Expected Returns, Yield Spreads, and Asset Pricing Tests Murillo Campello,∗ Long Chen,y and Lu Zhangz May 2006x Abstract We construct firm-specific expected equity risk premium using corporate bond yield spreads. We then replace standard ex-post, averaged measures of return with our ex- ante return measures in asset pricing tests. We find that the market beta plays a significant role in the cross-section of returns when expectations are measured ex-ante. The expected size and value premia are significantly positive and countercyclical, but there is no evidence of ex-ante positive momentum profits. JEL Classification: G12, E44 Key Words: Expected returns, risk factors, systematic risk, yield spreads ∗Department of Finance, College of Business, University of Illinois at Urbana-Champaign, Champaign, IL 61820; and NBER. E-mail: [email protected]. yDepartment of Finance, The Eli Broad College of Business, Michigan State University, East Lansing, MI 48824. E-mail: [email protected]. zWilliam E. Simon Graduate School of Business Administration, University of Rochester, Rochester, NY 14627; and NBER. E-mail: [email protected]. xWe thank John Ammer, Mike Barclay, Dan Bernhardt, Lawrence Booth, Cam Harvey, Raymond Kan, Jason Karceski, Naveen Khana, Mark Schroder, Jay Shanken (AFA discussant), Jerry Warner, Jason Wei, Jim Wiggins, Tong Yao, Guofu Zhou, seminar participants at University of Notre Dame, the 2005 AFA meetings, and the 2005 Federal Reserve Risk Premium Conference for their helpful comments. The usual disclaimer applies. 1 1 Introduction The standard asset pricing theory proposes that investors demand an ex-ante premium for acquiring risky securities (e.g., Sharpe (1964), Lintner (1965), and Merton (1973)). Because the ex-ante risk premium is not readily observable, empirical studies ordinarily use ex-post averaged stock returns as a proxy for expected stock returns. This practice is justified on grounds that for sufficiently long horizons, the average return will \catch up and match" the expected return on equity securities | the ex-post average excess equity returns provide for an easy-to-implement, plausibly unbiased estimate of the expected equity risk premium. Despite its popularity, the use of ex-post return averages has important limitations. For instance, the average realized return need not converge to the expected risk premium in finite samples.1 This, in effect, conditions any inferences based on ex-post returns on the properties of the particular data under examination. More general difficulties associated with the use of ex-post returns have been recognized in the literature, but little has been done to understand their implications.2 In his AFA presidential address, Elton (1999) observes that there are peri- ods longer than ten years during which stock market realized returns are on average lower than the risk-free rate (1973 to 1984) and periods longer than 50 years during which risky bonds on average underperform the risk-free rate (1927 to 1981). Based on these patterns, he argues: \[D]eveloping better measures of expected return and alternative ways of testing asset pricing theories that do not require using realized returns have a much higher payoff than any additional development of statistical tests that continue to rely on realized returns as a proxy for expected returns." (p. 1200) Since most results in the empirical asset pricing literature were established with the use of averaged realized returns, it is natural to ask whether extant inferences about risk{expected return tradeoff will hold under alternative, direct measures of expected returns. In this paper, we construct an ex-ante measure of risk premium based on data from bond yield spreads and investigate whether well-known equity factors, such as market, size, book-to- 1Using simulations, Lundblad (2005) and Pastor et al. (2005) show that, except for very long time windows, realized returns do not converge to expected returns and often yield wrong inferences regarding expectations. 2Earlier studies have discussed in some detail the noisy nature of average realized returns in a number of different contexts (see, e.g., Blume and Friend (1973), Sharpe (1978), and Miller and Scholes (1982)). market, and momentum, can explain the cross-sectional variation of expected stock returns. Our basic approach recognizes that debt and equity are contingent claims written on the same set of productive assets and hence must share common risk factors. The upshot of this obser- vation is that we can use corporate bond data to glean additional information about investors' required equity risk premium. In what follows, we derive an analytical formula that links ex- ante equity risk premia and bond risk premia, after adjusting bond yield spreads for default risk, rating transition risk, and the tax spreads between the corporate and the Treasury bonds. Why use bond yield data? While relevant information regarding a firm’s systematic risk is incorporated into both its stock and bond prices, the latter reveal key insights about in- vestors' return expectations. The