2.4 Empirical Results
2.4.2 Effects of Additional Design Elements
2.4.2.1 Alternative Estimation Method
The first variation from the base case is the estimation method of beta. Figure 2.3 shows the mean beta of the low-beta portfolio (three month estimation period, 150 stocks, beta weighting), based on the three different estimation methods for beta.15 The portfolio beta estimated with the basic and the Dimson method are similar, although the later varies much more and is generally lower. The portfolio beta based on Frazzini/Pedersen method is much more stable and always produces positive portfolio betas.
Figure 2.3: Beta of the Low-beta Portfolio for Different Estimation Methods
1995 2000 2005 2010 2015
−1.0−0.50.00.5
Time
Mean Beta
Basic Beta of Low−beta Portfolio
Frazzini/Pedersen Beta of Low−beta Portfolio Dimson Beta of Low−beta Portfolio
Note: Figure 2.3 shows the effects of the different estimation methods of beta. The displayed graphs are the beta-weighted beta of the low-beta portfolio in the base case scenario for the three different estimation methods. The figure shows substantially different outcomes for the three estimation methods, which also influence the weights of the other instruments invested in.
Figure 2.3 indicates, that the estimation method of beta may have substantial influence on the performance, as the portfolio weights of all strategies are based on these mean betas. Table 2.4 shows the performance of the four basic low-beta strategies with the Frazzini/Pedersen estimation method. The average return is higher for the EH strategy and lower for the EL strategy compared to the base case. Because of that, the return of the strategies are much more aligned. The standard deviation of all four strategies is lower, so that the Sharpe ratio for the strategies is more favorable compared to the base case.
The same can be concluded from the CEV.
In contrast to the base case, the risk-adjusted returns are significant and positive for all strategies. The EH strategy yields the highest risk-adjusted return, followed by BL, NM and EL. The ranking of the four low-beta strategies is completely reversed compared to the base case. In addition, the EH and BL strategies have a clear negative exposure towards the size factor and the NM and EL strategies have a positive exposure towards the value factor. The EH strategy is the only one that has no significant market exposure. These results differ substantially from the base case in various ways. The strategies with basic beta estimation have an exposure towards the momentum factor; only the NM and EL strategies produce significant positive risk-adjusted returns; and the EH and BL strategies have a significant positive market exposure. The more stable beta estimation with the Frazzini/Pedersen method is reflected in more steady returns of the resulting strategies.
As shown, the average returns are more aligned, the standard deviation is lower and the risk-adjusted returns are significant and in reverse ordering for the four low-beta strategies.
This might be due to the less varying mean beta of the low-beta and high-beta portfolio which has a direct influence on the weights of all instruments.
Table 2.4: Estimation Method: Frazzini/Pedersen – Return and Risk Panel A: Average Returns, Standard Deviations, Sharpe Ratios Panel A: and Certainty Equivalent Returns
Panel B: Risk-adjusted Returns and Factor Sensitivities
Strategy α βM arket βSM B βHM L βM OM Note: Table 2.4 shows, in Panel A, the annualized average returns (AvRet), standard deviations (SD), Sharpe ratios (SR), and certainty equivalent returns (CEV), and in Panel B, the annualized risk-adjusted returns (alphas) and factor sensitivities in a Carhart (1997) four-factor model for each of the four low-beta strategies (extreme high (EH), balanced (BL), no market investment (NM), extreme low (EL)).
The base case uses the S&P 1500 stocks as the investible universe, the Frazzini/Pedersen estimation, an estimation period of 3 months for the volatilities, and a 12-month holding period. The strategies are set up at the end of each month for the period December 1994 to April 2015. Each low-beta and high-beta portfolio consists of 150 stocks, which are beta-weighted within the portfolios. The average return is the yearly return earned by each strategy, and the standard deviation is calculated from the returns for the whole investigation period. The Sharpe ratio is calculated by dividing the average return by the standard deviation, and the certainty equivalent return is calculated for an investor with CARA utility function and absolute risk aversion of 1. The multiple linear regressions underlying the results of Panel B use four independent variables (market excess return, SMB, HML, MOM) and read Rt=α+βM arket·(RM,t−Rf,t) +βSM B·SM Bt+βHM L·HM Lt+βM OM·M OMt+t, where (RM,t−Rf,t) is the excess return of the market proxy at timet andSM Bt, HM Ltand M OMtare the returns of the
The average returns of the strategies based on the Dimson method16 presented in Table 2.5 are the highest and most aligned of all three estimation methods. Taking the standard deviations into account and comparing the Sharpe ratios of the strategies, the NM and the EL strategy are robust towards the estimation method. The performances of the EH and BL strategy improve even more when the Dimson estimation is used and the NM and EL strategies slightly fall back compared with the Frazzini/Pedersen estimation and the base case.
