Quantitative Stock Selection: Combining Value and Momentum Strategies
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Quantitative Stock Selection: Combining Value and Momentum Strategies
Table of Contents: Summary
4
Section I Value Strategies - Summary of Quantitative Academic Research Value Strategies – Foundational Academic Research Value Strategies – Further Evidence from Recent Studies
5 5 11
Section II Momentum Strategies - Summary of Quantitative Academic Research Momentum Strategies – Foundational Academic Research Momentum Strategies – Further Evidence from Recent Studies
13 13 16
Section III Combining Value and Momentum Strategies for Quantitative Stock Selection – Empirical Results Academic Research Supporting a Combined Stock Selection Strategy Empirical Results for a Combined Stock Selection Strategy using a Multi-Factor Value Model Combined with a Multi-Factor Momentum Model Backtesting the Multifactor Value Model Backtesting the Multifactor Momentum Model Backtesting the Combined Multifactor Value and Multifactor Momentum Strategy
19 19 20 21
Section IV Conclusion
23
Glossary
24
References
25
Important Information
26
For professional investor use only. Not for use with the public.
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Quantitative Stock Selection: Combining Value and Momentum Strategies
Summary: Traditional market capitalization weighted indexes are designed to measure the average performance of a group of stocks that are considered to be representative of either the broad market or a specific segment of the market. In order to be as representative as possible of the applicable group of underlying stocks, the performance goal of traditional market capitalization weighted indexes is to achieve a unitary “beta” versus their market segment. The emphasis on “beta” makes these indexes ideal for use in gauging the performance of active portfolio managers, who are trying to beat the index or generate “alpha”.“Alpha” has been elusive for many active portfolio managers that employ subjective stock selection methods. Some blame the failure of subjective analysis on the inherent lack of discipline of human managers who may follow hunches, or let emotions dominate their decision-making, leading to systematic biases. In contrast to subjective management, academic literature supports the possibility of generating outperformance through the use of purely quantitative measures. In order for a quantitative approach to stock selection to be successful, the model employed must capitalize on systematic deviations in the stock price from its fair value. The search for exploitable inefficiencies in equity prices has generally centered on value and momentum strategies. This paper will attempt to show the merits of a quantitative approach to stock selection that combines value and momentum strategies and is organized into three sections. Section I will describe the value effect, and present both well-known foundational academic literature and recently published research papers that provide further evidence for the outperformance of value stocks. Section II will describe the momentum effect and present evidence from early, as well as recent, studies documenting the outperformance of recently strong performing stocks (Winners) over recently poor performing stocks (Losers). Section III will provide evidence for the merits of an investment approach that utilizes value and momentum strategies as components in a combined quantitative stock selection strategy.
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Quantitative Stock Selection: Combining Value and Momentum Strategies
Section I Value Strategies - Summary of Quantitative Academic Research The Value effect is the term for the predictive power of scaled-price ratios such as book to market value or cash flow per share to price, where some measure of fundamentals is scaled by price. The higher the ratio, the cheaper a stock is on the basis of fundamentals relative to price. Empirically, there is evidence that Value stocks (relatively cheaper stocks) outperform Glamour stocks (relatively expensive stocks).
Value Strategies – Foundational Academic Research: A generation ago, the Sharpe-Lintner-Black model, commonly referred to as the Capital Asset Pricing Model (Sharpe 1964)19, was the generally accepted model of return prediction. The model held that there were two components of risk: stock-specific risk or idiosyncratic risk and risk related to a stock’s relationship to the market as a whole or systematic risk. Since stock-specific risk could be diversified away, investors would only be compensated for the systematic risk of their equity holdings, captured by the linear regression coefficient of each individual stock’s monthly returns on the monthly returns of a proxy for the broad market. Each stock’s estimated regression coefficient is referred to as the CAPM beta of the stock. A major challenge to this single factor view was presented by Fama and French in the early 1990s. Eugene Fama and Kenneth French popularized the use of Price/Book as a return predictor when they introduced their well-known three factor model of expected returns in 1992. They found that when size (market value of equity – ME) and the ratio of book value to price (BE/ME see table one) are taken into account, the predictive power of beta coefficients become statistically insignificant. Two tables of data from their 1992 publication demonstrate the relative importance of price to book and size in comparison to beta in explaining the future monthly returns of individual stocks. Table I summarizes the monthly returns of equallyweighted portfolios formed on size and book value to price from July 1963 to December 1990, while Table II shows the average monthly returns for equally-weighted portfolios of stocks sorted into deciles based on beta over the same period. As can be seen in Table I, over all size decile portfolios the highest book-to-price decile portfolio outperformed the lowest book-to-price decile portfolio by 99 basis points per month (≈ 12% per year). A clear upward trend can be observed from left to right across Table I; higher book-to-price portfolios generated higher returns at each decile when all size deciles of stocks are considered. While the effect is diminished somewhat for the very largest decile of stocks, the return difference is still 25 basis points per month for these stocks and the spread is consistently larger for all nine of the other size deciles, ranging from 52 basis points to 136 basis points per month. The relationship between beta and stock returns is less significant (see Table II), with the lowest beta decile stocks outperforming the highest beta stocks by 20 basis points per month. Significantly, not only is the spread between the highest beta decile portfolio and lowest beta decile portfolio much lower than the spread between highest and lowest book-to-price decile portfolios, the direction of the spread is the opposite of what the Capital Asset Pricing Model predicts. According to the CAPM, holders of higher beta stocks are supposed to be compensated for greater exposure to the risk in the overall market. As Fama and French have shown, empirically, this is not the case.
