### “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? I suspect that most managers either cringe or rejoice internally upon hearing this question depending on how they actually performed the previous month. Almost implied in the question is the notion that the manager’s recent performance is some sort of indicator of his ‘skill’ at investing. But was it skill or was it 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 should we say skillfully), there is a scientific way to approach 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 somehow decipher the trader’s abilities. 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 3 or fewer trades out of 10 is 17.2%, the chance of winning 6 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 a true 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 skill, it will be more obvious over the long run as opposed to 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’.

### Focusing on Short-Term Performance can be Dangerous

Placing undue focus on short term performance is a very slippery slope – it can be hazardous to one’s trading health. A seemingly ‘anomalous’ bad (or good) month may cause a manager to try to avoid (or replicate) his actions in that particular month going forward, when in reality, this ‘anomaly’ may have been nothing more than typical short term randomness. Yet by changing his actions the manager may lose some of his inherent ‘market edge’. It is not only dangerous to managers and the psychology they take into trading, but it is also dangerous to investors.