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 sample periods. Our findings are relevant for performance evaluation, for estimating the historical equity risk premium, and for investment simulation. Using a unique set of US equity data series, comprising monthly prices and dividends based on consistent definitions over the 132 year period 1871-2002, we investigate the complex effect of temporal return aggregation and sample estimation error. Our major finding is that holding period risk and return statistics show an extraordinary sensitivity to the choice of the starting point in calendar time. For example, over the period 1926-2002 there is a difference of almost 140 basis points between the average annual total return starting in January compared to starting in July, 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 this ambiguity in the underlying estimation process seems completely neglected in the current literature.