressors in the logit model. Economic growth, based on GDP increases, is a standard measure of the health of an economy. When the economy grows, corporate profits are also increasing. During these periods, the value and small-cap indexes outperform in general the growth and large-cap indexes. Industrial production can also be used instead of GDP. Indeed, fluctuations in industrial production have a large impact on corporate earnings, and hence on stock returns. According to Sorensen and Lazzara (1995), industrial production positively influences the difference between the returns of value and growth indexes. Kao and Shumaker (1999) also advocate the use of this variable in economic models of style timing. Regarding inflation, some studies show a negative correlation between stock returns and

inflation. Indeed, the P/E ratio tends to be generally higher when inflation is low; inflation is used in the model of Arnott et al (1989). The term spread, defined as the difference between interest rates in the long and short term, also matters for style switching. Growth shares having an expected profit growth higher than value shares in the long term therefore have a higher ‘duration’ than value stocks. Therefore, an increase in long-term interest rates will have a greater impact on discounted profit of growth shares than on value shares, and thus a greater effect on the growth index than on the value index. The use of this variable in economic forecasting models is thus advised by Lucas et al (2002). The yield spread is another important variable. Indeed, empirical evidence shows that the yield spread can serve as an indicator to predict future economic activity. Kao and Shumaker (1999) use the yield spread to determine when to change investment style. An indicator that reflects the confidence of investors is also an important variable to consider. Two indicators are possible in this case. The first is the ‘Barron’s Confidence Index’. It is obtained by dividing the average yield of high-quality bonds (or ‘investment grade bonds’) by the average yield of medium/low-quality bonds (or ‘junk bonds’). The second confidence indicator is the ‘Conference Board Leading Economic Index’. It is a US economic indicator intended to predict future economic activity. The value of this index is calculated on the basis of 10 key variables. History has shown that this index tends to decrease before a recession and generally increases before an expansion of the economic activity. The volatility of the S&P500 index, measured in standard deviation units or realized volatility, measures the magnitude of changes in the S&P500. By definition, the expected profit is greater when volatility is high, but the risk of loss as well. With regard to fundamental factors, Kao and Shumaker (1999) use the dividend yield or the P/E ratio as an indicator

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to determine whether a stock or index is more attractive than another.

RESULTS In each simulation, the value of our portfolio in the first quarter of 1970 is set at 100h. The simulation consists of choosing at the beginning of each quarter the style in which to invest: value or growth in the case of the first analysis, small-cap or large-cap in case of the second analysis. The logit model is estimated at the end of each quarter based on the past value of the selected economic variables. The probabilities obtained by this model allow us to determine the style in which to invest in the next period. In the case of the momentum strategies, we look at the end of each quarter at what happened in the previous periods to find out the style in which to invest in the next period.

Investment strategies in value and growth indexes Results If we apply a buy-and-hold strategy and we start investing in a growth index in the first quarter of 1970, the value of our portfolio is 1468 h at the end of 2008. If we had instead invested in a value index, the value of our portfolio at the end of 2008 would have been 14847 h. The first strategy is the Momentum 1 strategy. At the end of each quarter, we look at what style gave the best returns. Following this, the strategy consists of investing during the next quarter in the style that gave the best results in the past period. When we implement this strategy, we obtain a portfolio value of 7897 h at the end of 2008. The second strategy is the Momentum 2 strategy. We analyze here whether it is the same style that has given the best returns during the two previous periods. The results obtained by this strategy are better than in the case of the Momentum 1 strategy. However, with a portfolio value of 9968 h at the end of

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2008, this second momentum strategy gives better results than the buy-and-hold strategy in a growth index, but less successful results than the buy-and-hold strategy in a value index. In the third strategy, we perform economic forecasts thanks to the logit model and three economic variables to determine the style in which to invest. The three variables with the best predictive power are, as mentioned earlier, economic growth (defined by the GDP in this regression), the yield spread and an indicator of investor confidence in the market (defined by the Conference Board Leading Economic Index, in this case). The portfolio value obtained by this strategy at the end of 2008 is 11 388 h. This strategy is thus better than the buy-andhold strategy in a growth index, the Momentum 1 strategy and the Momentum 2 strategy. The last strategy is similar to the previous one. The difference lies in the fact that it adds two new variables to the previous model. In the case of style rotation in growth and value indexes, the two additional variables that have the highest predictive power are term spread and inflation. However, regarding the variable measuring investor confidence, the Barron’s Confidence Index has a better predictive power in the forecasting strategy with five variables than the Conference Board’s Leading Economic Index. The results obtained here are better as we reach at the end of 2008 a portfolio value of 18 200 h. Nevertheless, a ‘perfect’ forecasting strategy, where we invest systematically in the style that effectively gives the best performance would provide a portfolio value of 231 738 h at the end of 2008. It is therefore possible to see that even if an economic strategy with five variables gives very good results, they are incomparable to those that might be obtained if we made no error in the forecasts. Table 1 provides a summary of the results obtained by the different strategies. When looking at Figure 1, we note that it takes about 20 years for the portfolio value

