Changing Expected Returns Can Induce Spurious Serial Correlation

Abstract

Changing expected returns can induce spurious autocorrelation in returns and possible bias in other financial models. We show why this happens with some simple examples and then investigate its prevalence in actual equity data. Assets may undergo changes in expected returns for a variety of reasons. Hence, autocorrelations computed from extended records can be subject to spurious bias. The bias might be difficult to measure because of noise but a re-sampling method (the bootstrap) discloses its rather ubiquitous presence in US equity data. Turning the phenomenon on its head, return serial correlation in an efficient market is evidence of changing expected returns. Estimated risk measures such as “beta” might also be subject to bias induced by non-stationary mean returns, but the direction of the bias is more ambiguous.