A Better Portfolio Optimization Method

You may have heard of Markowitz’s Critical Line Algorithm, or CLA. CLA was Markowitz’s attempt to solve the problem of portfolio optimization using quadratic math. For a couple reasons is was an ingenious invention.

But it also has its problems.

The problem with CLA is that it demonstrates large changes in the portfolio with small changes in the forecasted returns of assets. This is a big problem that seems intuitive, but the widespread influence of CLA shows that people are not universally aware of a solution to this problem. While the Critical Line Algorithm isn’t used universally, its implications are everywhere in finance in the construction of portfolios.

So what causes these flaws?

According to Marcos Lopez de Prado in Advances in Financial Machine Learning, the problem with CLA is attributable to covariance matrices basically being unaware of asset classes. In other words, when the portfolio assets are calculated in a covariance matrix to determine whether the assets move together or against each other, the assets are all treated the same, as if they are each replaceable with any other of them. But the assets were added by asset classes and you would not consider replacing a large cap stock with a small cap stock if your portfolio approach said you need large caps in the portfolio. But you might replace a large cap stock with another large cap. So those two assets should be considered linked.

With CLA, the more you diversify, the more likely you have estimation errors in the resulting portfolio. This could entirely negate the benefits of diversification!

So using the covariance result, more effort is needed to keep like assets linked. How to do this? Using machine learning, we can cluster assets with like assets and not lose their linkage when optimizing allocations.

But will this work?

As with traditional portfolio optimization approaches, the covariance matrix should still be used. But instead of relying on its results in raw form, we can build the results into a hierarchical structure which is consistent with how most portfolio construction begins anyway. According to De Prado, now the head of machine learning for AQR Capital, a $226 Billion fund, this results in a portfolio optimization that generates less risky portfolios compared to traditional risk parity methods.