Holding Period Return-Risk Modeling : Ambiguity in Estimation

In this paper we explore the theoretical and empirical problems of estimating average(excess) return and risk of US equities over various holding periods and sampleperiods. Our findings are relevant for performance evaluation, for estimating thehistorical equity risk premium, and for investment simulation.Using a unique set of US equity data series, comprising monthly prices anddividends based on consistent definitions over the 132 year period 1871-2002, weinvestigate the complex effect of temporal return aggregation and sample estimationerror. Our major finding is that holding period risk and return statistics show anextraordinary sensitivity to the choice of the starting point in calendar time. Forexample, over the period 1926-2002 there is a difference of almost 140 basis pointsbetween the average annual total return starting in January compared to starting inJuly, and a difference of almost 7 (!) percentage points in estimated annual volatility.This is yet another way in which stock price seasonality manifests itself, but thisambiguity in the underlying estimation process seems completely neglected in thecurrent literature