EDHEC-Risk Institute October 2016

Multi-Dimensional Risk and Performance Analysis for Equity Portfolios — October 2016

3. Applications of Fundamental Beta

Figure 21: Mean Ex-Post Betas (Estimated on 5-Year Rolling Window) Over 1,000 Universes 1,000 maximum deconcentration portfolios of 30 random stocks subject to a beta neutrality constraint are constructed by using the rolling-window or the fundamental betas. The 30 stocks are picked among the 71 that remained in the S&P 500 universe for the period 1970-2015, and the portfolios are rebalanced every quarter. The control regression on Ken French’s market factor is done on a 5-year rolling window of quarterly returns. For each window, the market beta is averaged across the 1,000 universes.

Table 4: Targeting Beta Neutrality for Maximum Deconcentration Portfolios Based on Fundamental and Time-Varying Historical Betas (1970-2015) 1,000 maximum deconcentration portfolios of 30 random stocks subject to a beta neutrality constraint are constructed by using the rolling-window or the fundamental betas. The 30 stocks are picked among the 71 that remained in the S&P 500 universe for the period 1970-2015, and the portfolios are rebalanced every quarter. The control regression on Ken French’s market factor is done using quarterly returns over the period 1970-2015. The market beta and the market correlation are computed for each portfolio over the period 1970-2015 and are averaged across the 1,000 universes. Also reported are the standard deviations of the beta and the correlation over the 1,000 universes. Out-of-Sample Market beta Out-of-Sample Market correlation Mean Standard Deviation Mean Standard Deviation Historical 0.931 0.019 0.845 0.021 Fundamental 0.950 0.015 0.910 0.010

Eventually, the fundamental method appears to be a more reliable way of constructing market-neutral portfolios. The fact that it leads to portfolios that are ex-post more neutral suggests that it allows the prediction error in the estimation of the conditional betas to be reduced. In other words, it approximates the true conditional beta better than the classical rolling-window method does.

It can be argued that Figure 21 focuses only on the average situation and, as such, hides differences across the 1,000 universes. Thus, we look at the “worst” of the universes in Figure 22. At each date, the 1,000 absolute differences between the 5-year rolling-window beta and the target of 1 are computed, and the figure shows the highest value. More often than not, it is with the historical method that the largest deviation is observed. There are a number of months (March 1996, December 2005 and March 2007 being the most extreme examples) where the relative error exceeds 60%.

67

An EDHEC-Risk Institute Publication