Two essays in analyzing delegated portfolio management relationships through relative portfolio measures

Abstract

In my first essay, I demonstrate how the Cremers and Petajisto (2009) Active Share measure can be re-parameterized into the standard portfolio parameters we typically see in other portfolio management studies, namely betas and standard deviations. This demonstrates that Active Share is not very different than the measures we traditionally use to study portfolio management. One of the parameters that results from the re-parameterization is a measure of the risk of the manager's active bets, the volatility of the implied hedge position relative to the benchmark. This parameter is equally as strong as Active Share in predicting excess performance and helps give a better economic understanding of why Active Share exhibits predictive power. Active Share and this implied hedge measure are like a confidence and information problem. In my second essay, I use the idea of benchmark relative investment optimization as outlined in Roll (1992). These portfolios are sub-optimal but they can be better than the alternative, i.e., better than the portfolios that the principals could build themselves. I outline the conditions under which delegated managers increase the principal's utility. Additionally, if implemented properly, tracking error constraints, Jorion (2003) and beta constraints, Roll (1992), can force the delegated manager to buy a more efficient portfolio than the benchmark. Thus, even though relative utility maximization is sub-optimal, if the delegated manager is more skillful than the principal in portfolio construction, delegated portfolio management is still likely preferred to naively holding the benchmark.