Associations between Realized Returns and Risk Proxies Using Non-Random Samples

We provide evidence that associations between realized returns and common risk proxies (factor betas and implied cost of equity estimates) vary with properties of the sample returns distribution used to estimate those associations. We consider two forms of non-random sampling from a reference distribution of realized returns for all CRSP firms with at least 12 consecutive monthly returns during 1976-2009. First, using non-random sampling based on the sign of returns, we show that risk measures are negatively (positively) associated with realized returns in bad (good) states. Second, and more generally, we focus on the effects of sample selection criteria, in the form of data requirements, that result in non-random selection from the reference distribution, using the sample for which five implied cost of equity estimates can be estimated as an example. We show that the returns in the cost of equity sample are a non-random sample from the reference distribution, and that results of association tests with realized returns are sensitive to this form of non-random sampling. We illustrate a bootstrapping approach to adjust the cost of equity sample returns distribution to match the reference returns distribution. Reversing inferences from the unadjusted sample, associations of implied cost of equity estimates with realized returns are positive in the distribution-matched samples.