Implicit Timing and Pseudo Options in Stock Bulls and Bears

Abstract

An asymmetric risk metric constructed to capture the nonlinearity in covariation of stock returns with bullish and bearish states of the market has been found to be priced in the economy. Stocks can be represented as portfolios of claims on the assets of firms and claims contingent on the state of the market. A bullish stock has a convex return profile with respect to the market, is implicitly a good market timer and is long pseudo options on the market. A bearish stock has a concave profile, is implicitly a poor timer and is short pseudo options. Investors would demand compensation in the form of higher expected returns for bearish stocks to suffer negative insurance. Conversely, they would be willing to pay more, hence lower expected returns, for bullish stocks to gain protective insurance. This paper finds some empirical justification to thinking about asymmetric risk as pseudo positions in options. Evidence is also presented to support firm-level leverage as a plausible source of such options-like characteristics. Leverage and size do not appear to be correlated with each other and may well be two distinct factors associated with nonlinearity in stock returns. These results lead toward a nonlinear pricing framework comprising an asymmetric risk factor.