No-arbitrage conditions and expected returns when assets have different β’s in up and down markets

Abstract

We present a model of expected returns when assets have different β's in up and down markets. Using no-arbitrage argument, we show that upside and downside β's are priced separately, and their risk premiums can be expressed in terms of the price and expected payoff of a call and a put option, respectively, on the market index. For the upside β, the higher the price of the call option relative to its expected payoff, the smaller the risk premium; but for the downside β, the higher the price of the put option relative to its expected payoff, the larger the risk premium. Our model provides a useful perspective on what systematic risks are and how they are priced. Empirical evidence shows that contemporaneous stock returns are strongly correlated with downside β's, but weakly correlated with upside β's.