Our first distinction is the difference between “excess return” and “alpha.” We will use “excess return” for return outcomes that outperform some appropriate passive benchmark. Among the equity characteristics that have broadly documented associations with abnormal returns are “value,” “momentum,” “size” and “low volatility.”įor the purposes of this paper, we will use certain semantic conventions in the way we describe factor returns. There is also a massive literature of “factor anomalies” that describe persistent excess returns associated with security attributes in violation of the Efficient Markets Hypothesis (Fama, 1970). The amount of return associated with low beta stocks versus high beta stocks seems inconsistent with the Sharpe version of the CAPM. At the same time, there has been widespread criticism of the mostly commonly known asset pricing model, the CAPM (Sharpe, 1964) as failing to describe equity asset returns. This has led some researchers to argue that long-term investors should always be fully invested in equities (e.g., Siegel 2014). The most obvious is that the equity risk premium (return of equities minus the risk free rate) is widely considered to be unexpectedly high. There are several historical features of equity market asset pricing that we will seek to explain. By incorporating the probability of such rare events in equilibrium factor models, we conclude that strategies that focus on “alpha” (risk adjusted return) as defined in Jensen ( 1967) are structurally superior to “smart beta” strategies that attempt to outperform an equity index by active exposure to one or more recognized factors. Most importantly, we will examine how including the potential for such large events changes traditional views of equity returns and the known factors that contribute to those returns. This paper presents a contribution to the financial literature by proposing a functional form for equity asset pricing that is both realistic and can be easily tested with a widely used data set extending over 30 years. At the individual firm level, such events also impact the likelihood of bankruptcy, a feature that is not well represented in the basic asset pricing literature. These events represent periods of increased volatility and in some cases very negative market returns for extended periods. The ongoing COVID-19 pandemic has strongly reminded equity investors that rare but extreme events occur from time to time. On the basis of empirical examination of a dataset stretching over 30 years without survivorship bias, we conclude that when the probabilities of rare extreme events are considered, strategies that focus on “alpha” (risk adjusted return) as defined in Jensen (J Finance 23(2):389–416, 1967) are structurally superior to “smart beta” strategies that seek to outperform a market index benchmark. Most importantly, we will demonstrate how including the potential for such large events changes traditional views of equity returns and the known factors that contribute to those returns. This paper presents a functional form for equity asset pricing that is realistic, and reconciles the observed high equity risk premium with the observed lower than expected slope of the Security Market Line. At the individual firm level, such events also impact the likelihood of bankruptcy, a feature that is not well represented in the traditional Capital Asset Pricing Model.
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