As previously written by Covenant Capital Management

“So, how did you guys do last month?”

It seems like the most natural and logical question to ask an investment manager. But is it the right question to ask? Most managers either cringe or rejoice internally upon hearing this question, depending on how they performed the previous month. Almost implied in the question is the notion that the manager’s recent performance indicates his ‘skill’ at investing. But was it skill or luck (good or bad) that constituted that month’s performance? And how can one possibly separate the two?

#### A Laboratory for Luck and Skill

Luckily (or skillfully), there is a scientific approach to the problem. We can consider a game of chance with some known degree of ‘inherent skill.’ For instance, imagine a trader who has a 50% chance of winning each trade he takes. Suppose the trader makes twice as much on his winning trades than he loses on his losing trades. This is equivalent to being paid 2 to 1 on a fair coin flip. The long-run expected outcome of each trade is \$0.501. This \$0.50 expectancy is the ‘inherent skill’ of the trader. But an outside observer does not have this knowledge. The outside observer only has the trader’s track record and must use it to decipher the trader’s abilities somehow. So how is this best accomplished?

#### Time Will Tell

The key to separating ‘skill’ from ‘luck’ lies in the fact that the odds in the scenarios given above actually change depending on the number of (independent) observations3. For instance, while the chance of winning three or fewer trades out of 10 is 17.2%, the chance of winning six or fewer trades out of 20 is only 5.8%. Figure 1 illustrates how the odds of observing a winning percentage of less than or equal to 30% for a situation with an actual winning percentage of 50% diminish as the number of observations increases.

From the exercise above, it should be clear that if a trader truly has the skill, it will be more evident over the long run than in the short run. Put another way, the short-term good and bad luck offset over the long run, and all that remains is the manager’s skill or ‘market edge.’