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Quantitative Stock Selection: Combining Value and Momentum Strategies AlphaDEX®
Table I: Average Monthly Returns on Portfolios Formed on Size and Book-to-Market Equity; Stocks Sorted by ME (Down) and then BE/ME (Across): July 1963 – December 1990 In June of each year t, the NYSE, AMEX, and NASDAQ stocks that meet the CRSP-COMPUSTAT data requirements are allocated to 10 size portfolios using the NYSE size (ME) breakpoints. The NYSE, AMEX and NASDAQ stocks in each size decile are then sorted into 10 BE/ME portfolios using the book-to-market ratios for year t – 1. BE/ME is the book value of common equity plus balance sheet deferred taxes for fiscal year t – 1, over market equity for December of year t – 1. The equal-weighted monthly portfolio returns are then calculated for July of year t to June of year t + 1. Average monthly return is the time-series average of the monthly equal-weighted portfolio returns. The All column shows average returns for equal-weighted portfolios of the stocks in each BE/ME group
Book-to-Market Portfolios Size All 1(Small) 2 3 4 5 6 7 8 9 10 (Large)
All 1.23% 1.47 1.22 1.22 1.19 1.24 1.15 1.07 1.08 0.95 0.89
1 (Low) 0.64% 0.70 0.43 0.56 0.39 0.88 0.70 0.95 0.66 0.44 0.93
2 0.98% 1.14 1.05 0.88 0.72 0.65 0.98 1.00 1.13 0.89 0.88
3 1.06% 1.20 0.96 1.23 1.06 1.08 1.14 0.99 0.91 0.92 0.84
4 1.17% 1.43 1.19 0.95 1.36 1.47 1.23 0.83 0.95 1.00 0.71
5 1.24% 1.56 1.33 1.36 1.13 1.13 0.94 0.99 0.99 1.05 0.79
6 1.26% 1.51 1.19 1.30 1.21 1.43 1.27 1.13 1.01 0.93 0.83
7 1.39% 1.70 1.58 1.30 1.34 1.44 1.19 0.99 1.15 0.82 0.81
8 1.40% 1.71 1.28 1.40 1.59 1.26 1.19 1.16 1.05 1.11 0.96
9
10 (High) 1.50% 1.63% 1.82 1.92 1.43 1.79 1.54 1.60 1.51 1.47 1.52 1.49 1.24 1.50 1.10 1.47 1.29 1.55 1.04 1.22 0.97 1.18
Source: From Fama and French (1992).9
Table II: Average Monthly Returns on Portfolios Formed Beta (β): July 1963 – December 1990 Portfolios are formed yearly. All NYSE, AMEX and NASDAQ stocks that meet the CRSP-COMPUSTAT data requirements are allocated to into 10 β portfolios using pre-ranking βs of individual stocks, estimated with 2 to 5 years of monthly returns (as available) ending in June of year t (t = 1963-1990). The equal-weighted monthly returns on the resulting portfolios are then calculated for July of year t to June of year t + 1. The average return is the time-series average of the monthly equal-weighted portfolio returns. Beta (β) - Portfolios Size
All- β
Low-β
β -2
β -3
β -4
β -5
β -6
β -7
β -8
β -9
High -β
All-sizes
1.25%
1.34%
1.29%
1.36%
1.31%
1.33%
1.28%
1.24%
1.21%
1.25%
1.14%
Source: From Fama and French (1992).9
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Quantitative Stock Selection: Combining Value and Momentum Strategies
At about the same time as Fama and French’s three-factor model study on the U.S. market, Chan, Hamao and Lakonishok (1991)6 tested the predictive power of three different valuation measures in the Japanese stock market: book value to price, cash flow to price, and earnings-to-price. Examining fundamental data for both first and second section stocks listed on the Tokyo Stock Exchange from July 1971 to December 1988, they found that after accounting for beta and size that both book value to price and cash flow to price were statistically significant predictors of future returns.* They found a 1.1% monthly return difference on average between portfolios formed using the highest quartile of book-to-price stocks versus portfolios formed using the lowest quartile of book-to-price stocks. When stocks were sorted by cash flow to price, the highest quartile of cash flow to price stocks outperformed the lowest quartile of cash flow to price stocks by 79 basis points per month. It is important to note that the valuations in the surging Japanese market were very different from the U.S. market during the time of the study; as a result the evidence from Japan helps to set aside critiques that the value outperformance is merely the result of data snooping. Further international confirmation of the profitability of value strategies was presented by Fama and French (1998)11. They examined the return spreads between portfolios comprised of the highest 30 percent book-toprice stocks and portfolios formed with the lowest 30 percent book-to-price stocks using data for 13 countries over a twenty year period from 1975 - 1995. In 12 out of 13 markets the high book-to-price portfolios outperformed the low high book-to-price portfolios (see Table III). Similarly, high-low portfolio combinations using cash flow to price (see Table III), earnings to price and dividends to price resulted in positive return spreads in 12, 12 and 10 out of 13 countries respectively.
*Earnings to price was not unambiguously significant in Chan, Hamao and Lakonishok’s (CHL) study.6 While significant in univariate tests, the regression coefficient of earnings yield was either not significant or reversed its sign when other variables (B/P, CF/P) were included under various different estimation methods. CHL suggest the low quality of Japanese earnings due to rules on depreciation methods and the reliance of earnings on manipulable accruals are two potential explanations.
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Quantitative Stock Selection: Combining Value and Momentum Strategies
Table III: Annual Dollar Returns in Excess of U.S. T-Bill Rate for Market, Value and Growth Portfolios: 1975 – 1995 Value and growth portfolios were formed at the end of each year 1974 to 1994, based on sorted values of B/M, E/P, C/P, and D/P. P and M are based on price per share at the time of portfolio formation. E, C and D are the most recent available trailing year of earnings, cashflow (earnings plus depreciation), and dividends per share. B is the most recent available book common equity per share. Value portfolios (indicated with a leading H, for high) include firms whose ratio (B/M, E/P, C/P, or D/P) is among the highest 30 percent for a given country. Growth portfolios (indicated with a leading L, for low) include firms in the bottom 30 percent. H – L is the difference between the high and low returns. Market is the global market portfolio return. The global market portfolios are comprised of all 13 countries listed. Firms are market capitalization weighted in the country portfolios; countries are weighted by Morgan Stanley’s country weights in the global portfolios. The first row for each country is the average annual return. The second is the standard deviation of the annual returns (in parentheses) or the t – statistic testing whether H – L is different from zero [in brackets]. (results for E/P, D/P omitted for brevity).
Market U.S. Japan U.K. France Germany Italy Netherlands Belgium Switzerland Sweden Australia Hong Kong Singapore
9.57 (14.64) 11.88 (28.67) 15.33 (28.62) 11.26 (32.35) 9.88 (31.36) 8.11 (43.77) 13.30 (18.81) 12.62 (25.88) 11.07 (27.21) 12.44 (24.91) 8.92 (26.31) 22.52 (41.96) 13.31 (27.29)
H B/M 14.55 (16.92) 16.91 (27.74) 17.87 (30.03) 17.10 (36.60) 12.77 (30.35) 5.45 (35.53) 15.77 (33.07) 14.90 (28.62) 13.84 (30.00) 20.61 (38.61) 17.62 (31.03) 26.51 (48.68) 21.63 (36.89)
L B/M 7.75 (15.79) 7.06 (30.49) 13.25 (27.94) 9.46 (30.88) 10.01 (32.75) 11.44 (50.65) 13.47 (21.01) 10.51 (27.63) 10.34 (28.57) 12.59 (26.26) 5.30 (27.32) 19.35 (40.21) 11.96 (27.71)
H–L B/M 6.79 [2.17] 9.85 [3.49] 4.62 [1.08] 7.64 [2.08] 2.75 [0.92] -5.99 [-0.91] 2.30 [0.44] 4.39 [1.99] 3.49 [0.80] 8.02 [1.16] 12.32 [2.41] 7.16 [1.35] 9.67 [2.36]
H C/P 13.74 (16.73) 14.95 (31.95) 18.41 (35.11) 16.17 (36.92) 13.28 (29.05) 11.05 (43.52) 11.66 (33.02) 16.46 (28.84) 12.32 (36.58) 17.08 (30.56) 18.32 (29.08) 29.33 (46.24) 13.42 (26.24)
L C/P 7.08 (15.99) 5.66 (29.22) 14.51 (26.55) 9.30 (31.26) 5.14 (26.94) 0.37 (38.42) 11.84 (23.26) 12.03 (25.57) 9.78 (27.82) 12.50 (23.58) 4.03 (27.46) 20.24 (42.72) 8.03 (28.92)
H –L C/P 6.66 [2.08] 9.29 [3.03] 3.89 [0.85] 6.86 [2.29] 8.13 [2.62] 10.69 [1.73] -0.19 [-0.03] 4.44 [1.27] 2.53 [0.41] 4.58 [0.90] 14.29 [2.85] 9.09 [1.37] 5.39 [1.49]
Source: From Fama and French (1998).11 The universe for each country listed in the above table is compiled from the constituents of the MSCI EAFE Index®.