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Table 1: Portfolio value obtained by each strategy at the end of 2008, and quarterly arithmetic average return of each strategy between 1970 and 2008 Strategy used

Portfolio value at the end of 2008 (h)

Quarterly arithmetic average return between 1970 and 2008(%)

1468 14847 231738 7897 9968 11388 18200

1.231 0.754 1.84 1.111 1.159 1.174 1.293

Buy-and-hold strategy in a growth index Buy-and-hold strategy in a value index ‘Perfect’ forecasting strategy Momentum 1 strategy Momentum 2 strategy Economic strategy with three variables Economic strategy with five variables

Figure 1: Portfolio values obtained by each strategy over time.

obtained by the economic strategy with five variables to exceed the value of the portfolio obtained by the buy-and-hold strategy in a value index.

Table 2: Success rate of prediction of each strategy Strategy used

Success rate(%)

Momentum 1 strategy Momentum 2 strategy Economic strategy with three variables Economic strategy with five variables

55.13 58.33 53.21 57.05

Some additional comments When analyzing what each strategy predicted and what really happened, we see that it is not the strategy that achieves the best success rate that gives the best portfolio value at the end of 2008. We also observe that the percentage of success4 of each strategy is between 50 per cent and 60 per cent (see Table 2).

Therefore, one might ask whether these success rates are significantly different from 50 per cent (‘skill’ versus ‘luck’). The results of the Pesaran–Timmermann market-timing test show that with a significance level of

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Table 3: Sharpe ratio of each strategy used Strategy used

Sharpe ratio

Buy-and-hold strategy in a growth index Buy-and-hold strategy in a value index ‘Perfect’ forecasting strategy Momentum 1 strategy Momentum 2 strategy Economic strategy with three variables Economic strategy with five variables

0.041666119 0.198555202 0.393862789 0.152102942 0.166050396 0.178177037 0.206888089

10 per cent the success rate of the Momentum 1 and Momentum 2 strategies is statistically different from 50 per cent. These two strategies are thus significant. In particular, the Momentum 2 strategy is significantly different from 50 per cent with a very small P-value. The economic strategy with three variables is not statistically significant, but the one with five variables is. In addition, we also report the Sharpe ratio5 for each strategy in Table 3. A first observation is that the buy-andhold strategy in a growth index is riskier than the one investing in a value index. The Sharpe ratios of the Momentum 1, Momentum 2 strategies and the economic strategy with three variables are somewhat lower than that of the buy-and-hold strategy in a value index. It is thus a little bit riskier to follow one of these three strategies rather than investing only in a value index over time. Nevertheless, the economic strategy with five variables has a Sharpe ratio slightly higher than that of a buy-and-hold strategy in a value index.

Investment strategies in largecap–small-cap indexes Results Starting to invest 100 h with a buy-and-hold strategy in a large-cap index in the first quarter of 1970, the value of our portfolio is 2715 h at the end of 2008. If the investor decides instead to follow a buy-and-hold investment strategy in a small-cap index from

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the first quarter of 1970, the value of its portfolio at the end of 2008 is 2630 h. With the Momentum 1 strategy since 1970, we obtain at the end of 2008 a portfolio value of 2786 h. The results obtained by the Momentum 2 strategy are much better as the value of the portfolio at the end of 2008 is 8227 h. In the third strategy, we again use the logit model (with three economic variables) to predict in what style to invest in the next period. In this case, the three variables that enable to make the best forecasts are the economic growth (based on the GDP), the yield spread and the Conference Board Leading Economic Index. The results obtained by this strategy are better than those obtained by the buy-and-hold strategies and the Momentum 1 strategy, but worse than those of the Momentum 2 strategy. Indeed, the portfolio value at the end of 2008 is now equal to 5014 h. The last strategy is the same as the previous strategy, but adds two variables in the logit to attempt to gain greater accuracy in its forecasts. In this case, the two additional variables that provide the best forecasting power are the P/E ratio for the S&P500 index and a consumer price index as a measure of inflation. The results obtained by this strategy are again better than the strategy with three variables. The end value of our portfolio is 8648 h. Last, if we analyze what a ‘perfect’ forecasting strategy would deliver, we realize that even if a Momentum 2 strategy or an economic strategy with five variables gives good results, they are incomparable to a ‘perfect’ prediction strategy. Indeed, the portfolio value obtained in this case is 508 993 h. Table 4 provides a summary of the results obtained by the different strategies. Figure 2 plots the portfolio values obtained by each strategy over time.

