Harry Markowitz, father of modern portfolio theory, has a new paper out with Sander Gerber and Punit Pujara titled Enhancing multi-asset portfolio construction under Modern Portfolio Theory with a robust co-movement measure. You can download it here.
The big take away is the introduction of a new co-movement measure called the Gerber Statistic, which is designed to be more robust to outlier data in measuring co-movement among asset classes.
The Gerber Statistic is computed on a rolling basis using a trailing measure of standard deviation for both assets. Looking at the trailing N pairs of returns, pairs are thrown away if the absolute value of either asset’s returns falls below a threshold level (in the paper, 0.5 trailing standard deviations). Otherwise, a value M is calculated for that pair. M is 1 if both pairs are simultaneously above (or below) the threshold; M is -1 if one asset is above and the other is below.
The Gerber Statistic is then the sum of the M values divided by the number of pairs that were not thrown out.
In this way, the Gerber Statistic ignores “insignificant” returns but ignores how significant a return is – so long it is above the threshold – from a standard deviation stand-point.
In the paper a matrix of Gerber Statistics is used instead of the standard covariance matrix to perform a rolling portfolio optimization. This robust measure is able, for the testing period, to push the efficient frontier up and to the left. Simply put: more return for less risk.
As always, an image is worth 1000 words…
This work is interesting because it reminds us that asset allocation is not a solved problem. Even the father of modern portfolio theory continues to explore ways in which we can improve our methods.
Corey Hoffstein
Corey is co-founder and Chief Investment Officer of Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Corey is responsible for portfolio management, investment research, strategy development, and communication of the firm's views to clients. Prior to offering asset management services, Newfound licensed research from the quantitative investment models developed by Corey. At peak, this research helped steer the tactical allocation decisions for upwards of $10bn. Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University. You can connect with Corey on LinkedIn or Twitter.
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