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Quantitative Stock Selection: Combining Value and Momentum Strategies
As the above studies demonstrate, the fact that value (e.g. high book to price, high cash flow to price) stocks have historically outperformed glamour (e.g. low book to price, low cash flow to price) is well documented. There are differing views on what causes the outperformance. Fama and French (1992)9 argued that value stocks are fundamentally riskier and, in a rational market, investors are compensated for bearing this extra risk. Others, such as DeBondt and Thaler (1985)8 argued that behavioral errors by investors, such as a tendency to extrapolate past earnings growth into the future cause stocks to be overvalued or undervalued. Lakonishok, Shleifer and Vishny (1994)16 evaluate the risk-based explanation. As they point out, if the risk-based explanation is plausible, value stocks must underperform during “bad states” of the world, when the marginal utility of wealth is high and risk-averse investors demand a greater premium. Using data from 1968 to 1989, Lakonishok, Shleifer and Vishny compared the return performance of high book to price stocks (value) with low book to price stocks during the worst stock market months and the worst GNP growth quarters (see Table IV).
Table IV: Performance of Value Portfolios in Best and Worst Times: 1968 – 1989 Panel 1: All months in the sample are divided into the 25 worst stock market months based on the equally weighted index (W25), the remaining 88 negative months other than the 25 worst (N88), the 122 positive months other than the 25 best (P122) and the 25 best months (B25) in the sample. At the end of each April between 1968 and 1989, 10-decile portfolios are formed based on the ratio of end-of-previous year’s book value to end-ofApril market value of equity (B/M). For each portfolio (changing every April), Panel 1 presents its average return over the W25, N88, P122, and B25 months. Panel 2 has the same structure as Panel 1, but the states are defined in terms of the best and worst quarters for GNP growth. All quarters in the sample are divided into 4 sets: 10 quarters of the lowest real GNP growth during the sample period (W10), 34 next lowest real GNP growth quarters (N34), 34 next worst growth quarters (NB34), and 10 highest real GNP growth quarters(B10). Panel 1: Portfolio Returns across Best and Worst Stock Market Months
B/M W25 N88 P122 B25
B/M W10 N34 NB34 B10
Low B/M (Glamour) 1 2
3
4
5
6
7
8
High B/M (Value) 9 10
-0.112 -0.110 -0.104 -0.100 -0.097 -0.091 -0.093 -0.092 -0.098 -0.102 -0.029 -0.028 -0.026 -0.025 -0.023 -0.020 -0.021 -0.02 -0.018 -0.022 0.038 0.040 0.039 0.037 0.036 0.037 0.038 0.037 0.038 0.039 0.114 0.114 0.119 0.113 0.112 0.113 0.117 0.126 0.133 0.148 Panel 2: Portfolio Returns across Best and Worst GNP Growth Quarters Low B/M (Glamour) 1 2 -0.004 0.011 0.022 0.092
0.001 0.008 0.028 0.102
3
4
5
6
7
8
0.012 0.011 0.027 0.118
0.018 0.009 0.025 0.117
0.009 0.008 0.030 0.117
0.016 0.010 0.035 0.135
0.017 0.010 0.036 0.132
0.028 0.016 0.035 0.141
High B/M (Value) 9 10 0.021 0.017 0.041 0.145
0.015 0.012 0.039 0.151
ValueGlamour (9, 10 t-statistic – 1, 2) 0.011 1.802 0.008 2.988 -0.001 -0.168 0.026 1.729
ValueGlamour (9, 10 t-statistic – 1, 2) 0.020 0.983 0.005 0.494 0.012 1.555 0.051 2.685
Source: Lakonishok, Shleifer and Vishny (1994)16
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Quantitative Stock Selection: Combining Value and Momentum Strategies
The evidence provided in Table IV demonstrates that value stocks have actually outperformed glamour stocks during the worst 25 months in the sample, with the top quintile book to price stocks outperforming the lowest quintile book to price stocks by an average of 1.10% per month. During the worst 10 quarters for GNP growth, high book to price stocks outperformed low book to price stocks by a full 2 percent. In addition to the univariate results on book to market and other valuation measures that have already been discussed, there is evidence that the use of multiple quantitative measures can improve returns even further. Chan and Lakonishok (2004)7 tested the use of a composite valuation measure that combined book to price, cash flow to price, earnings to price and sales to price. Using a regression model to weight the four value factors, both small and large capitalization portfolios formed using the composite valuation measure outperformed both broad and value only benchmarks (See Table V). Piotroski (2001)17 attempts to refine a value-based stock selection model by adding fundamental factors to focus on financially strong firms within a universe of high book to price stocks. He found that indicator variables for positive return on assets and cash flow were the most correlated with higher returns among alternative measures of financial health.
Table V: Geometric Mean Returns to Value and Growth Strategies using a Composite Valuation Measure: 1969 – 2001 Large-cap stocks Portfolio years 1969-2001 1979-2001 1990-2001
1 (glamour)
2
9
4.5% 7.9 3.8
6.7% 10.4 6.0
1 (glamour)
2
10 (value)
Russell 1000 Value Return
15.6% 16.4% 18.6 20.4 16.1 18.0 Small-cap stocks
NA 15.4% 12.9
S&P 500 Return 11.4% 15.1 12.9
(Deciles 9,10) (Deciles 1,2) 10.4% 10.4 12.2
Portfolio years 1969-2001 1979-2001 1990-2001
-2.8% -1.8 -6.2
4.8% 7.8 3.6
9
10 (value)
16.6% 20.8 18.4
18.3% 22.8 17.7
Russell 2000 Russell 2000 (Deciles 9,10) Value Return Return (Deciles 1,2) NA 16.0% 13.4
NA 13.8% 11.0
16.5% 18.8 19.4
Source: Chan and Lakonishok (2004).7
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Quantitative Stock Selection: Combining Value and Momentum Strategies
Value Strategies – Further Evidence from Recent Studies: The foundational academic studies cited earlier presented evidence from both domestic and international markets that the use of valuation ratios such as book to price would be a reasonable approach to security selection. Fama and French recently updated their original study (Fama/French 1992, cited in section I)9 to examine whether value stocks still provided excess returns over growth stocks. Examining more recent data from 1990 – 2011, the authors found that value premiums existed in four developed market regions: North America, Europe, Japan and Asia-Pacific. Table VI contains data from their new study (Fama/French 2012)12, which divides stock universes within each region by size quintiles before separating them further into value quintiles based on Book to Market Value (B/M). As can be seen on the table in North America as well as other regions, there is a pattern of stocks in the highest B/M quintile (Value) outperforming stocks in the lowest B/M quintile, and that the outperformance of value is generally stronger in smaller market cap quintiles.
