A common refrain from investors is that they have bad luck hiring managers, but it’s more likely to be a consequence of how they hire managers.

Some investors chase performance, which is a risky business. Performance for the investment managers they hire tends to regress towards zero, which leads to disappointment relative to expectations. Often it means strong managers will either not be hired or not be retained.

In Chasing Performance is a Dangerous Game, INTECH Investment Management provides a framework for mitigating the detrimental effects of chasing performance by putting historical performance in its proper analytical perspective and focusing on the investment process.

A manager’s historical performance is the result of signal (positive, negative or zero) and noise. Some managers, of course, have positive true alphas. Investors know that these managers will beat managers with zero true alphas over time. The question is: how long do you need to identify the managers with positive true alphas?

Many believe a 10-year record is sufficiently long to make it easy to spot strong managers, but it is statistically unlikely that the strong ones will stand out over this time-frame.

Hypothetically, take a strong manager whose true average relative return is 200 basis points (bp) annually and true tracking error (standard deviation of relative return) is 800bp. This manager’s information ratio is 0.25.

And take 20 poor managers with true average relative returns of 0bp annually, true tracking error of 1,000bp annually, hence information ratios of 0.00.

Assume that all of the managers have uncorrelated relative returns.

INTECH has calculated the probability that a strong manager beats all 20 weak managers over a 10-year period at just 9.6%. It implies that chasing performance leaves the investor with the strong manager just 9.6% of the time, and the weak manager 90.4% of the time.

A practical approach is to ask how long a historical performance record is necessary to be 75% sure that the strong manager will beat all the weak managers. Given the same managers as above, the answer is 157 years. Naturally performance histories that long do not exist.

What to focus on
The investor should be interested in estimating the probability that a manager’s true performance is positive, given historical performance. This depends on three probabilities; the link between them is Bayes Theorem, which gives the probability of the causes of events.

To make things simple, assume that there are two possible “causes” for a manager’s historical alpha: an effective investment process, one with positive true alpha; or an ineffective investment process, with a zero true alpha.

The investor would like to know the probability that the manager’s true alpha is positive in light of his historical alpha.

The investor’s statistical alpha-beta analysis provides the probability of the observed alpha assuming that the manager’s true alpha is zero. This probability tends to be low if the manager’s observed alpha is high. There is little chance that a manager with a true alpha of zero will have a high observed alpha.

The investor can change the analysis to provide the probability of observed alpha given that the manager’s true alpha is positive. This probability tends to be higher because it’s more likely that a manager with a positive true alpha will achieve a high observed alpha.

The investor must assess the probability that the manager’s true alpha is positive, given the observed alpha. Obtaining this probability requires an analysis of the manager’s investment process without regard to historical performance. It requires the a priori probability that the manager has a positive true alpha.

Suppose the investor examines a manager’s investment process and concludes there is only modest reason for thinking it should be effective. The investor decides that the a priori probability that the manager’s true alpha is positive is 0.25.

The investor then uses that standard alpha-beta statistical analysis to obtain the probability of the manager’s observed alpha, given that the manager’s true alpha is zero. Suppose the observed alpha is moderately positive. Then a reasonable expectation for this probability might be about 0.25 – the observed alpha is above the manager’s true alpha of zero, hence not very likely to be achieved.

Next, the investor uses a modified alpha-beta analysis to obtain the probability of the observed alpha given that the manager’s true alpha is positive. Suppose the observed alpha is, again, moderately positive. Then a reasonable expectation for this probability might be about 0.50, because the observed alpha is then in line with the manager’s assumed true alpha.

Using Bayes Theorem, the investor calculates the manager’s probability of a true positive alpha, given the manager’s historical alpha at 40% and has substantial doubt that his true alpha is positive.

If the same analysis is applied to a manager with an investment process credible enough to assign a 0.75 a priori probability of a positive true alpha, the investor calculates there’s an 86% probability that the manager has a positive true alpha given his historical alpha, hence concludes that the manager probably does have a positive true alpha.

It’s notable how much the answer changes based on the investor’s assessment of the a priori credibility of the manager’s investment process.

In conclusion, historical performance alone is not an effective basis for identifying a strong manager. It’s not useless, but it must be combined with other information. The correct use of historical performance relegates it to a secondary role. The primary focus in manager choice should be an analysis of the investment process.

INTECH’s paper Chasing Performance Is A Dangerous Game was written by Robert Ferguson, Jason Greene and Carl Moss. INTECH, a Janus Capital Group company, uses an investment process based on a mathematical theorem that attempts to capitalise on the random nature of stock price movements. INTECH® is a registered trade mark in the US of INTECH Investment Management, and is known in Australia as Enhanced Investment Technologies. This is not a solicitation and past performance is not a guarantee of future results.