Alpha is the most popular measure for evaluating the performance of both individual assets and funds. The alpha of an asset with respect to a given benchmark portfolio measures the change in the portfolio’s Sharpe ratio driven by a marginal increase in the asset’s portfolio weight. Thus, alpha indicates which assets should be marginally over/underweighted relative to the benchmark weights, and by how much. This study shows that alpha is actually a bad guideline for portfolio optimization. The reason is that alpha only measures the effects of infinitesimal changes in the portfolio weights. For small but finite changes, which are those relevant to investors, the optimal weight adjustments are almost unrelated to the alphas. In fact, in many cases the optimal adjustment is in the opposite direction of alpha – it may be optimal to reduce the weight of an asset with a positive alpha, and vice versa. Rather than employing alphas as a guideline, one can do much better by direct optimization with the desired constraint on the distance from the benchmark.
We provide new evidence for diseconomies of scale at the mutual fund level. Building on Berk and Green (2004) and allowing for gradual adjustment to equilibrium, we show that (quarterly) changes in fund performance are strongly negatively related to lagged predicted fund flows. We find that alphas would be more cross-sectionally dispersed and more persistent without the damping effect of flows. Thus, flows are an important factor behind the lack of predictability in mutual fund performance. This flow mechanism is strongest for smaller and more active funds with higher expense ratios, suggesting that it is related to the stock illiquidity and costly search for investment opportunities.