Horizon Pricing

An extensive literature documents heterogeneity in the delay of stock-price reaction to systematic shocks, implying that relevant asset risk depends on investment horizon. We study pricing of common risk factors across investment horizons. We …nd that liquidity risk is priced over short horizons and market risk is priced over intermediate horizons. Value/growth risk is priced over long horizons and as a non-risk-based characteristic at all horizons. Size and momentum are priced as characteristics rather than risk factors at all horizons. The results highlight the importance of investment horizon in determining risk premia. Kamara: Foster School of Business, University of Washington, Seattle, WA 98195-3226; email: [email protected]. Korajczyk: Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, IL 60208-2001; email: [email protected]. Lou: Lerner College of Business and Economics, University of Delaware, Newark, DE 19716; email: [email protected]. Sadka: Carroll School of Management, Boston College, Department of Finance, 140 Commonwealth Ave., Chestnut Hill, MA 02467; email: [email protected]. We would like to thank Pierluigi Balduzzi, Mikhail Chernov, Kent Daniel, Wayne Ferson, Carole Gresse, Alan Marcus, and seminar participants at Boston College, University of Connecticut, George Washington University, London School of Economics, London Business School, DePaul University, Chinese University of Hong Kong, Center for Accounting Research and Education conference, State Street Global Advisors, Deutsche Bank Quant Conference, Conference of Financial Economics and Accounting, American Finance Association meetings, Hedge Fund Research Conference (Paris), and Cirpée Applied Financial Time Series Workshop (HEC Montreal) for comments. Korajczyk would like to acknowledge the …nancial support of the Zell Center for Risk Research. A number of asset-return and macroeconomic variables have been proposed in the asset-pricing literature as systematic priced risk factors. For example, market risk (MKT, e.g., Treynor (1962, 1999), Sharpe (1964), Lintner (1965)), size and value (SMB and HML, respectively, e.g., Fama and French (1993)), momentum (UMD, e.g., Carhart (1997)), and liquidity (LIQ, e.g., Pástor and Stambaugh (2003)). This paper studies the role of return horizon in the pricing of systematic risk. Horizon can potentially impact pricing because of several e¤ects: (1) delays in price reactions imply that measured systematic risk is horizon-speci…c, (2) risk factors exhibit autocorrelation, implying that factor volatility, and possibly the risk premium demanded by investors, depend on horizonspeci…c volatility, and (3) heterogeneous investors might have di¤erent investment horizons and, hence, horizon-speci…c sensitivities to factor exposures. There is a long line of research suggesting that there is a delay in the reaction of prices of certain stocks to news about systematic factors (Lo and MacKinlay (1990), Brennan, Jegadeesh, and Swaminathan (1993), Badrinath, Kale, and Noe (1995), and Zhang (2006)). Several studies investigate the premise that market participants need more time to process the implications of shocks to complicated or opaque …rms than they need for transparent …rms. For example, Hou and Moskowitz (2005) report that delays in information processing account for part of several widelystudied asset-pricing anomalies, while Hou (2007) shows that di¤erences in speed of information processing are a leading cause of the lead-lag e¤ect in intra-industry returns. More recently, Cohen and Lou (2012) document that monthly returns of focused or easy-to-analyze …rms (i.e., …rms that operate solely in one industry) incorporate industry-speci…c shocks faster than returns of complicated …rms (i.e., conglomerates with multiple operating segments). As a result, monthly returns of easyto-analyze …rms predict the returns of more complicated, within-industry, peers. Such delayed price reaction implies that systematic risk will di¤er across investors investment horizons. That is, a stock that appears “defensive”at one horizon may appear much riskier at another horizon. Factors might also exhibit autocorrelation either because of autocorrelation in required factor risk premia, delayed response to news for some stocks, or because of non-synchronous trading (e.g., Scholes and Williams (1977), Dimson (1979), and Cohen et al. (1983)). Note, however, that even if risk factors are serially uncorrelated and without delays in price reactions, investment horizon could still impact the appropriate measure of risk. For example, Levhari and Levy (1977) show that discreet compounding leads to estimates of systematic risk are biased when estimated at horizons di¤erent from the horizon at which a single factor asset-pricing model holds. Several empirical studies have shown that risk and risk premia estimates seem to depend on horizon. Roll (1981) suggests that the di¤erence in short-horizon and long-horizon beta estimates might explain the size e¤ect of Banz (1981). Handa, Kothari, and Wasley (1989) …nd that the premium associated with market risk is insigni…cant when beta is estimated over monthly horizons but signi…cant when beta is estimated over annual horizons and that the annual market beta drives out the size e¤ect. Kothari, Shanken, and Sloan (1995) …nd a signi…cant market premium using betas estimated over annual horizon, but that the annual market betas do not subsume the size e¤ect. Daniel and Marshall (1997) …nd that long consumption horizons do a better job in explaining the equity risk premium and risk-free rate puzzles in a model with habit formation. Jagannathan and Wang (2007) …nd that the Consumption Capital Asset Pricing Model (CCAPM) does a much better job explaining the cross-section of asset returns using an annual horizon than a quarterly horizon. In particular, an annual horizon ending in the fourth quarter has much higher explanatory power than annual periods ending in the other quarters. They suggest that investors tend to plan their consumption and investment choices in the last quarter of the year. Brennan and Zhang (2011) and Beber, Driessen, and Tuijp (2011) estimate asset-pricing models for various investment horizons and …nd that the data …t long horizons better than a one-month horizon. There is also evidence that investment horizon varies over time and across investors. While some investors choose to trade frequently and may be concerned with risk over short horizons, others may choose to trade infrequently due to costs of monitoring their portfolios and trading costs (Du¢ e and Sun (1990), Abel, Eberly, and Panageas (2007, 2009), Du¢ e (2010)) and may be concerned with risk over longer horizons. In particular, Abel, Eberly, and Panageas (2009) derive a model in which investors face proportional and …xed costs of rebalancing their portfolio in addition to a utility cost of observing the state of their portfolio. In general, the horizon chosen to observe and rebalance a portfolio is state-dependent, and hence, an investor’s horizon is stochastic. However, for …xed rebalancing costs that are su¢ ciently small, an optimally inattentive investor’s strategy is purely time-dependent with a …xed horizon. Empirically, many investors seem to have long rebalancing horizons. Ameriks and Zeldes (2004) …nd that, for a sample of de…ned contribution retirement plan participants, 47% (21%) made no changes (one change) to their allocation of contributions over a ten-year period. Similar results are found for 401(k) plans by Mitchell et al. (2006). Chakrabarty, Moulton, and Trzcinka (2013) …nd a large amount of heterogeneity in the holding periods for equities held by a large sample of institutional funds. To the extent that horizon a¤ects the measurement of systematic risk, it is sensible that it might a¤ect the measured risk premia of risk factors. In this paper, we examine whether there exist