The Skewness and Kurtosis of European Options and the Implications for Trade Sizing

Abstract

Long vanilla call option positions have unlimited profit potential and limited loss potential, and the opposite is true for short call option positions. Long vanilla puts do not have unlimited profit potential but, for commonly traded strikes, the maximum profit of a long put will be far greater than the maximum loss (the premium of the option). Again, the opposite is true for short put positions: their maximum loss is far greater than the potential gain. Equivalently, option returns are highly skewed and kurtotic. In this note, we calculate the skewness and kurtosis for European calls and puts. Next, using a power series expansion, we derive a simple approximation to the Kelly fraction for optimal trade sizing when returns are non-normal. Taken together, these two results are used to show that the higher order moments of option positions have an economically significant effect on optimal trade sizing when using the Kelly criterion.