Alpha Alchemy: Diversifying Without Diluting Alpha

Abstract

Managers are often evaluated and selected on the basis of their portfolio’s stand-alone risk and return properties. This is too narrowly focused. The basics of mean-variance optimization tells us that covariance and the relationship of a security’s returns within the context of the overall portfolio is important. We illustrate how the basics of portfolio construction with individual securities also applies to building a portfolio of managers. First, we show the statistical properties of different asset classes, as more and more managers are used to get exposure to the asset class. Depending on the asset class, tracking error, relative skewness, and relative excess kurtosis improve at different rates. This is important for considering how many managers may be necessary to get exposure to an asset class. We then illustrate an optimization method of combining the managers. Although the managers, on their own, may not have statistically positive alphas, they can be combined in a way to improve the likelihood that the portfolio of managers has a statistically positive alpha. The optimization method is not a substitute for traditional due diligence. It is just one additional tool useful for manager selection and portfolio construction.

TOPICS: Wealth management, portfolio construction, manager selection

Key Findings

• • Combining managers can reduce tracking error, but the relationship between tracking error reduction and manager addition depends on the asset class. Specifically, it depends on the average tracking error and average correlation of excess returns within an asset class.

• • A slightly modified Sharpe ratio is equivalent to a t-value. An information ratio (with Jensen’s alpha in the numerator) can also be interpreted as t-value. Maximizing these ratios is equivalent to maximizing confidence that the excess return or alpha will be positive.

• • Individual managers with no or even negative alpha can be combined to give positive alpha.