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.