Improved Risk Reporting with Factor-Based Diversification Measures

Improved Risk Reporting with Factor-Based Diversification Measures — February 2014

Executive Summary

use five years of historical weekly returns before the date at which we perform the computation. In Figure 2, we display the distributions of the ENC and ENB measures. When looking at the evolution of each diversification measure, it seems that a change occurred between 2007 and 2012, as most US pension funds seem to have increased the diversification level in their portfolio between these two dates. For instance, between 2002 and 2007, the mean of the distribution of the ENCs increases by 1.3%, while between 2007

for the equally-weighted portfolio, is a naive diversification measure that does not account for the presence of differences in risk and correlation levels within the set of asset classes. As recalled above, this is in contrast with the ENB measure, which is based on normalised uncorrelated factors. On the other hand, the ENB measure is an instantaneous observable quantity, while the ENC measure requires an estimate for the covariance matrix of asset returns so as to apply the minimum torsion methodology. In order to estimate the covariance matrix needed to compute the ENB measure, we

Figure 2: Distribution of Diversification Measures of US Pension Funds These figures display the distribution of the effective number of constituents (ENC) and the effective number of bets (ENB) for the US pension funds of the P&I database in 2002, 2007 and 2012

12

An EDHEC-Risk Institute Publication