The Alpha Bias in Asset Allocation Performance Measurement

Professional asset allocators frequently report positive alphas, and the generation of alpha is widely discussed in the context of asset allocation. This paper demonstrates that two-fund asset allocation strategies contain a positive-alpha bias and derives an expression for the alpha of an asset allocator. An examination of the properties of the alpha of an asset allocator show that while it does capture an element of asset allocation ability, it is influenced by a factor unrelated to ability and subject to manipulation so that randomly chosen positions can lead to long-term positive estimated alphas. Only extremely large but impractical sample sizes can eliminate the bias, which can add as much as 25 basis points to the performance of a manager using a random number generator. Artificially setting the beta to the proportion of periods in the market can eliminate this bias, but alpha still cannot separate capable asset allocators from those using random number generators. Widely-used alternatives such as Henriksson-Merton, Treynor-Mazuy, and the Sharpe ratio show some ability to discriminate but have unacceptably large Type I errors. Thus, this paper provides new results that show why asset allocators are so enthusiastic about reporting alphas, why such results must be looked upon with skepticism, and why alternatives do not perform any better. In general, alpha and these performance evaluation techniques are able to recognize good managers, but bad managers are lumped in with good ones