Table VI: Value Effect in Developed Markets Average Monthly Excess Returns for 25 Portfolios Formed on Size Quintiles and Book to Market Value (B/M) Quintiles: November 1990 – March 2011 Low B/M
2
3
4
High B/M
Global Small 2 3 4 Big
0.07 0.09 0.21 0.37 0.29
0.48 0.46 0.40 0.43 0.36
0.77 0.59 0.52 0.52 0.49
0.83 0.69 0.57 0.60 0.53
1.12 0.79 0.74 0.69 0.53
North America Small 2 3 4 Big
0.50 0.34 0.90 0.80 0.54
0.75 0.73 0.70 0.73 0.56
1.13 0.95 0.87 0.89 0.62
1.04 0.94 0.86 0.84 0.66
1.42 1.08 1.08 0.96 0.64
Europe Small 2 3 4 Big
-0.13 0.10 0.21 0.39 0.31
0.29 0.42 0.54 0.57 0.52
0.44 0.53 0.62 0.66 0.65
0.66 0.78 0.62 0.64 0.76
0.88 0.89 0.86 0.88 0.73
Japan Small 2 3 4 Big
-0.17 -0.45 -0.42 -0.50 -0.33
-0.08 -0.37 -0.39 -0.18 -0.10
0.02 -0.13 -0.27 -0.21 -0.10
0.08 0.01 -0.16 0.00 0.18
0.22 0.03 0.13 0.05 0.35
Asia Pacific Small 2 3 4 Big
0.39 0.17 0.10 0.90 0.69
0.61 0.51 0.77 0.96 0.97
0.87 0.63 0.88 0.66 0.95
1.17 0.79 1.00 1.08 0.94
1.61 1.06 0.92 1.16 1.13
Source: Fama and French (2012)12
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Quantitative Stock Selection: Combining Value and Momentum Strategies
While the recent Fama and French study provided more evidence for the value effect within developed markets, Cakici, Fabozzi and Tan (2013)4 recently performed a similar study of the value effect in emerging markets. Examining the same time period (1990 – 2011), Cakici and his co-authors found that value premiums existed in three emerging market regions: Asia, Latin America and Eastern Europe. Table VII contains data from their research, which, following Fama and French’s methodology, divides stock universes within each emerging region by size quintiles before separating them further into value quintiles based on Book to Market Value (B/M). As can be seen on the table, in emerging markets, there is a pattern of stocks in the highest B/M quintile (Value) outperforming stocks in the lowest B/M quintile, and that the outperformance of value stocks (i.e. the difference between the highest B/M column on the table and the lowest B/M column) is generally stronger in emerging markets overall than in developed markets overall over the time period.
Table VII: Value Effect in Emerging Markets Monthly Excess Returns for 25 Portfolios Formed on Size and Book to Market Value (B/M): January 1991 – December 2011 Low B/M
2
3
4
High B/M
Asia Small 2 3 4 Big
-0.32 -0.33 0.10 0.13 -0.16
0.61 0.31 0.66 0.18 0.05
0.26 0.74 0.61 0.50 0.30
0.84 0.82 0.74 0.54 0.56
1.80 1.44 1.17 0.88 1.23
Latin America Small 2 3 4 Big
1.30 1.37 1.13 1.64 -0.06
0.67 0.88 0.68 0.90 0.81
0.77 0.56 1.19 1.07 0.90
1.10 1.37 1.09 1.14 1.48
2.28 2.80 2.04 1.19 1.77
Eastern Europe Small 2 3 4 Big
-0.44 1.10 0.49 0.49 0.49
1.30 0.69 0.46 1.44 0.78
2.27 1.17 0.47 0.20 0.57
2.69 2.35 1.40 0.86 1.55
3.02 1.92 1.69 2.64 2.98
All Emerging Small 2 3 4 Big
0.31 0.47 0.45 0.30 -0.13
0.41 0.68 0.40 0.21 0.31
0.77 0.76 0.52 0.66 0.39
1.05 0.80 0.67 0.62 0.62
1.87 1.54 1.21 1.23 1.45
U.S. Small 2 3 4 Big
0.35 0.67 0.60 0.89 0.68
1.05 0.94 0.97 0.96 0.80
1.18 1.12 1.07 0.87 0.70
1.27 1.01 0.96 1.05 0.63
1.30 1.04 1.31 0.82 0.54
All Developed Small 2 3 4 Big
0.36 0.34 0.49 0.63 0.54
0.67 0.65 0.61 0.65 0.60
0.94 0.80 0.75 0.75 0.71
1.02 0.87 0.82 0.83 0.76
1.31 0.99 0.96 0.91 0.68
Source: Cakici, Fabozzi and Tan (2013)4
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Quantitative Stock Selection: Combining Value and Momentum Strategies
Section II Momentum Strategies - Summary of Quantitative Academic Research Price momentum is the tendency for stocks that have generated superior returns in certain past intervals (3 months, 6 months and 12 months) to continue to outperform low past return stocks over the next 3 to 12 months. It is an asset pricing anomaly that has confounded efficient markets adherents. Eugene Fama (1996, p 81)10 has said that the “main embarrassment of the three-factor model” is “its failure to capture the continuation of short-term returns documented by Jegadeesh and Titman (1993)13 and Asness (1994)1.”
Momentum Strategies – Foundational Academic Research: Jegadeesh and Titman are among the most commonly cited early researchers of the momentum anomaly. Table VIII summarizes results from an update (2001)14 of their initial study (1993)13. All stocks that trade on the three major U.S. exchanges are sorted into equally weighted decile portfolios on the basis of past performance over the previous six months. From 1965 to 1998, the strongest past performance stocks (i.e. past winner decile) outperformed the worst performing stocks over the prior six months by an average of 1.23% per month over the next six months. The effect was statistically significant in both large and small capitalization stocks, and was robust over both the time period of their original study (1965 – 1989) and the additional subperiod covered by their updated research (1990 -1998).
Table VIII: Momentum Portfolio Returns This table reports the monthly returns for momentum portfolios formed based on past six-month returns and held for six months. P1 is the equal-weighted portfolio of 10 percent of the stocks with the highest returns over the previous six months; P2 is the equal-weighted portfolio of 10 percent of the stocks with the next highest returns, and so on. The “All Stocks” sample includes all stocks traded on the NYSE, AMEX, or NASDAQ excluding stocks priced less than $5 at the beginning of the holding period and stocks in the smallest market cap decile (NYSE size decile cutoff ). The “Small Cap” and “Large Cap” subsamples comprise stocks in the “All Stocks” sample that are smaller and larger than the median market cap NYSE stock respectively. “EWI” is the return on the equal-weighted index of stocks in each sample. All Stocks
P1 (Past Winners) P2 P3 P4 P5 P6 P7 P8 P9 P10 (Past Losers) P1-P10 t statistic EWI
1965 1998 1.65 1.39 1.28 1.19 1.17 1.13 1.11 1.05 0.90 0.42 1.23 6.46 1.09
1965 1989 1.63 1.41 1.3 1.21 1.18 1.15 1.12 1.05 0.94 0.46 1.17 4.96 1.10
Small Cap 1990 1998 1.69 1.32 1.21 1.13 1.12 1.09 1.09 1.03 0.77 0.30 1.39 4.71 1.04
1965 1998 1.70 1.45 1.37 1.26 1.26 1.19 1.14 1.09 0.84 0.28 1.42 7.41 1.13
1965 1989 1.69 1.50 1.42 1.34 1.33 1.26 1.20 1.17 0.95 0.35 1.34 5.60 1.19
Large Cap 1990 1998 1.73 1.33 1.23 1.05 1.06 1.01 0.99 0.89 0.54 0.08 1.65 5.74 0.98