first thing to notice is that bond yields are calculated in the spirit of forward-looking internal rates of return. To wit, bond yield is the expected return if the bond does not default and the yield does not change in the next period. Bond prices impound the probability of default and yield spreads contain the expected risk premium for taking default risk. Controlling for default risk, firms with higher systematic risk will have higher yield spreads; a relation that holds period-by-period, cross-sectionally. This contrasts sharply with what can be gauged from realized equity returns. Equity returns reflect both cash flow shocks and discount rates shocks, and ex-post averaging overshadows conditional, forward-looking information.3 Another key reason for looking at bonds is that the time variation of expected equity re- turns works against the convergence of average realized returns towards the expected return. To see this, suppose investors require a higher equity risk premium from cyclical firms during economic downturns. To reflect this premium effect, those firms’ equity prices should drop and their discount rates rise during recessions. Cyclical firms’ equity values indeed fall during economic downturns, reflecting value losses in those firms’ underlying assets. However, by averaging ex-post a cyclical firm’s returns over the course of a recession, one might wrong- fully conclude that the cyclical firm is less risky because of its lower \expected" return. Bond yield spreads, in contrast, increase during recessions: they move in the same direction of the discount rate and spreads are higher for cyclical firms. 3As pointed out by Sharpe (1978), the CAPM only holds conditionally and expected returns might have nothing to do with future realized returns. Risk premia recovered from bond yields, in contrast, reflect conditional information. 2 The main goal of our paper is to establish the empirical applicability of a basic insight linking yield spreads and expected equity returns. To formalize our arguments, we build on Merton's (1974) classic framework. We then test those arguments fitting standard multi-factor pricing models on monthly return series over three decades. As we explain below, since we must resort to existing default information to gauge the expected default loss, our constructed default risk premium is not entirely \ex-ante." Fortunately, however, research has shown that the yield spread is too large to be explained by the expected default loss (see, e.g., Huang and Huang (2003)). Since we restrict the use of past data to the estimation of a small portion of the yield spread, we are able to capture relevant forward-looking information on the risk premium contained in yield spreads. Our tests provide new insights into the determinants of the cross- section of expected returns, complementing inferences based on average realized returns.4 Our main empirical findings can be summarized as follows. First, the market beta plays a much more important role in explaining the cross-sectional variation of expected equity re- turns than what is typically reported under ex-post return measures. Its explanatory power remains significant even after we control for size, book-to-market, and prior returns. This finding is surprising given the weak relation between market beta and average returns reported in well-known studies in the literature (e.g., Fama and French (1992)). Second, the expected value premium and size premium are significantly positive and coun- tercyclical. Our evidence is consistent with the view that book-to-market and size capture relevant dimensions of risk that are priced ex-ante in equity returns (Fama and French (1993, 1996)). The countercyclicality of the ex-ante value premium also lends support to studies high- lighting the effects of business cycles and conditional information on the value premium (e.g., Ferson and Harvey (1999) and Lettau and Ludvigson (2001)). The finding that the expected size premium remains large (3.61% annually) and significant for the 1982{1998 period | after Banz's (1981) discovery | contrasts with results from tests using ex-post averaged returns. Finally, we find no evidence of ex-ante positive momentum profits. In fact, momentum 4Since we gauge investors' expectations using public bonds, our approach naturally focuses on data from bond issuers. This, in turn, constrains our analysis to a sample universe that is smaller than the typical CRSP{ COMPUSTAT universe. Although previous studies show that common equity factors are present across var- ious subsamples of the CRSP{COMPUSTAT spectrum (e.g., Fama and French (1992) and Lakonishok et al. (1994)), one could question whether our data engender those common factors in the first place. We verify below that we can recover in our data the same realized return factors used in standard asset pricing studies. 3 is priced ex-ante with a negative sign. This finding is consistent with several interpretations. First, investors may not expect stocks with high prior returns to be riskier and earn higher returns in the future.