Capital Asset Pricing with a Stochastic Horizon

In this paper we present empirical tests of an extended version of the capital asset pricing model (CAPM) that replaces the single-period horizon with a probability distribution over different horizons. Adopting a simple parameterization of the probability distribution of the length of the horizon, we estimate the parameters of the distribution as well as the parameters of the CAPM. We find that the extended model is not rejected for several different samples of common stocks, and for these samples it outperforms not only the standard CAPM but also the Fama–French (1993) 3-factor model. The probability distribution over horizon dates varies over time with the New York Stock Exchange (NYSE) turnover rate. We also find that returns satisfy the Euler equation of a representative financial institution that holds the market portfolio and has horizon probabilities estimated from 13F filings.