Least Squares Predictions and Mean-Variance Analysis

In an economy with one riskless and one risky asset, we compare the Sharpe ratios of investment funds that follow: i) timing strategies which forecast the market using simple regressions; ii) a strategy which uses multiple regression instead; and iii) a passive allocation which combines the funds in i) with constant weightings. We show that iii) dominates i) and ii), as it implicitly uses the linear forecasting rule that maximizes the Sharpe ratio of actively traded portfolios, but the ranking of i) and ii) is generally unclear. We also discuss under what circumstances the performance of ii) and iii) coincides