1965 1998 1.56 1.25 1.12 1.10 1.05 1.09 1.09 1.04 1.00 0.7 0.86 4.34 1.03
1965 1989 1.52 1.24 1.10 1.07 1.00 1.05 1.04 1.00 0.96 0.68 0.85 3.55 1.00
1990 1998 1.66 1.27 1.19 1.20 1.19 1.20 1.23 1.17 1.09 0.78 0.88 2.59 1.12
Source: Jegadeesh and Titman (2001).14
13 For professional investor use only. Not for use with the public.
Quantitative Stock Selection: Combining Value and Momentum Strategies
To test for a risk-based explanation of the effect, Jegadeesh and Titman calculated alphas using two of the most popular models of expected return; the Fama-French three factor model and the Capital Asset Pricing Model (Table IX). Both the CAPM alpha (1.24) and the Fama-French alpha (1.36) are slightly larger than the unadjusted average return spread and are statistically significant with t-statistics of 6.5 and 7.04, respectively. Since neither a CAPM nor a Fama-French risked-based explanation could now be deemed likely, Jegadeesh and Titman examined behavioral explanations such as underreaction to fundamental news. Past strong price performance of individual firms is presumably the result of strong past fundamental performance, such as quarterly earnings surprises. As Bernard and Thomas (1990)3 have documented, year over year quarterly earnings changes display significant positive autocorrelation for two subsequent quarters. As a result of this pattern, it is evident that there is information about future earnings changes in past fundamental news releases. In the absence of underreaction, investors should anticipate this pattern. Upon detailed examination, Jegadeesh and Titman (1993)13 found that a disproportionately large and statistically significant percentage of the subsequent excess returns generated by price momentum portfolios are realized in a three-day period around subsequent earnings announcements. The implication is that investors are surprised by the results of the subsequent earnings announcements and have not fully incorporated the information contained in prior period earnings releases.
Table IX: CAPM and Fama-French Alphas of Momentum Portfolios: January 1965 – December 1998 This table reports the intercepts from the market model regression (CAPM Alpha) and Fama-French threefactor model regression (FF Alpha). The t-statistics are reported in parentheses. CAPM Alpha 0.46 (3.03) 0.29 (2.86) 0.21 (2.53) 0.15 (1.92) 0.13 (1.70) 0.10 (1.22) 0.07 (0.75) -0.02 (-0.19) -0.21 (-1.69) -0.79 (-4.59) 1.24 (6.50)
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P1 – P10
FF Alpha 0.50 (4.68) 0.22 (3.51) 0.10 (2.31) 0.02 (0.41) -0.02 (-0.43) -0.06 (-1.37) -0.09 (-1.70) -0.16 (-2.50) -0.33 (-4.01) -0.85 (-7.54) 1.36 (7.04)
Source: Jegadeesh and Titman (2001).14
14 For professional investor use only. Not for use with the public.
Quantitative Stock Selection: Combining Value and Momentum Strategies
Like the value-driven stock selection strategies discussed earlier, price momentum based strategies may be refined with the use of multiple factors. Jegadeesh and Livnat (2006)15 confirm that earnings surprises that are driven primarily by sales changes rather than expense changes are more likely to produce future earnings surprises. As a result, strategies such as momentum that rely on underreaction to past earnings information could potentially be improved when combined with revenue change data. The use of multiple intervals to measure past price performance may also be useful. Alan Scowcroft and James Sefton (2005)18 provide a recent survey of the literature supporting the value of utilizing various price momentum based stock selection strategies. Table X is from their survey and provides updated evidence of momentum driven future returns. As can be seen in the table, three different past price performance intervals - 3 months, 6 months and 12 months are useful indicators of future returns.
Table X: Monthly Returns to Long-Short Momentum Strategies for Varying Portfolio Formation and Holding Periods: January 1992 – March 2003 Holding Period (K, months) Formation Period (J, months) 1 3 6 12 24 36
1 -0.78% (0.48) 0.04 (0.57) 0.59 (0.63) 0.92 (0.64) 0.67 (0.67) 0.35 (0.67)
3 0.11% (0.34) 0.42 (0.50) 0.87 (0.59) 1.05 (0.60) 0.75 (0.65) 0.48 (0.66)
6 0.31% (0.27) 0.71 (0.43) 1.00 (0.51) 0.93 (0.56) 0.66 (0.63) 0.37 (0.64)
12 0.38% (0.20) 0.65 (0.33) 0.86 (0.42) 0.79 (0.53) 0.36 (0.61) -0.23 (0.59)
24 0.18% (0.16) 0.32 (0.27) 0.38 (0.36) 0.25 (0.46) -0.34 (0.50) -0.75 (0.53)
36 0.04% (0.12) 0.10 (0.21) 0.14 (0.28) -0.02 (0.36) -0.53 (0.43) -1.02 (0.49)
Source: From Scowcroft and Sefton (2005).18 All returns measured in U.S. dollars; there was no gap between formation and holding period. Standard errors in parentheses.
15 For professional investor use only. Not for use with the public.
Quantitative Stock Selection: Combining Value and Momentum Strategies
Momentum Strategies – Further Evidence from Recent Studies: After the foundational academic studies cited earlier documented evidence for the outperformance of winners vs. losers, some academics (see Carhart 1997)5 suggested that the Fama and French three factor model should be extended to include momentum as a fourth factor in a standard model of expected equity returns. With the acceptance of momentum into the academic literature and as an addition to their well-known three factor model, Fama and French (2012)12 decided to test the more recent time period used in their updated work on value to see if the momentum effect was still evidenced in stock returns. Examining recent data from 1990 – 2011, the authors found that the outperformance of winner stocks (high past local currency return over the last 12 months, omitting the most recent month) has persisted in three out of four developed market regions: North America, Europe, and Asia-Pacific, with the lone exception of Japan.** Table XI contains data from the study, which divides stock universes within each region by size quintiles before separating them further into momentum quintiles based on past performance. As can be seen on the table, in developed markets overall, as well as regionally in North America, Europe, and Asia-Pacific, there is a pattern of recent strong performers (winner quintile) outperforming stocks with lower recent past returns (loser quintile), and that the outperformance of momentum is generally stronger in smaller market cap quintiles.
Table XI: Momentum Effect in Developed Markets Monthly Excess Returns for 25 Portfolios Formed on Size and Momentum: November 1990 – March 2011 Low Past Return
2
3
4
High Past Return
Global Small 2 3 4 Big
0.20 0.17 0.28 0.26 0.12
0.66 0.52 0.46 0.46 0.32
0.80 0.54 0.55 0.52 0.38
1.15 0.78 0.57 0.57 0.55
1.57 1.12 0.85 0.86 0.61
North America Small 2 3 4 Big
0.54 0.52 0.57 0.54 0.36
0.96 0.95 0.75 0.79 0.52
1.19 0.95 0.90 0.84 0.44
1.51 1.00 1.07 0.82 0.74
1.96 1.50 1.27 1.29 0.97
Europe Small 2 3 4 Big
-0.28 -0.16 0.19 0.27 0.22
0.38 0.46 0.43 0.52 0.47
0.61 0.66 0.63 0.65 0.69
1.03 0.88 0.77 0.77 0.65
1.75 1.45 1.11 1.11 0.77
Japan Small 2 3 4 Big
0.17 -0.10 -0.14 -0.11 -0.10
0.26 -0.03 -0.22 -0.11 -0.28
0.15 -0.06 -0.12 -0.18 -0.31
0.24 0.03 -0.02 -0.16 -0.12
-0.05 -0.09 -0.05 -0.05 -0.06
Asia Pacific Small 2 3 4 Big
0.60 -0.14 0.18 0.48 1.11
1.04 0.83 0.60 0.96 0.72
1.31 0.85 0.71 0.85 1.07
1.95 1.08 1.19 0.99 1.06
1.73 1.18 1.24 1.23 1.12
Source: Fama and French (2012)12 **Alternative explanations cited in the paper (Fama/French 2012)12 for the lack of evidence for Momentum in Japan over the recent period include the low return of the Japanese market over the period, cultural differences in Japanese investors, and chance. Fama/French seem to prefer chance as the best explanation.
