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Coskewness Risk Decomposition Coskewness Risk Decomposition Leon Zolotoy Melbourne Business School, University of Melbourne Petko S. Kalev Centre for Applied Financial Studies, University of South Australia Business School This draft 10 September 2013 Abstract This paper investigates the relative importance of aggregate cash–flow and discount–rate news components in the context of higher–moment asset pricing model of Kraus and Litzenberger (1976) which includes coskewness risk. We break down coskewness of the stock with the market into the coskewness with the cash–flow news, coskewness with the discount–rate news and the covariance with the product of the two — the covariation risk. Using US data from 1963 to 2010, we observe that stocks with high past returns have higher exposure to the covariation risk in comparison to the stocks with low past returns. We also document positive and economically significant market price of the covariation risk, while no such evidence is found for the cash–flow and discount–rate components of the coskewness risk. When augmented with the covariation risk component, the two–beta model of Campbell and Vuolteenaho (2004a) captures about 73% of the return variation across size/book–to– market, size/momentum and industry–sorted portfolios. In addition, we complement our analysis by examining the effects of the coskewness component on the expected rate of return of individual stocks using the implied cost of equity capital approach. Once again, we find the covariation risk to be the dominant factor that drives the positive relation between the expected returns and coskewness risk. JEL classification: G12, G14 Keywords: Asset pricing; Coskewness risk; Cash–flow news; Discount–rate news; Momentum. *We thank John Campbell, Erik Theissen, Pavel Savor, Terry Walter for their constructive comments which helped improve the paper substantially.The usual caveat applies. The central objective of this paper is to examine the relative importance of the cash–flow and discount rate news components in context of higher–moment asset pricing model which includes coskewness risk (Kraus and Litzenberger, 1976). Specifically, we decompose the overall coskewness risk into the coskewness with the cash–flow news, coskewness with the discount–rate news, and the covariation risk components. We examine the ability of the extended Campbell and Vuolteenaho (2004a) model, augmented with the coskewness components, to correctly price portfolios sorted by size, book–to–market and past performance (momentum) and compare its performance with the popular empirical multifactor models considered in prior literature. Further, acknowledging potential drawbacks associated with utilizing realized portfolio returns as a proxy for the required returns (Elton, 1999), we complement our analysis by examining the relation between the coskewness components and expected returns using an implied cost of equity approach. Our paper is motivated by the following three strands of asset pricing literature. One strand of research examines the relative importance of cash–flow news and discount–rate news in explaining the cross–sectional variation in expected returns. In his seminal paper Campbell (1991) employs a vector autoregression method to break unexpected stock returns into two components: news about cash–flows and news about discount–rate. Campbell finds discount–rate news to account for most of stock return variation.1 Campbell and Vuolteenaho (2004a) use this methodology to disaggregate the Capital Asset Pricing Model (CAPM) betas into the cash–flow and discount–rate betas. They find that it is the cash–flow beta risk that is priced by the market, while no such evidence is found for the discount–rate beta risk. In a more recent study, Campbell et al. (2010) show that cash–flows of growth stock are particularly sensitive to changes in the equity risk premium (market–wide discount rate news), while the cash–flows of value stocks are particularly sensitive to the market–wide 1 Related early studies that employed this methodology include among others are Campbell and Mai (1993) and Campbell and Ammer (1993). shocks to cash–flows. Overall, prior studies in this vein of research emphasize the importance of decomposing the overall changes in stock prices into those driven by shocks to cash–flows and those driven by changes in expected returns. Another strand of literature examines whether the risks associated with higher moments, in particular the coskewness risk, are priced by the market. Kraus and Litzenberger (1976) provide a rational for the three–moment CAPM. In their model coskewness of the stock with the market, estimated as the covariance of stock return with the square of market return, measures the marginal contribution of the stock to the skewness of market portfolio. They show that coskewness matters since investors with a non–increasing absolute risk aversion have a preference for positive skewness. Harvey and Siddique (2000) show that some of the profitability of the momentum–based trading strategies can be explained by the coskewness factor. Barone-Adesi et al., (2004) find that Fama-French (1993) factors lose their explanatory power when the coskewness is taken into account. In related papers Vanden (2006) and Smith (2007) find coskewness to be an important determinant of the equity risk premium. Martellini and Ziemann (2010) emphasize the importance of taking into account higher moments, coskewness and cokurtosis, for the optimal portfolio selection. A third related strand of literature analyzes whether cross–sectional differences in exposure to correlation risk can account for cross–sectional differences in expected returns. Changes in market–wide variance are driven by shocks to both individual variances and correlations (Driessen, Maenhout, and Vilkov, 2009). If correlation risk is priced, then assets whose returns covary positively with correlation provide a hedge against unexpected correlation increases and earn negative excess returns relative to what is justified by their exposure to standard risk factors. Consistent with this notion, Krishnan, Petkova and Ritchken (2009) and Driessen, Maenhout, and Vilkov (2009) document a significant risk premium for correlation risk. Pollet and Wilson (2010) show that changes in average 2 correlation between stock returns predict subsequent stock market returns. In a related study, Ball, Sadka and Sadka (2009) point out that focusing solely on the cash–flow and discount– rate betas, as in Campbell and Vuolteenaho (2004a), may not be sufficed if investors care about the covariance of stock returns with the interaction/correlation of the cash–flow news and discount–rate news. Motivated by these three strands of research we examine the relation between the cash–flow news, discount–rate news, and the coskewness risk. Note that, coskewness measures the asset exposure to changes in variation in market returns. While applying Campbell and Vuolteenaho’s (2004a) decomposition to the square of the unexpected market return, it is straightforward to show that changes in market return variation can be driven by (1) shocks to cash–flow news variation, (2) shocks to discount–rate news variation, and (3) shocks to covariation between the two Accordingly, the overall measure of coskewness risk can be decomposed into three components, which are: the coskewness with the cash–flow news, coskewness with the discount–rate news and the covariance of stock return with the product of the two — the covariation term. The first two terms measure the asset exposure to changes in variations in the cash–flow and discount–rate news, respectively, while the last term measures asset exposure to changes in covariation between these two components. Our key findings are as follows. First, we find that stocks that experienced high past returns have higher exposure to the covariation risk in comparison to the stocks with low past returns. Second, using returns on size/book–to–market, size/momentum and industry sorted portfolios for the period 1963 to 2010, we document positive and statistically significant market price of the covariation risk. The market prices of cash–flow and discount–rate coskewness terms are both not statistically significant. Third, we show that the two–beta model of Campbell and Vuolteenaho (2004a), augmented with the covariation risk term, explains about 73% of the return variation across size/book–to–market, size/momentum and 3 industry–sorted portfolios. Further, the null hypothesis of the augmented Campbell and Vuolteenaho (2004a) two–beta model correctly pricing returns on size/book–to–market and size/momentum sorted portfolios cannot be rejected at conventional significance levels. We supplement our analysis by examining the effects of the coskewness components on the expected stock return using the implied cost of equity approach (Hail and Leuz, 2009; Chen et al., 2011). Our results continue to hold. We also compare the performance of the augmented two–beta model with the number of competing models. In particular, we find the explanatory power of Campbell and Vuolteenaho (2004a) two–beta model augmented with the covariation term to be comparable to the influential Fama–French (1993) three–factor and Carhart (1997) four–factor models. It is noteworthy that Fama–French (1993) size and value factors and Carhart (1997) momentum factor were constructed ex post to explain the size, book–to–market and momentum effects, while the factors of the augmented Campbell and Vuolteenaho (2004a) model were constructed ex ante. Taking this
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