Don’t fall for the “we don’t have enough observations for CVaR optimization” excuse.

I keep seeing this claim from mean-variance proponents, but it requires just a bit of CVaR experience to reject.

Below, you see an optimization of an equity portfolio consisting of 10 US indices.

Each quarter of the past 15 years, we simulate 100 synthetic future paths and minimize the variance and 90%-CVaR.

90%-CVaR and 100 joint scenarios implies that we use just 10 observations to compute the tail risk each quarter.

As you can see, this still leads to a portfolio that nicely outperforms the variance optimized one. In fact, the cumulative outperformance is 77% over the past 15 years.

Mean-variance exposes you to unnecessary tail risks and leaves a lot of money on the table. It should not be used for investment management in practice.