The value of expected return persistence

Abstract

This work utilizes the fractional Black–Scholes model to estimate the option-implied Hurst exponents, interpreted as forward-looking expectations of return persistence. The focus of the paper is on how corresponding believes enter into factor based asset pricing models. Empirical analyses are carried out for the cross-section of S &P 500 stocks. We make the important observations that (i) stock returns show significant patterns of time-varying persistence and (ii) corresponding believes are reflected within option prices. Incorporating the Hurst exponents allows us to split up CAPM betas into pure market correlation risk (around 70–80%) and into excess persistence believes (about 20–30% of the risk loading). A direct comparison to standard CAPM shows that incorporating persistence believes significantly improves the predictability of future realized returns, and partially releases the beta anomaly. The effects become even stronger the greater the prediction horizon. Hence, the concept of fractal motions enables a deeper understanding of risk structures without the need of additional risk factors.