Predicting stock returns

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Abstract

This paper studies whether incorporating business cycle predictors benefits a real time optimizing investor who must allocate funds across 3,123 NYSE-AMEX stocks and cash. Realized returns are positive when adjusted by the Fama-French and momentum factors as well as by the size, book-to-market, and past return characteristics. The investor optimally holds small-cap, growth, and momentum stocks and loads less (more) heavily on momentum (small-cap) stocks during recessions. Returns on individual stocks are predictable out-of-sample due to alpha variation, whereas the equity premium predictability, the major focus of previous work, is questionable.

Introduction

Previous work identifies business cycle and firm-level variables that predict future stock returns.1 These predictive variables, when incorporated in studies that deal with the time-series and cross-sectional properties of expected returns, provide fresh insights into investment management and asset pricing. For example, Kandel and Stambaugh (1996) show that current values of predictive variables can exert substantial influence on asset allocation. Moreover, Lettau and Ludvigson (2001) and Avramov and Chordia (2006), among others, demonstrate that asset pricing models with time varying market premium or risk are reasonably successful relative to their unconditional counterparts. Notwithstanding, stock return predictability continues to be a subject of research controversy. Skepticism exists due to concerns relating to data mining, statistical biases, and weak out-of-sample performance of predictive regressions,2 and moreover, if firm-level predictability indeed exists, it is not clear whether it is driven by time varying alpha, beta, or the equity premium.

This paper develops and applies an optimization framework within which to investigate the economic value and determinants of predictability at the stock level. Specifically, we seek to understand whether considering business cycle predictors benefits a real time investor who must allocate funds across 3,123 NYSE-AMEX stocks and the risk-free asset over the 1972–2003 period. The proposed framework is quite general as it allows alphas, betas, and the equity premium to vary with the predictive variables, it explicitly incorporates estimation risk, and it permits investments based on different stock return histories. This last aspect is desirable in analysis of real time investments because stocks enter (IPO) and leave (merger, acquisition, bankruptcy) the sample periodically. Relative to Stambaugh (1997), who develops an approach for analyzing investments whose histories differ in length, we allow expected returns, variances, and correlations to vary with the business cycle variables.

We implement several trading strategies and examine their ex post out-of-sample performance. If investment strategies that condition on macro variables outperform their unconditional counterparts, as well as common benchmarks, then they exploit superior information about the cross-section of future returns and the degree of superior performance provides a measure of the economic value of predictability. Moreover, our methodology allows one to explore whether the superior performance comes from time varying alphas, betas, and/or the risk premium. For instance, if investments based on time varying alphas outperform their constant alpha counterparts, then time varying alpha is a determinant of predictability.

Our investment universe consists of a risk-free asset, which we proxy by the short-term Treasury, and 3,123 individual stocks belonging to the three largest quartiles of NYSE- and AMEX-listed firms. Implementing a firm-level analysis is attractive because it addresses concerns about data snooping and loss of information that arise in procedures applied to equity portfolios sorted on firm characteristics or industry classifications, as noted by Litzenberger and Ramaswamy (1979) and Lo and MacKinlay (1990). In addition, Ferson and Harvey (1991) find that changes in risk premia explain most of the predictable variation of future returns, with changes in beta of second-order importance. However, Ferson and Harvey use portfolios and not individual stocks, and they suggest that the importance of beta variation for portfolios may be understated because much of the variation of individual firm's beta could be attenuated at the portfolio level.

The empirical evidence shows that over the 1972–2003 period, investment strategies that condition on business cycle variables, the dividend yield, the default spread, the term spread, and the Treasury bill yield deliver superior performance. To illustrate, the Sharpe ratio attributable to the market portfolio is 0.10 per month. The ex post out-of-sample Sharpe ratio is 0.10 when beta varies with business cycle variables, 0.17 under time varying alpha, and 0.20 under time varying equity premium. In addition, the Jensen's alpha that obtains by regressing investment excess returns produced by a no-predictability strategy on both the market index (αcpm) and the Fama and French (1993) benchmarks (αff) is statistically indistinguishable from zero at conventional levels. In contrast, predictability-based strategies produce positive and significant αcpm and αff. For example, when the equity premium varies with business cycle variables, αcpm=2.10%/month and αff=1.73%/month. Both are statistically significant at conventional levels. For perspective, a 1% risk-adjusted monthly return obtains by implementing the momentum strategy of Jegadeesh and Titman (1993), which is one of the most prominent and intriguing puzzles documented in financial economics. Moreover, over the 1972–2003 investment period, taking a long position in a strategy that allows for alpha, beta, and equity premium variation with business conditions and taking a short position in the market portfolio generates a cumulative payoff of $717 per $1 investment. The corresponding figure is only $18 when optimal portfolio strategies do not account for business conditions.

In related work, Schwert (2003) notes that the so-called financial market anomalies related to profit opportunities often disappear, reverse, or attenuate following their discovery. For example, he shows that the relation between the aggregate dividend yield and the equity premium is much weaker, based on both statistical and investment measures, after the discovery of that predictor by Keim and Stambaugh (1986) and Fama and French (1989). Consequently, we study investment performance before and after the discovery of the business cycle variables. Consistent with Schwert (2003), we demonstrate that strategies conditioned only on predictable equity premium are much stronger over the pre-discovery period than over the post-discovery period. Nevertheless, considering the business cycle variables is still beneficial in the post-discovery period because such variables drive stock-level alpha variation. To illustrate, in the post-discovery period, a strategy that allows alpha to vary with business cycle variables produces an out-of-sample Sharpe ratio of 0.25, αcpm of 2.55%, and αff of 1.80%. Indeed, earlier work that documents no out-of-sample predictability does not consider variation in stock-level parameters. In particular, Bossaerts and Hillion (1999), Goyal and Welch (2003), and Schwert (2003) all analyze equity premium predictability only. By implementing firm-level analysis, we provide new evidence about stock return predictability: individual stock returns are predictable in real time, based on macro variables, while the equity premium predictability, the major focus of previous work, is questionable.

