| Description |
According to classical portfolio theory, two implications follow when an asset has a positive alpha against some benchmark: (1) the benchmark is mean-variance inefficient; (2) by combining the positive alpha asset with the benchmark, one can improve the mean- variance efficiency of the benchmark. The first implication is well known, but the second is largely ignored in the existing literature. This dissertation tests and applies the second implication. The dissertation has two chapters. Chapter 1 empirically tests the theory. Specifically, we test whether the alpha of an investment relative to one's existing portfolio can be used to improve out-of-sample performance as measured by Sharpe ratio and four-factor alpha. For the period 2000 - 2014, we confirm this for the Vanguard S&P 500 Index Fund and the Growth and Small Index Fund, which we extend by adding various Exchange Traded Funds. Chapter 2 applies the theory in the mutual fund context in order to shed light on the relation between active management and fund performance. Recent studies have documented a positive relation between the degree of active management and mutual fund performance. We show that this relation holds only for fund managers who trade in an optimal way. The optimality measure that we develop, "investment alpha," captures whether a mutual fund is trading towards mean-variance optimality, which, we argue, is the first-best choice for mutual fund managers within a mean-variance framework. This investment alpha is similar to previous work using evaluation alphas such as Jensen's alpha, except that our benchmark is the manager's own portfolio. We show that if the investment alpha of a fund's incremental portfolio - defined as the portfolio obtained by collecting the changes in a manager's positions over a given period - is positive then the fund is trading in the "right" direction. We show empirically that managers who do so outperform, and the more so if they are more active, and that investors react to the correct direction through increases in fund flows in the subsequent quarter. Actively managed funds that don't trade toward mean-variance optimality do not outperform. |