Some additional comments If we compare the predictions made with the actual outcomes, we see that the strategy with the best success rate is not necessarily the one

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Table 4: Portfolio value obtained by each strategy at the end of 2008, and quarterly arithmetic average return of each strategy between 1970 and 2008 Strategy used

Portfolio value at the end of 2008 (h)

Quarterly arithmetic average return between 1970 and 2008 (%)

2715 2630 508993 2687 8227 5014 8648

0.834 0.991 2.053 0.893 1.139 0.914 1.173

Buy-and-hold strategy in a large-cap index Buy-and-hold strategy in a small-cap index ‘Perfect’ forecasting strategy Momentum 1 strategy Momentum 2 strategy Economic strategy with three variables Economic strategy with five variables

Figure 2: Portfolio values obtained by each strategy over time.

that gets the best value of the investment portfolio at the end of 2008. As in the case of the growth-value analysis, the percentage of success of each strategy is above 50 per cent (see Table 5). The Pesaran–Timmermann markettiming test shows that, with a significance level of 10 per cent, the Momentum 2 strategy and the logit strategy with five variables are statistically significant. The Momentum 1 strategy and the economic strategy with three variables are, in turn, not statistically different from 50 per cent and

Table 5: Success rate of prediction of each strategy Strategy used

Success rate (%)

Momentum 1 strategy Momentum 2 strategy Economic strategy with three variables Economic strategy with five variables

52.56 57.05 53.21 57.69

therefore not significant. Table 6 provides the Sharpe ratios of the strategies. Table 6 shows that the buy-and-hold strategy in a large-cap index is riskier than the one investing in a small-cap index. The

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Table 6: Sharpe ratio of each strategy used Strategy used

Sharpe ratio

Buy-and-hold strategy in a large-cap index Buy-and-hold strategy in a small-cap index ‘Perfect’ forecasting strategy Momentum 1 strategy Momentum 2 strategy Economic strategy with three variables Economic strategy with five variables

0.079 0.087 0.408 0.081 0.15 0.086 0.151

Momentum 1 strategy and the economic strategy with three variables are somewhat more risky than the buy-and-hold strategy in a small-cap index, but less risky than the one investing in large-cap index. Finally, the Momentum 2 strategy and the economic strategy with five variables are significantly less risky strategies than the buy-and-hold strategies, although the strategy with five variables has a Sharpe ratio slightly higher than the Momentum 2 strategy. Following a Momentum 2 investment strategy or an economic strategy with five variables enables thus to obtain a portfolio value at the end of 2008, which is higher than that obtained by the buy-and-hold strategies, while reducing its risk.

computed Sharpe ratios and Pesaran– Timmermann market-timing tests. In the first part of the analysis (growth and value indexes), the logit style-switching strategy with five economic variables (economic growth, the yield spread, an indicator of investor confidence in the market, the term spread and inflation) gave the highest value of the portfolio at the end of the investing period and it was also the least risky. This strategy is also statistically significant in terms of market switching (Pesaran–Timmermann test). As far as small-cap and large-cap indexes are concerned (second part of the analysis), we concluded that the least risky strategy and the one leading to the highest portfolio value was again the logit style-switching strategy strategy with five variables (the term spread, used in the first part of the analysis, is replaced here by the P/E ratio of the S&P500 index). This strategy is also statistically significant in terms of market switching. Although the choice of variables to include in the logit models and the investment results probably depend on the time period considered and the country under analysis, our study shows that style switching could give interesting investment results, at least before transaction costs.

CONCLUSION In this study, we examined whether an investor should choose a style rotation strategy (that is style investing) rather than a buy-and-hold strategy or a momentum strategy. We ran out-of-sample forecasting/ investing horse races between style rotation strategies (based on logit models), simple momentum strategies and buy-and-hold strategies. Regarding style rotation strategies, we considered logit switches between value and growth indexes, and small-cap and largecap indexes (we used the freely available Fama-French dataset that segments US stocks into value and growth stocks, and small-cap and large-cap stocks). In addition to the usual end-of-period return measures, we also

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ACKNOWLEDGEMENTS The authors thank the National Bank of Belgium for a research grant that helped them with the data and empirical analysis. All scientific reponsibilities are assumed by the authors.

NOTES 1. Value stocks are stocks for which demand is currently low, that is stocks generally believed to be undervalued by the market. These shares have some common characteristics: a low P/E ratio, a high book-to-market ratio and a high ‘cash-flow/share price’ ratio. In contrast, growth stocks are stocks that have performed well recently, for which there is high demand and that may therefore be overvalued by the market. Their characteristics are: a high P/E ratio, a low book-to-market ratio and a low ‘cash-flow/share price’

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2.

3. 4.

5.

ratio. Small-cap stocks are companies whose market capitalization is small, unlike the large-cap stocks whose market capitalization is important. Such evidence can be found in Capual et al (1993), Arshanapalli et al (1998), Fama and French (1998), Bauman et al (1997) and Reinganum (1999). http://mba.tuck.dartmouth.edu/pages/faculty/ ken.french/data_library.html The percentage or success rate is the ratio between the number of times that the prediction of investment in the style that gave the best returns, corresponded with reality, and the number of predictions made. The Sharpe ratio is calculated as follows: The arithmetic performance of the portfolio less the risk free rate, divided by the standard deviation of the portfolio.

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