# Skill versus luck: Should that be the question?

MANY STUDIES HAVE BEEN conducted distinguishing manager skill from luck ‒ most with inconclusive outcomes ‒ and very few cases where skill can be identified with statistical accuracy. Even in South Africa, a number of asset management houses that provided good performance for a few years but then disappeared from the limelight or from existence ‒ BoE, Norwich, Quaystone, to name just a few.

Part of the difficulty in distinguishing skill from luck lies in a disconnection that often occurs between a manager’s views on stocks and financial markets and what’s actually represented in his portfolio. That happens uninten- tionally. Investment constraints are the main culprit, as they limit the manager’s ability to express his view in the portfolio. But volatilities and correlations between stocks also play a part. That latter phenomenon is hardly ever mentioned and is the focus of this article.

First, a few definitions. The correlation between a manager’s view and the active weights in his portfolio ‒ that is, how well the portfolio reflects the manager’s view ‒ is called the “transfer coefficient” of the portfolio. Transfer coefficients vary between 0 and 1.* A low transfer coefficient means a large portion of the risk in a portfolio is in fact random and hence there’s little connection between the manager’s view and the final return on the portfolio.

For a transfer coefficient of 0,5 only 25% of a portfolio’s return variance is related to skill (see C Holt, 2007). If the transfer coefficient is lower, then even less of the return variance can be attributed to skill with any degree of statistical accuracy. That is: for low transfer coefficients you’d need many years of data ‒ longer than the average portfolio manager’s working career ‒ before you could distinguish between luck and skill.

What that means is if your manager has good performance over a period but a low transfer coefficient, then you have no way of predicting whether his good performance