How many managers should you review before you pick one?

Choices, choices, choices. There are just so many managers to choose for a portfolio. Look at the major database, and you will find hundreds of managers of all sizes, styles and skill. Using some simple criteria, the list can be reduced significantly. Minimum size, minimum track record, max drawdown, and max volatility could be just a few ways of reducing the pool of managers, yet there could still be a sizable number of managers. So how many managers do you have to look at before you find the right one? 

This a classic decision science problem given a specific name, "The Marriage Problem" and more recently "The Secretary Problem". The lay-out of the problem is simple. How many candidates for marriage or a job should you review before you make a decision? This is assuming that once you make a decision the game stops and you cannot go back. If you look at all candidates and have not made a decision, you will have to take the last one. You offer or go on with the process. Martin Gardner solved the problem in a 1960 Scientific American article. For an in-depth review on the math see, "Who Solved the Secretary Problem?" and the rejoinder.

A simple algorithm based on optimal stopping times has been developed which states that 36.8% of the total sample of choices should be reviewed before a decision is made. So if you take a large sample and reduce the number based on some simple criteria, you may still be left with 10 candidates. The question is how many should you interview before you make a final decision. The answer is 36.8% (4 out of 10) of the sample or 1/e should be reviewed. Then choose the first candidate that is better than the set reviewed earlier. Of course, if the best manager was in the initial 36.8% of the sample, you will be stuck with a second best solution. Nevertheless, you will end with a good choice if you follow this algorithm. 

Now this may seem far-fetched as an explicit way to choose managers within the hedge fund space, but like many fun math problems there is a kernel of useful information that can help with other more serious problems. So what can be done for hedge fund managers selection and due diligence? 

1. Use a filter mechanism to cut the number of managers to a smaller size based on set minimum standards. A simple filter could be size, length of track, and worst drawdown.

2. Set criteria for what you are looking for in the due diligence.

3. Set the number that can be initially interviewed.

4. Start reviewing managers to get a "feel for the sample" formed.

5. After reviewing the initial sample, pick the first manager that is better than the set reviewed. 

This is not perfect and can be subject to criticism, but it forms a simple algorithm that can start the process and lead a good outcome. I am open to other ideas, so let me know what you think.