Overconfident Forecasts and Active Portfolio Performance

The paper examines the problem of portfolio selection based on the forecasts of unknown quality in a mean-variance framework. Early work by Treynor and Black (1973) established a relationship between the correlation of forecasts, the number of independent securities available and the Sharpe ratio which can be obtained. Thier framework forms an important part of the practitioners' guide to active portfolio management as described in Grinold and Kahn (1999). Treynor-Black analysis was based on the assumption that the correlation between the forecasts and outcomes is known precisely. In practice, given the low levels of correlation possible, an investor may believe himself to have a different degree of correlation from what he actually has.The current paper therefore describes how the portfolio performance depends on both the anticipated and true correlation when these differ. The portfolio performance is assessed according to the Sharpe Ratio and a measure of expected utility obtained from investing on the basis of the forecasts. We find that the investor's degree of self-confidence plays an important role in the performance obtained.Investor's Sharpe Ratio is maximised when his estimated correlation coincides with his true correlation. Provided that his true correlation is above zero, an overconfident investor attains almost as good Sharpe ratio as the one who can accurately estimate his forecasting skills, while underconfidence results in a significantly lower Sharpe ratio. However, the Sharpe ratio is unable to capture all the efficiency loss which, except for the change in reward for risk, is attributed to the loss in utility due to being led to hunt for an inappropriate portfolio. We quantify the utility obtained under this information set in terms of the Sharpe ratio that would give the same utility. We find that the measure of expected utility stays almost symmetric to both over and underestimation errors