Institutional investors often hear the following claim: It takes approximately 40 years of live performance to determine whether an active manager can outperform a chosen benchmark.
Indeed, there is a mathematical basis for this proposition. Assume a money manager can outperform a benchmark by 1% a year, with a tracking error of 3% per annum. To obtain a t-statistic* of 2 will take (2X3%/1%)2 or 36 years.
Although this proposition is not without merit, such a lengthy trial period is impractical for plan sponsors and other institutional investors. In addition, it carries within it the seeds of an unsettling corollary. Because most money managers have been in business for less than 36 years, they cannot know if their strategy adds value. Worse still, they cannot identify and rectify any problems if it takes that long to determine whether a problem exists!
But most money managers are confident of their ability to add value and believe they can identify any performance problems that their products may experience. In effect, they behave as if the claim were utterly false, and, as we shall soon see, it is. In fact, both plan sponsors and money managers can rapidly detect underperformance in one of two ways:
1. Settle for a lower t-statistic; or
2. Extract as much information as possible from the manager's returns.
Both methods work. The first is rooted in the observation that major capital markets are very efficient. Consequently, it is difficult to outperform a passive benchmark. A lower standard of proof might therefore suffice. This view can be formalized in a Bayesian framework by specifying the a-priori probability of a randomly chosen manager outperforming the chosen benchmark.
The second method is rooted in the observation that changes in the mean of a random process can be detected rapidly using a statistical process control technique known as the Cusum procedure. "Cusum" derives from the procedure's use of the cumulative arithmetic sum of excess returns to determine when a change in a manager's performance has taken place.
The accompanying chart plots a sequence of monthly excess returns overlaid with the cumulative sum of this sequence. The sequence of excess returns is noisy, and it is difficult to determine the average excess return or to tell when, if ever, the mean of the sequence changed. In sharp contrast, the cumulative sum of the sequence shows a clear-cut pattern of outperformance followed by underperformance with a transition in the 25th month. The manager's current excess return is given by the current slope of the Cusum plot (0.1% per month in the first half and -0.1% per month in the second half).
The human eye detects changes in slope surprisingly quickly, so the transition from outperformance to underperformance in the 25th month is readily apparent. In essence, the Cusum procedure formalizes our visual ability to detect changes in slope into a statistical test that rapidly discriminates acceptable from unacceptable performance. In this particular example, it raises an alarm in the 35th month, 10 months after the performance starts to deteriorate.
In formal statistical terms, the Cusum test is a likelihood ratio test. It compares the probability that a sequence of excess returns is generated by a superior manager to the probability that the same sequence is generated by an inferior manager. In doing so, it discards old returns intelligently, keeping only the data required to maximize its ability to discriminate between superior and inferior managers. When the likelihood ratio exceeds a predetermined threshold, an alarm is raised.
The choice of a threshold involves a trade-off. If we lower the threshold, underperformance will be detected quickly, but many false alarms may be raised. Raising it will result in fewer false alarms, but poor performance will take longer to detect. In practice, we find that setting the threshold to detect benchmark-like performance in 31/2 years is a practical compromise between detection speed and the rate of false alarms. For any given rate of false alarms, no other procedure can detect underperformance faster.
Paradigm Asset Management uses the Cusum procedure to monitor its portfolios. If and when performance starts to flag, we can detect it relatively quickly, and take the measures necessary to turn performance around.
Plan sponsors, too, can use Cusum to monitor their money managers. By rapidly identifying weak performers, it allows plan sponsors to revisit their initial due diligence process at an opportune time to determine whether the underperformance is merely accidental or the unhappy result of a fundamentally flawed process.
Routinely applying the Cusum procedure to active portfolios will almost certainly enhance a money manager's process, reduce the likelihood of a plan sponsor retaining a chronically underperforming manager, and foster better communication between managers and plan sponsors.
*A t-statistic is a measure of the level of confidence in a statement being accurate. For investing, it reflects the likelihood that a manager's excess returns are because of skill rather than luck. A t-statistic of 2 would be 95% confidence that the manager's excess returns are due to skill.
Thomas K. Philips is chief investment officer of Paradigm Asset Management, New York