16 For professional investor use only. Not for use with the public.
Quantitative Stock Selection: Combining Value and Momentum Strategies
Cakici, Fabozzi and Tan (2013)4 recently performed a similar study of the momentum effect in emerging markets, which is published in the same paper as their work on the value effect in emerging markets. Examining the same time period (1990 – 2011), Cakici and his co-authors found that winner stocks (high past local currency return over the last 12 months, omitting the most recent month) have outperformed in emerging markets overall and in two out of three emerging market regions: Asia and Latin America, with the lone exception of Emerging Europe. Table XII contains data from the study, which divides stock universes within each region by size quintiles before separating them further into momentum quintiles based on past performance. As can be seen on the table, in emerging markets overall, as well as regionally in Asia and Latin America, there is a pattern of recent strong performers (winner quintile) outperforming stocks with lower recent past returns (loser quintile), and, as in developed markets, the outperformance of momentum is generally stronger in smaller market cap quintiles.
Table XII: Momentum Effect in Emerging Markets Monthly Excess Returns for 25 Portfolios Formed on Size and Momentum: January 1991 – December 2011 Low Past Returns
2
3
4
High Past Returns
Asia Small 2 3 4 Big
0.88 0.50 0.22 0.09 0.10
1.06 0.58 0.32 -0.07 -0.10
1.32 1.13 0.82 0.46 0.11
1.56 1.51 1.11 0.84 0.46
1.74 1.45 1.18 1.10 0.62
Latin America Small 2 3 4 Big
0.14 -1.16 0.17 0.95 -0.23
0.64 0.39 0.37 0.02 -0.63
1.36 0.94 0.24 0.37 0.01
1.57 0.78 0.87 0.35 -0.14
1.55 0.38 -0.04 0.90 -0.19
Eastern Europe Small 2 3 4 Big
2.10 0.93 1.02 1.00 1.47
1.89 1.51 1.35 0.52 0.33
2.01 1.45 1.54 0.70 0.27
2.96 1.89 1.87 1.13 0.88
1.76 1.22 2.03 0.61 0.72
All Emerging Small 2 3 4 Big
1.09 0.50 0.17 0.01 0.45
0.98 0.77 0.37 0.27 -0.06
1.23 1.15 0.80 0.50 0.33
1.68 1.31 1.11 0.88 0.63
1.59 1.69 1.34 1.27 0.85
U.S. Small 2 3 4 Big
0.62 0.79 0.92 0.68 0.50
1.04 1.07 0.98 1.02 0.82
1.23 1.19 1.11 1.08 0.74
1.49 1.31 1.13 1.08 0.95
1.86 1.55 1.37 1.23 1.04
All Developed Small 2 3 4 Big
0.35 0.34 0.46 0.45 0.33
0.87 0.71 0.69 0.68 0.55
1.00 0.77 0.79 0.75 0.63
1.35 1.00 0.83 0.81 0.76
1.74 1.31 1.07 1.12 0.83
Source: Cakici, Fabozzi and Tan (2013)4
17 For professional investor use only. Not for use with the public.
Quantitative Stock Selection: Combining Value and Momentum Strategies
Section III Combining Value and Momentum Strategies for Quantitative Stock Selection – Empirical Results Academic Research Supporting a Combined Stock Selection Strategy As discussed previously, academic literature supports the possibility of generating outperformance through the use of purely quantitative measures in the stock selection process. The question that naturally follows from the encouraging evidence presented above is how to go about designing a stock selection model that benefits from this research. The theoretical building blocks for a quantitative stock selection model are generally related to two different behaviorally motivated investor errors, extrapolation of past results, posited to drive the Value effect, and underreaction to new information, which may drive the Momentum effect. If these two effects are not perfectly correlated, then investors should derive a diversification benefit from employing a combination of the two separate investment strategies. In a recent paper, Asness, Moskowitz and Pedersen (Asness et. al. 2013)2 evaluated the relationship between the two strategies and found a low correlation between momentum and value strategies in both the U.S. market (correlation = -.53, see Table XIII) and global developed markets overall (correlation = -.52). The correlation of returns was based on the return spread between the top third and the bottom third portfolio for each strategy, with the holdings market value weighted. Interestingly, the authors found even lower correlations (-0.65 for US, -0.60 Global) when the portfolios were weighted based on their factor rankings, supporting the notion that the underlying strategies (Value, Momentum) are a source of the low correlation. The authors also examined the return history of a 50/50 blend of the two strategies vs. each strategy alone and found that in the U.S. a combination strategy provided both lower standard deviation of returns (6.8% monthly std. dev. vs. 14.8% for Value, 17% Momentum on a factor weighted basis) and a superior Sharpe Ratio (0.86 Sharpe vs. 0.26 for Value, 0.45 for Momentum on a factor weighted basis). Globally the combination strategy lowered standard deviation (5.3% std. dev. vs. 11.4% for Value, 12.0% Momentum on a factor weighted basis) and improved Sharpe Ratios as well (1.28 Sharpe vs. 0.51 for Value, 0.59 for Momentum on a factor weighted basis). In summary, the results of the study provide evidence in favor of a quantitative selection process that employs both strategies to exploit both the Value and Momentum effects.
Table XIII: Performance of Value and Momentum: January 1972 – July 2011 Value Portfolios P1
P2
P3
Momentum Portfolios
P3-P1 Factor
P1
P2
P3
50/50 Combo
P3-P1 Factor
P3-P1 Factor
U.S. Stocks Mean
9.5% 10.6% 13.2% 3.7%
3.9%
8.8%
9.7% 14.2% 5.4%
7.7%
4.6%
5.8%
(t-stat)
-3.31
-1.66
-2.96
-4.14
-2.84
-3.98
-5.40
Stdev
17.9% 15.4% 15.9% 12.8% 14.8%
18.6% 14.8% 18.5% 16.4% 17.0%
7.2%
6.8%
0.63
0.86
Sharpe
0.53
-4.33 0.69
-5.19 0.83
-1.83 0.29
0.26
0.47
0.66
-4.82 0.77
-2.08 0.33
0.45
Alpha
-1.7% 0.8%
3.6%
5.3%
5.8%
-2.3% 0.2%
3.7%
6.0%
8.7%
5.7%
7.2%
(t-stat)
(-1.59) -1.02
-3.17
-2.66
-2.49
(-1.68) -0.29
-2.34
-2.30
-3.22
-5.05
-7.06
-0.53
-0.65
Correlation (Val, Mom): Global Stocks Mean
8.1% 11.0% 14.6% 6.2%
5.8%
(t-stat)
-3.17
-3.18
Stdev
16.6% 15.2% 15.7% 10.9% 11.4%
-4.54
-5.84
-3.6
8.5% 11.1% 14.1% 5.6%
7.1%
6.3%
6.8%
-3.1
-3.73
-6.52
-8.04
17.1% 14.5% 16.2% 12.0% 12.0%
6.1%
5.3%
-4.82
-5.46
-2.94
Sharpe
0.50
0.72
0.93
0.57
0.51
0.49
0.77
0.87
0.47
0.59
1.04
1.28
Alpha
-2.3% 0.7%
4.2%
6.6%
6.1%
-3.3% 0.5%
3.1%
6.4%
8.1%
6.8%
7.5%
(t-stat)
(-1.70) -0.69
-3.49
-3.79
-3.37
(-3.00) -1.00
-2.78
-3.37
-4.31
-7.09
-8.98
-0.52
-0.60
Correlation (Val, Mom): Source: Asness, Moskowitz and Pedersen (2013)
18 For professional investor use only. Not for use with the public.
Quantitative Stock Selection: Combining Value and Momentum Strategies
Empirical Results for a Combined Stock Selection Strategy using a Multi-Factor Value Model Combined with a Multi-Factor Momentum Model Previously in this paper, we summarized the research from academic studies supporting the use of a variety of value and momentum factors. Additionally, we cited academic evidence that the two types of factors may not be perfectly correlated, and that combining them may improve a stock selection strategy. We now present a quantitative stock selection model which combines a multi-factor value model with a multi-factor momentum model.
