Mandate and the montroid

May 15, 2018
Yoshiki Obayashi

A precise and tight investment mandate is the bedrock of performance measurement. Evaluating managers without properly accounting for their mandate is like scouting athletes without knowing for what sport. A deep understanding of how investment mandates impact performance allows allocators to quantify the true value added by active managers.

An investment mandate sets the rules of the active management game, and dictates what the manager can and cannot do. A clear mandate specifying well-defined risk limits and universe of tradable securities lays out every possible decision the manager could make. Combined with market data, it further defines every possible outcome the manager could have achieved. In other words, the mandate uniquely determines the manager’s opportunity set.

Take two long-only US large capitalization equity managers benchmarked to the S&P 500 where one is unconstrained and the other cannot exceed 50 positions at a time. The opportunity sets of these two managers are vastly different–one is playing baseball while the other is playing softball–so how can an allocator quantify or compare the performance of these two managers?   

Montroid: an objective, skill-less benchmark 

Quantifying a manager’s value-add requires a measure of distance from a baseline outcome that can be achieved without active decisions. To identify the correct skill-less benchmark among the trillions of potential outcomes in an opportunity set, we must consider what is achievable without skill, or, equivalently, with only luck.

Luck is a factor in most professions, but more so in some than others. The nation’s top surgeon performing an intricate operation may have an 80% success rate, whereas I could not cure a single patient. Rafael Nadal may have an 85% chance of beating Roger Federer on clay courts, while Vegas odds would reach infinity before anyone bets a single dollar on me. Yet, when it comes to investments, there’s a decent chance that I can outperform, while blind-folded, the most talented fund managers in the world on a given week.

In medicine and professional sports, as with many other disciplines, not a single instance of success can be achieved solely by luck. In contrast, the extreme opposite is true in active management: every possible outcome within an opportunity set is achievable by random buy and sell orders that comply with the mandate. Let the implications sink in for a moment.

If every outcome is accessible by chance, then one can find the expected outcome of the opportunity set in the same way that one can calculate the expected value from the roll of a 6-sided die to be 3.5. This, which we call the montroid, has natural interpretations of being the outcome an allocator can expect from an unskilled manager and also the performance of the mandate itself. Every mandate generates its own bespoke benchmark, its montroid.

Measuring true value-add

The montroid serves as an objective, skill-less baseline against which the manager’s value-add may be measured. It is an investable, passive alternative to the manager that yields the mandate’s performance without active decisions. As long as the opportunity set is constructed meticulously and accounts for market frictions such as transaction costs, there is not much room for debate as to the fairness of the montroid, and takes the guessing and arguing out of the traditional benchmark selection process.

As long as the risk limits are internally consistent, no two distinct mandates have the same opportunity set. It’s mathematically possible for two distinct opportunity sets to have the same montroid, but it is not something that can be safely assumed even if the mandates feel qualitatively similar. If there are far more distinct mandates than there are benchmark indices being used, in the long-only equity space for example, benchmark misspecification is likely the norm and not the exception.

Vague mandates eliminate accountability 

Without a clear investment mandate, success and failure are undefined concepts, and one cannot measure true value-add. Without objective measurement, an allocator has no ability to quantify the return on fees paid, which also deprives value-adding managers of due credit. Vague mandates only benefit unskilled managers, at the expense of allocators and skilled managers. 

You may be wondering where the word montroid comes from. It's derived from the mathematical concept of a centroid, which identifies the most mediocre outcome along one or more dimensions from the manager's opportunity set. Unofficially, it may also be used as an all-purpose jab, as in "don't be such a montroid."

The views and opinions expressed in this article are those of the author(s) and do not necessarily reflect the views of Applied Academics LLC or any of its affiliates.  

Photograph by Mikihiko Obayashi