Luck versus skill

Can we tell the difference between luck and skill? This is not an easy task, yet it is critical for separating good from bad managers. The worst combinations for investment decisions are cases of the poor manager who gets lucky and the good manager who get unlucky. In both of these cases, there should be mean reversion in returns which will affect portfolio performance for the negative. Lets take the simple case if you make the wrong choices of managers. In the case of a poor manager who is lucky added to a portfolio, performance will suffer as the returns move back to the longer-term true mean. The mean reversion from the good luck will lead to future lower returns. In the case of a good manager who faces bad luck, there will be under performance in the portfolio because of exclusion. The bad luck will filter out what could be a good manager. The portfolio will not get the bounce back to the true mean.

Luck creates noise in a performance numbers. There is a true distribution of returns for a manger based on his skill. The addition of luck will increase the span of the distribution. It will create error in measuring the true distribution. Over a short time period, it creates sample error. There will be greater volatility which will drop the information ratio of the manager and make him less attractive. The increase in the spread of the distribution will also mean that the sample properties may not match the true distribution. You will need more data to determine the true distribution. Luck is bad for the skill manager since it masks the true distribution of performance.

One could argue that all market participants face good and bad luck so everyone is affected the same. Other will say that skill managers can have a better chance at making good luck which makes sense at a high level but in reality is a somewhat empty comment. However, it can be put differently by asking whether some markets are more prone to luck versus others. Or, are there strategies that can reduce the impact of luck?

We can go back and look at the fundamentals of active management. We can say that more trading can reduce the chance of luck driving returns. If there are more trades, there will be a greater sample of trading behavior. Les trading means that any one trade could be lucky. Chance will be reduced if there is more activity. Of course, there is a problem that effort and work can be confused.Still, looking at trade level behavior helps to answer the luck skill problem.