This paper examines the expected returns of a family of option trading strategies on individual stocks to test whether the (projected) stochastic discount factor (SDF) is monotonic in the terminal stock price. We characterize a class of option trading strategies whose expected returns are increasing in the strike price under a monotonic SDF. Call and put options are special cases, but the set also includes butterfly spreads, bullish call spreads, and binary options. Based on our empirical results, we find that expected returns are increasing in the strike price for all the option trading strategies considered in this paper which is consistent with a monotonic SDF. The framework outlined in this paper can be used to test classes of asset pricing models like the CAPM, representative agent models with expected utility and the Black-Scholes model.
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