To understand the source of investment profitability, we relate our strategies to the size, book-to-market, and momentum effects. We show that investors who use business cycle predictors hold small-cap, growth, and momentum stocks and they load less heavily (more heavily) on momentum (small-cap) stocks over the NBER-designated recession periods. Ultimately, these investors realize returns that are positive when adjusted by the Fama-French and momentum benchmarks as well as by the size, book-to-market, and prior return characteristics. To illustrate, the strategy that allows for predictability in alpha, beta, and the equity premium yields alpha of 1.32% (1.17%) per month when investment returns are adjusted by the Fama-French and momentum benchmarks with fixed (time varying) factor loadings, and it yields 1.14% per month when investment returns are adjusted by characteristics as in Daniel, Grinblatt, Titman, and Wermers (1997). All of these are significant at the 5% or 10% level.

In sum, earlier work that extensively studies equity premium predictability demonstrates only weak or even nonexistent out-of-sample predictability, especially in the period after the discovery of the macro variables. In this paper, we show that a focus on the equity premium fails to deliver evidence of predictability at the stock level. In particular, returns are predictable out-of-sample if one is willing to undertake a stock-level analysis allowing beta and especially alpha to vary with the dividend yield, the default spread, the term spread, and the Treasury bill yield. Our findings are based on a comprehensive set of performance evaluation measures and we are careful to analyze the determinants of predictability over the pre- and post-discovery periods as well as to associate our trading strategies with the size, book-to-market, and momentum effects. Indeed, a formal framework that uses macroeconomic variables generates trading strategies with long-only positions in individual stocks that outperform strategies that take long and short positions in the size, book-to-market, and momentum benchmarks as well as strategies that hold stocks with the same (potentially time varying) size, book-to-market, and momentum characteristics.

The remainder of the paper proceeds as follows. Section 2 develops an optimization framework for analyzing the profitability of predictability-based trading strategies that account for estimation risk. Section 3 describes the data. Section 4 presents the results. Section 5 offers conclusions and potential avenues for future research. Unless otherwise noted, all derivations are presented in the appendix.

Section snippets

Understanding firm-level predictability

This section sets forth a framework for studying the profitability of various portfolio strategies that incorporate macroeconomic variables to invest in individual stocks.

Data

The data consists of monthly excess returns, size, book-to-market, turnover, and lagged 1-year returns for a sample of NYSE- and AMEX-listed common stocks as well as the four macroeconomic variables we describe below. The sample period is from July 1962 through December 2003. To be included in the investment universe, a stock has to satisfy the following criteria. First, its return through the investment date and over the past 60 months must be available from CRSP. Second, there must be

Results

We form portfolio strategies as in Eq. (10) subject to (i) no short selling of stocks and (ii) the overall investment in stocks cannot exceed 200% per Regulation T of the Federal Reserve Board, which requires an initial margin of 50%. In forming optimal portfolios, we take ft in Eq. (1) to be the excess return on the market portfolio. In addition, we replace μt and Σt by the first and the second moments of the Bayesian predictive distribution in Eq. (14). The difference (1/γt)-rft in Eq. (10)

Conclusions

A long-standing question in financial economics is whether future stock returns can be predicted based on public information. Keim and Stambaugh (1986) and Fama and French (1989) identify macroeconomic variables such as the aggregate dividend yield, the term spread, and the default spread that explain a substantial portion of future return variations. Basu (1977), Banz (1981), Jegadeesh (1990), Fama and French (1992), and Jegadeesh and Titman (1993) demonstrate the predictive power of the

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      It is demonstrated that distributional regressions are promising in the financial context and can be modified to fit other forecasting models to enhance timing strategies. This study is related to the literature on the prediction of market returns and the equity premium (among others Lettau and Ludvigson, 2001; Goyal and Welch, 2003; Lewellen, 2004; Avramov and Chordia, 2006; Ang and Bekaert, 2007; Spiegel, 2008; Cochrane, 2008; Campbell and Thompson, 2008; Kellard et al., 2010; Pollet and Wilson, 2010; Rapach et al., 2010; Faria and Verona, 2018). Welch and Goyal (2008) provide a comprehensive overview of the most common macroeconomic predictors of the market return.

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    We thank Amit Goyal, Rick Green, Narasimhan Jegadeesh, Lubos Pastor, Nagpurnanand Prabhala, Jay Shanken, Avi Wohl, an anonymous referee, and seminar participants at Arizona State University, Emory University, the 2005 Prudential Quantitative Research Conference, Institute for Advanced Studies and the University of Vienna—joint seminar, University of Georgia, University of Maryland, University of North Carolina, Chicago Quantitative Alliance, Tel Aviv University, Texas A&M, Tulane, the 2005 Inquire-Europe meetings, and the 2004 Western Finance Association meetings for helpful comments and suggestions. All errors are our own.

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