In contrast to the base case, the EH and the BL strategies obtain positive and significant risk-adjusted returns. Again, the relative advantageousness of the strategies is the exact opposite compared to the base case. All four basic low-beta strategies have a positive market exposure and experience a size exposure that is negative for EH and BL, but positive for NM and EL. In addition, the NM and EL strategies have an significant value exposure. The returns of the low-beta strategies based on the Dimson method are the ones that are the most exposed to common risk factors compared to all other variations of design elements, but still the strategies overweighting high-beta stocks attain risk-adjusted returns. It is remarkable that the zero ex-ante beta strategies all experience a distinct market exposure. For the Dimson method, the ex-ante beta seem to differ substantially from the ex-post beta in the holding period of the portfolio, which clearly influences the performance of the low-beta strategies. A possible explanation is the more pronounced low and high beta as seen in Figure 2.3. The weights of the different instruments in each strategy depend on the estimated beta and if the betas are more severe, it is not surprising that the performance of the strategy differs markedly.
16The results and their qualitative interpretation hold if the estimation method is adjusted, so that only backward-looking information is included as described in the previous section.
Table 2.5: Estimation Method: Dimson – Return and Risk
Panel A: Average Returns, Standard Deviations, Sharpe Ratios Panel A: and Certainty Equivalent Returns
Panel B: Risk-adjusted Returns and Factor Sensitivities
Strategy α βM arket βSM B βHM L βM OM Note: Table 2.5 shows, in Panel A, the annualized average returns (AvRet), standard deviations (SD), Sharpe ratios (SR), and certainty equivalent returns (CEV), and in Panel B, the annualized risk-adjusted returns (alphas) and factor sensitivities in a Carhart (1997) four-factor model for each of the four low-beta strategies (extreme high (EH), balanced (BL), no market investment (NM), extreme low (EL)). The base case uses the S&P 1500 stocks as the investible universe, the Dimson estimation, an estimation period of 3 months, and a 12-month holding period. The strategies are set up at the end of each month for the period December 1994 to April 2015. Each low-beta and high-beta portfolio consists of 150 stocks, which are beta-weighted within the portfolios. The average return is the yearly return earned by each strategy, and the standard deviation is calculated from the returns for the whole investigation period. The Sharpe ratio is calculated by dividing the average return by the standard deviation, and the certainty equivalent return is calculated for an investor with CARA utility function and absolute risk aversion of 1. The multiple linear regressions underlying the results of Panel B use four independent variables (market excess return, SMB, HML, MOM) and readRt=α+βM arket·(RM,t−Rf,t)+βSM B·SM Bt+βHM L·HM Lt+βM OM·M OMt+t, where (RM,t−Rf,t) is the excess return of the market proxy at timet andSM Bt, HM LtandM OMtare the returns of the factor-mimicking portfolios for size, value, and momentum effects, respectively. The
The favorability of the four basic low-beta strategies based on alternative beta estimation methods clearly differs from the base case when comparing average returns as well as risk-adjusted returns. The risk-adjusted returns of the strategies with the alternative estimation methods, seem to be more driven by common risk factors, except momentum.
Remarkably, the average returns are more aligned and all four strategies based on the Frazz-ini/Pedersen estimation are able to generate significant risk-adjusted returns. Summarizing, the estimation method has a substantial impact on the risk and return characteristics of the low-beta strategies. Although significant risk-adjusted returns can be achieved, the performance is much more driven by risk factors.