EDHEC-Risk Institute October 2016

Multi-Dimensional Risk and Performance Analysis for Equity Portfolios — October 2016

2. From Historical Betas (and Alphas) to Fundamental Betas (and Alphas)

higher expected returns, and some papers question their role in asset pricing.

There are several justifications for our choice of conditioning information. First, several studies have shown that market risk is linked to accounting variables. Beaver, Kettler and Scholes (1970) use the following accounting variables: dividend payout (dividend/earning), growth, leverage, liquidity, asset size, variability of earnings, and covariability of earnings within the context of ‘intrinsic value’ analysis. They find high degree of contemporaneous association between accounting risk measure and the market risk exposure. Jarvela, Kozyra and Potter review and update this study in 2009. With OLS estimation conducted on 222 randomly selected publicly traded companies, they determine the correlation between the risk measures related to accounting variables (earnings variability, dividend payout, and leverage) and those determined by the market. Their results confirm those of Beaver, Kettler and Scholes in 1970 and show correlation between market risk and accounting risk measures. They conclude that accounting information is a possible alternative to market risk information. Second, our choice of state variables echoes of course the definition of the Fama French and Carhart factors. These factors are empirical pricing factors that account for several of the empirical regularities that are left unexplained by the CAPM: rather unsurprisingly, they capture the size and the value effects and the continuation of short-term returns, but together with the market factor, the size and the value factors are also able to capture the return spread across portfolios formed on earnings-to-price, cash flow-to-price, past sales growth and past long-term returns (Fama and French, 1996). In spite of this empirical success, there is no undisputed economic explanation for why exposure to these factors should be rewarded with

Ang and Chen (2007) show that in a conditional version of the CAPM, the long termvalue premium is no longer statistically significant. In a related contribution, Bandi et al. (2010) study long-run relation between expected returns and market beta risk in the post-1963 period. Using Fama and MacBeth (1973) cross-sectional regression they estimate the market risk premium over a five to ten year period at economically-reasonable values between 6 and 11% per annum. Conversely, size and value factors become less statistically significant. Market risk factor increases its statistical and economic relevance with the horizon and appears in the long run to be the major contributing factor. Value and size, which are still broadly considered as important risk factors when adopting a short-term perspective, become less statistically significant with long horizon. Overall, there is currently no definitive evidence that the size and value factors are economically justified asset pricing factors and that they are required to explain the cross-section of expected returns. Thus, as a first approximation, it is not unreasonable to stay in the context of a one-factor model in order to design a conditional asset pricing model. Since there are size, value and momentum premia that the standard CAPM cannot explain, we include size, value and momentum scores in the set of instrumental variables in an attempt to capture these premia through the market beta. Inwhat follows, wemeasure a “fundamental alpha” and a “fundamental beta” expressed as functions of the three aforementioned scores. The objective of this construction is to achieve a better estimation of the

49

An EDHEC-Risk Institute Publication