Backtesting the Multifactor Value Model The value model that will be used in the strategy to be tested is based on three factors - the price to book ratio, the price to cash flow ratio and return on assets (ROA). Price to book and price to cash flow are complementary valuation metrics. Price to book is a purer measure of long-term value, as book value only changes incrementally each year when a portion of net income is accrued to retained earnings. As discussed in section 1, price to cash flow avoids the potential distortions of the accrual-based portion of net income. Return on assets is an important indicator of balance sheet quality, and therefore may serve as a good complementary measure to the price to book ratio. Given these incremental benefits of differing factors (e.g. P/B long-term value, ROA balance sheet quality) we believe that utilizing a mix of value factors provides a more robust value driven methodology than the use of a single factor valuation model. Using the Value model we have specified, we tested its usefulness on the largest 1000 U.S. listed stocks by market capitalization. We apply the model by ranking each security separately on each of the value factors (i.e. book to price ratio, cash flow to price ratio and return on assets), and then summing the resulting single factor ranks. The resulting sums of the three individual factor ranks are then ordered to arrive at a final composite Value model ranking for each stock. The 1000 stocks are then subdivided into quintile groups based on their final composite value model ranking. Equally weighted portfolios are then formed based on these quintile groupings. Starting with the initial selection as of January 1st 1990, this methodology is repeated every three months to rebalance and reselect holdings. Figure 1 displays the value strategy’s risk and return results for each of the composite value model quintiles from the start of January 1990 to the end of August 2014. As can be seen in the figure, the top quintile of the strategy had the highest returns in the backtest, with only a small increase in risk over quintiles 2, 3, and 4. Conversely the bottom quintile not only earned the lowest returns over the period tested, but also recorded the highest standard deviation of returns. These results provide evidence that the composite value model provides some skill in separating more and less attractive stocks from the initial universe.
Figure 1: Multifactor Value Model: Average Annualized Risk/Reward for Largest 1000 Stocks by Market Value: January 1990 – September 2014 16%
Top Quintile
Reward (Annualized Returns)
14% Quintile 3
12%
Quintile 2 Quintile 4
Bottom Quintile
10%
8%
6%
4% 0%
5%
10%
15%
20%
25%
Risk (Annualized Standard Deviation) Data Source: Clarifi
19 For professional investor use only. Not for use with the public.
Quantitative Stock Selection: Combining Value and Momentum Strategies
Backtesting the Multifactor Momentum Model The multi-factor momentum model that will be used in the strategy to be tested will employ three measures of price momentum: past three month return, past six month return and past twelve month return. Two additional factors, one year sales growth and the sales to price ratio, are designed to complement the price momentum factors and will be integrated into the multi-factor momentum model for a total of five factors. The three price momentum factors are chosen to capitalize on the theory of investor underreaction to changes in earnings or other fundamentals, referenced in the survey of academic papers on the momentum effect earlier in the paper. Strong sales growth tends to provide some evidence that recent positive price movement is due to more repeatable improvements in underlying business activity, rather than unsustainable cost cutting. The sales to price ratio is a valuation metric often used to evaluate high growth firms. Like the value factors, the momentum model factors were chosen based on evidence presented in academic literature and the informational value of the factors. Now that the multi-factor momentum model has been specified, the strategy can be tested in a similar process to that performed for the value model backtest. As in the case of the value model, we examine the momentum model’s usefulness on the largest U.S. listed 1000 stocks by market capitalization. We apply the model by ranking each security separately on each of the five momentum factors (i.e. three, six and twelve month price momentum, one year sales growth, and the sales to price ratio), and then summing the resulting single factor ranks. The resulting sums of the five individual factor ranks are then ordered to arrive at a final composite momentum model ranking for each stock. Just as in the value model, the 1000 stocks are then subdivided into quintile groups based on their final composite momentum model ranking. Equally weighted portfolios are then formed based on these quintile groupings. Starting with the initial selection as of January 1st 1990, this methodology is repeated every three months to rebalance and reselect holdings. Figure 2 displays the momentum strategy’s risk and return results for each of the multi-factor momentum model quintiles from the start of January 1990 to the end of August 2014. As can be seen in the figure, the top quintile of the strategy had the highest returns in the backtest, albeit with an increase in standard deviation over quintiles 2, 3, and 4. The bottom quintile not only significantly underperformed the returns of the highest ranked quintile, but also recorded the highest standard deviation of returns. As in the case of the value model backtest, these empirical results provide evidence that the multi-factor momentum model provides some skill in separating more and less attractive names within the initial universe.
Figure 2: Multifactor Momentum Model: Average Annualized Risk/Reward for Largest 1000 Stocks by Market Value: January 1990 – September 2014 16% Top Quintile
Reward (Annualized Returns)
14%
12%
Quintile 3 Quintile 2
Quintile 4
Bottom Quintile
10%
8%
6%
4% 0%
5%
10%
15%
20%
25%
Risk (Annualized Standard Deviation) Data Source: Clarifi
20 For professional investor use only. Not for use with the public.
Quantitative Stock Selection: Combining Value and Momentum Strategies
Backtesting the Combined Multifactor Value and Multifactor Momentum Strategy In a paper discussed earlier, the relationship between the value effect and the momentum effect, and the diversification benefit that can be derived by employing a combination of the value and momentum strategies was explored by Asness, Moskowitz and Pedersen (Asness et. al. 2013)2. Drawing inferences from their paper, we will also attempt to gain from a diversification benefit by utilizing a “dual lens” approach that will apply both our multi-factor value model, and our multi-factor momentum model in our quantitative stock selection methodology. In order to test the combined value and momentum strategy, we begin with the same universe previously examined by each of the single model strategies, the top 1000 U.S. listed stocks by market capitalization. Next we calculate a composite value model ranking and a composite momentum model ranking using the multifactor models specified in the separate value and momentum backtests described earlier. We then assign each stock its best ranking of the two models (value and growth), and rank the results to determine a final combined model ranking for each stock.*** Following the methodology used in the single strategy backtests, these final combined model rankings are then used to subdivide the universe in quintiles. Equally weighted portfolios are then formed based on these quintile groupings. Starting with the initial selection as of January 1st 1990, this methodology is repeated every three months to rebalance and reselect holdings. Figure 3 displays the strategy’s risk and return results for each of the combination multi-factor value and momentum model quintiles from the start of January 1990 to the end of August 2014. As can be seen in the figure, the top quintile of the strategy had the highest returns in the backtest, and clearly dominated the bottom quintile portfolio, which had the lowest returns and most risk among the five portfolios.
