## Efficient Frontier

For those with any exposure to quantitative portfolio management you’ve probably come across something known as the Efficient Frontier. In simplistic terms its the optimal percentage one should invest in various assets (stocks, bonds, funds, etc) to maximize return and minimize risk. The common graphical interpretation is shown below. The problem is that although the mathematics and solution are elegant, Markowitz portfolio optimization just doesn’t work in real time. That is because returns, volatility, and correlation’s are constantly changing.

There is another major problem with portfolio optimization and that involves one’s definition of “risk”. The traditional financial/mathematical framework defines risk as standard deviation or volatility. But as most normal people quickly realize, standard deviation is NOT a good measure of risk. Most people actually measure risk by draw down or negative returns. The standard deviation framework penalizes large positive outlier returns along with negative ones. Most people don’t mind big lottery ticket gains but are very uncomfortable with negative returns.

Attain Capital has a newsletter focused on managed futures and did some interesting work when optimizing for minimal draw down or negative kurtosis (negative returns). Their conclusion is the optimal mix looks far different then using volatility:

If we expand our asset classes even further, the picture looks really different:

This analysis is interesting but also suffers from the same problems of data mining and look back bias that the traditional framework does. That being said, at least the definition of risk is more aligned with practitioners. One step at a time I guess. Here is a link to the full article.