Analyzing investments whose histories differ in length

This study explores multivariate methods for investment analysis based on return histories that differ in length across assets. The longer histories provide greater information about moments of return, not only for the longer-history assets, but for the shorter-history assets as well. To account for the remaining parameter uncertainty, or ‘estimation risk’, portfolio opportunities are characterized by a Bayesian predictive distribution. Examples involving emerging markets demonstrate the value of using the combined sample of histories and accounting for estimation risk, as compared to truncating the sample to produce equal-length histories or ignoring estimation risk by using maximum-likelihood estimates.