![]() To assess this notion, the authors took a different approach and formed portfolios based on either two-parameter shrunk betas, volatility, or a combination of these two variables. For portfolio construction purposes, these results could be seen as a reason to allocate less weight to estimated correlations than forecasted relative volatilities. In their paper, the researchers found that beta predictions were more accurate when correlations were shrunk more to their cross-sectional average than relative volatilities. Comparing low beta and Low Volatility portfolios Finally, the long-short portfolio delivered a CAPM alpha that was almost 2% higher (from 10.14% to 11.87%) and that was statistically significant. This also indicates that risk can be better predicted on an overall portfolio level. In addition, the D10 portfolio had a higher volatility and a higher ex-post beta. Meanwhile, the long-short portfolio exhibited an alpha of 10.14% relative to the CAPM.įor the strategies based on the two-parameter shrinkage beta estimates, the D1 portfolio had a lower ex-post beta (from 0.45 to 0.42) and a lower realized volatility (from 11.04% to 10.79%). On the other hand, the D10 portfolio also had an average return of 7.26%, but a volatility of 32.59%, Sharpe ratio of 0.22, and a market beta of 1.65. In addition, a long-short strategy based on a long position in the D1 portfolio (lowest beta estimates) and short position in D10 portfolio (highest beta estimates) was constructed.įor the strategies based on historical beta estimates, the results showed that the D1 portfolio had an average excess return of 7.26%, volatility of 11.04%, Sharpe ratio of 0.66, and market beta of 0.45. The same exercise was performed using the two-parameter shrinkage beta forecasts. They ranked stocks on their historical beta estimates and allocated them to 10-decile portfolios. The authors also assessed whether these improved ex-ante beta estimates at the individual stock level led to lower ex-post portfolio betas. Indeed, Figure 1 shows the ex-post absolute beta forecast error for both the no shrinkage and two-parameter shrinkage settings for each of the 10-decile portfolios, while the horizontal axis reflects the differences in ex-ante average beta estimates between the two methods. The results revealed that the two-parameter shrinkage method had lower forecasting errors than the other two approaches. The average ex-ante beta estimates for these portfolios were then compared with their realized betas over the full sample period. Thereafter, the stocks were ranked on the differences in beta forecasts between these methods and allocated to 10-decile portfolios. This comparison was also made between the related estimates of the one-parameter shrinkage and two-parameter shrinkage settings. The researchers also scrutinized stocks that had the most dissimilar beta predictions when the no shrinkage and two-parameter shrinkage approaches were applied. Moreover, one-parameter settings generally delivered suboptimal results. Meanwhile, a two-parameter approach – that reduced correlations (0.5 shrinkage factor) more than relative volatilities (0.2 shrinkage factor) – produced the best outcome (or lowest MSE). The analysis confirmed that the largest estimation error – or highest MSE – occurred when no shrinkage was implemented. This ranged from a shrinkage factor of 0 to 1 for both parameters. To investigate the effect of implementing shrinkage on correlations and relative volatilities, they looked at the resulting mean squared errors (MSE) of the beta estimates when correlations and relative volatilities were shrunk at different levels. To examine which approach best forecasts beta, they analyzed a range of methods, from those that shrink the beta in its entirety, to others that reduce estimation errors in correlations and relative volatilities to their cross-sectional averages separately. For the study, the authors assumed that correlations and relative volatilities are independent of each other, such that beta expectations are equal to the product of these two estimated components.
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