Volatility Trading and Risk Management

Last week was interesting.

There is actually NOT a Chinese curse that says, “may you live in interesting times”. Apparently, the whole thing was made up by a British diplomat. Nonetheless, a lot of volatility funds were cursed by last week being interesting.

There are many things volatility funds can do, so their returns have a wide range. I’ve seen numbers ranging from up 25% to down 95% (we made a few percent and thank you for your concern). The median was a loss of about 30%. This is because most volatility funds are option sellers trying to collect the volatility premium. I’ve written about this a lot. It is a perfectly viable strategy. So how did a professional fund lose 95%?

I don’t know. Thankfully I wasn’t in that trading room. But some of it may be down to misunderstanding trade sizing when returns are highly negatively skewed, as they are when short volatility. I’ve written about trade sizing in these situations before, but the general problem can be seen in a simple example.

Optimal trade sizing according to the Kelly Criterion boils down to maximizing the function:
where p gives the probabilities of each outcome, b give the results of the bet and f is the bankroll fraction that we bet.

Consider a situation where we win a dollar 55% of the time and lose a dollar the other 45%. This trade has an expected value of 10c, and a Kelly fraction of 10% (i.e. to maximize account growth we should bet 10% of our money on each trade).

Now imagine a slightly different case where we win a dollar 54.75% of the time, lose a dollar 45% of the time and lose 10 dollars 0.025% of the time. This trade has an expected value of 7.25c but its optimal investment fraction is only 0.0489, less than half of the symmetrical case. To be clear, these trades have practically indistinguishable expected returns, but one should be traded half as big as the other.

Option strategies have enormous skew, and sometimes this can’t be accurately guessed at from looking at historical data. But if you don’t take skewness into account you could find yourself massively over betting. And possibly this is what short volatility funds didn't take into account.

Euan Sinclair6 Comments