Figure 3: Combined Value/Momentum Model: Average Annualized Risk/Reward for Largest 1000 Stocks by Market Value: January 1990 – September 2014 18% Top Quintile
Reward (Annualized Returns)
16% 14%
Quintile 2
12%
Quintile 3 Quintile 4
10% Bottom Quintile 8% 6% 4% 0%
5%
10%
15%
20%
25%
Risk (Annualized Standard Deviation) Data Source: Clarifi
***Examining both the value and momentum ranking and taking the best score eliminates overlap holdings between the two strategies, and is intended to lower the correlation between the two models. In the final combined ranking step, ties go to the value strategy ranking, which should only impact stocks near quintile breakpoints.
21 For professional investor use only. Not for use with the public.
Quantitative Stock Selection: Combining Value and Momentum Strategies
Table XIV summarizes the risk and return results by quintile for each of the strategies tested. As can be seen in the table, in comparison with the single model strategies, the combined model not only increased the return spread between the top and bottom quintiles, indicating greater selection skill, but also increased the return relative to risk, evidenced by a higher Sharpe Ratio.
Table XIV: Combined Value/Momentum, Value and Momentum Model Summary: Average Annualized Risk/Reward for Largest 1000 Stocks by Market Value: January 1990 – September 2014 Model Quintile Model
Top Quintile
Quintile 2
Quintile 3
Quintile 4
Bottom Quintile
Combined: Value/Momentum
16.50% -17.20% [.78]
13.60% -15.50% [.68]
11.70% -15.30% [.56]
11.30% -15.50% [.52]
8.70% -19.90% [.28]
Value
15.00% -17.00% [.70]
12.50% -15.50% [.60]
12.20% -15.10% [.60]
11.60% -16.20% [.53]
10.30% -22.00% [.32]
Momentum
15.60% -18.60% [.67]
11.20% -15.10% [.53]
11.60% -15.50% [.55]
11.80% -16.60% [.52]
11.90% -21.00% [.42]
Data Source: Clarifi Annualized average return with annualized standard deviation, annualized Sharpe Ratio in parentheses.
22 For professional investor use only. Not for use with the public.
Quantitative Stock Selection: Combining Value and Momentum Strategies
Section IV Conclusion Drawing on evidence from often cited foundational papers, as well as recent scholarship, there is ample support for the possibility of achieving superior stock selection through the use of value and momentum strategies. Additionally, we have suggested the use of a combined approach that employs both a multi-factor value strategy and a multi-factor momentum strategy, and presented empirical evidence that lends credence to such an approach. Upon examination of the academic literature and our own results, we arrive at the conclusion that the discipline of a quantitative stock selection methodology should be foundational in any attempt to construct a portfolio that aims to achieve superior investment returns over time.
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Quantitative Stock Selection: Combining Value and Momentum Strategies
Glossary: B/M = Book to Market Beta is a measure of price variability relative to the market. C/P = Cash Flow/Price D/P = Dividends/Price E/P = Earnings/Price Geometric Mean is technically, the Nth root product of N numbers. The geometric mean is used to calculate average historical returns for a portfolio or stock. For example the average annual return over the last three years would be calculated as follows: ((1+YR1)*(1+YR2)*(1+YR3))1/3 - 1 where YR1, YR2 and YR3 are the first, second and third year annual returns. Information Coefficient is a measure of the quality of a forecasting factor or signal to the forecast of stock returns. Standard Error is the standard deviation of an estimate. The statistic measures the precision of an estimate, with a higher error indicating less precision. Standard Deviation is a measure of price variability (risk). T-Statistic is the ratio of an estimate to its standard error. A t-statistic of 2 or above indicates statistical significance at a 95% level of confidence. Sharpe Ratio is a measure of excess reward per unit of volatility.
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Quantitative Stock Selection: Combining Value and Momentum Strategies
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Asness, Clifford S. 1994. “The power of past stock returns to explain future stock returns.” Manuscript, June.
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Asness, Clifford, Tobias Moskowitz and Lasse Pedersen. 2013. “Value and Momentum Everywhere.” Journal of Finance, vol. 68, no. 3 (June): 929-985.
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Bernard, Victor, and Jacob Thomas. 1990. “Evidence that stock prices do not fully reflect the implications of current earnings for future earnings.” Journal of Accounting and Economics, vol. 13, no. 5 (December): 1739-64.
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Cakici, Nusret, Frank Fabozzi and Sinan Tan. 2013. “Size, Value and Momentum in Emerging Market Stock Returns.” Emerging Markets Review, vol. 16: 46-65.
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Carhart, M.M. 1997. “On Persistence in Mutual Fund Performance.” Journal of Finance, vol. 52: 57-82.
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Chan, Louis K.C., Yasushi Hamao and Josef Lakonishok. 1991. “Fundamentals and Stock Returns in Japan.” Journal of Finance, vol. 46, no. 5 (December): 1739-64.
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Chan, Louis K.C., and Josef Lakonishok. 2004. “Value and Growth Investing: Review and Update.” Financial Analysts Journal, vol. 60, no. 1 (January/February): 71-86.
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De Bondt, Werner, and Richard Thaler. 1985. “Does the Stock Market Overreact?” Journal of Finance, vol. 40, no. 3 (December): 793-805.
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Fama, Eugene F., and Kenneth R. French. 1992. “The Cross-Section of Expected Stock Returns.” Journal of Finance, vol. 47, no. 2 (June): 427-465.
10. Fama, Eugene F., and Kenneth R. French. 1996. “Multifactor Explanations of Asset Pricing Anomalies.” Journal of Finance, vol. 51, no. 1 (March): 55-84. 11. Fama, Eugene F., and Kenneth R. French. 1998. “Value versus Growth: The International Evidence.” Journal of Finance, vol. 53, no. 6 (December): 1975-99. 12. Fama, Eugene F., and Kenneth R. French. 2012. “Size, Value and Momentum in International Stock Returns.” Journal of Financial Economics, vol. 105: 457-472. 13. Jegadeesh, Narasimhan, and Sheridan Titman. 1993. “Returns to buying winners and selling losers: Implications for stock market efficiency.” Journal of Finance, vol. 48, no. 1 65-91. 14. Jegadeesh, Narasimhan, and Sheridan Titman. 2001. “Profitability of Momentum Strategies: An Evaluation of Alternative Explanations.” Journal of Finance, vol. 56, no. 2 (April): 699-720. 15. Jegadeesh, Narasimhan, and Joshua Livnat. 2006. “Post-Earnings-Announcement Drift: The Role of Revenue Surprises.” Financial Analysts Journal, vol. 62, no. 2 22-34. 16. Lakonishok, Josef, Andrei Shleifer, and Robert W. Vishny. 1994. “Contrarian Investment, Extrapolation, and Risk.” Journal of Finance, vol. 49, no. 5 (December):1541-78. 17. Piotroski, Josef D. 2001. “Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers.” Journal of Accounting Research, vol. 38, supplement 1-41. 18. Scowcroft, Alan, and James Sefton. 2005. “Understanding Momentum.” Financial Analysts Journal, vol. 61, no. 2 64-82. 19. Sharpe, William F. 1964."Capital Asset Prices - A Theory of Market Equilibrium Under Conditions of Risk." The Journal of Finance, vol. 19, no. 3, (September): 425-442.
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Quantitative Stock Selection: Combining Value and Momentum Strategies
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