A reader got in touch with me asking for more details on Peter Urbani's Cornish Fisher strategy.
It's a pull-all-your-money-of-the-table strategy designed to avoid catastrophic losses and keep returns compounding smoothly over time.
How do we think about potential catastrophic returns?
By measuring skewness and kurtosis of course!
If we estimate the probability of incurring a loss using the Normal distribution (which is blissfully ignorant of the third and fourth moments) we can use it as a baseline.
Now estimate the probability of incurring a loss using the Cornish Fisher expansion.
Any differences should chiefly come from more negative skewness and excess kurtosis.
If you spot a large difference you should pull your money out.
The issue is that it uses backward looking statistics, if we inserted in forward looking implied measures perhaps it would become more agile in avoiding large losses.
Taking a step back, the Cornish Fisher use of cumulants is very interesting. I need to make time to learn about cumulants and their applications.