Means, Medians and Mistakes

The mean is the average value of a sample and the median is the 50th percentile value, the middle number.

The difference is straightforward and is known by anyone with a high school education. But a lot of traders, particularly option traders, seem to misunderstand what it means in practice. Any trade with edge needs to have a positive expected value, which is the mean return. Unfortunately, if your trade has highly skewed returns you are much more likely to observe a median value than a mean value. So returns like 1%, 1%,  1%, 1%, 1%, 1%,1%, 1%,1%, 1% lead you to believe you have a mean return of 1%, but the next day you get a minus 21% return. Median = 1%. Mean = -1%.  This is the downside of the median being more robust to outliers. Obviously the way to avoid these nasty surprises is to use a larger sample when testing an idea. But many option traders seem to have no idea how large their sample needs to be. And that is why selling strangles seems to be a much better idea than selling straddles. The strangles will be profitable far more often. But this is confusing median for mean. For a given volatility premium the straddles have much better risk/reward characteristics. 

And that is even before the compounding mistake of thinking there is always a variance premium. Blindly selling strangles isn't a good idea. It is a terrible idea.

A similar statistical error happens with trade sizing. Many traders like to claim they "don't make predictions". Not only is this an odd thing to insist upon, it is completely wrong. Every buy order is a prediction that the market is going up. Their justification for this (wrong) denial of prediction is that they can only know probabilities rather than specific outcomes. And this part is clearly correct. A prediction can have uncertainty and still be useful. But then these traders (literally the same ones!) insist they can't use an idea like the Kelly Criterion for sizing trades, because they have uncertainty in their prediction (which they insist isn't a prediction). First, it is possible to incorporate uncertainty into Kelly. And second, how can someone be confident enough to trade but not confident enough to size?

Euan SinclairComment