Returns-based style analysis is often used to understand the average asset allocation of a portfolio over time. It produces the set of asset weights that best explains the variability of a portfolio's returns.
The difference between an average portfolio's return and the average return from the portfolio with a fixed mix of asset returns is the alpha. The alpha might be due to successful market timing, or it might be due to successful security selection. Traditional returns-based style analysis does not provide any insights into the source of the alpha.
In their 1981 Journal of Business article, Robert Merton and Roy Henriksson developed a method to identify successful market timing by incorporating an option-like market timing asset into their analyses.
In this article, we combined the two approaches and included market-timing hybrid assets into returns-based style analysis. By including hybrid assets, we can understand how much of a portfolio's pattern of returns can be explained by its average asset mix and how much can be explained by the portfolio manager moving from one asset class to another. In that way, we can gain insights into the source of a manager's alpha. We can learn if it is due to market timing or security selection.
In the analyses, we incorporated three hybrid assets into the returns-based style analysis framework. The hybrid stock/bond market-timing asset produces the return of a market timer that shifts between stocks and bonds with perfect foresight. In months in which the stock market outperforms the bond market, the hybrid asset has the return of the stock market. In months in which the bond market outperforms the stock market, the hybrid asset has the return of the bond market. The hybrid stock/cash and bond/cash assets have similar structures.
The accompanying table shows the results of including the hybrid assets in the analyses. It describes the performance of 26 years of monthly returns from Mellon Capital Management's asset allocation strategy. To attribute the performance to the average stock, bond and cash weightings, we used monthly returns for the Standard & Poor's 500 stock index, 20-year AA industrial bonds and 90-day Treasury bills. Those results are shown in the row labeled "Without market timing." They show that a portfolio with a constant weight of 49.7% stocks, 36.6% bonds and 13.7% T-bills best describes the variability of returns of the portfolio. It explains 81% of the portfolio's variance. Compared with a portfolio of indexes that was rebalanced to that fixed mix each month, the asset allocation strategy generated an alpha of 0.32% per month gross of management fees.
The other seven rows show the evidence of successful market timing. To calculate them, we added various combinations of the three hybrid time series to the analyses. As in traditional style analysis, the asset weights were calculated to maximize correlation between the fitted time series of returns and the portfolio's actual returns. The analyses were performed with the constraints that the weights for eligible assets add up to one and the average monthly alpha is equal to zero. The zero alpha constraint was added to force the routine to fully explain the portfolio's relative performance. It is appropriate in this case, because the portfolio was managed by switching between passive portfolios so there was not any value added through security selection.
The second row of the table, labeled "With stock/bond timing," introduces the hybrid stock/bond market-timing asset into the analysis. It shows a portfolio that was rebalanced each month to 39.9% stocks, 25.8% bonds, 14.7% cash and 19.7% hybrid stock/bond asset best describes the portfolio's performance. Compared to the stock/bond/cash analysis, it reduced the average stock exposure by 9.8 percentage points, bonds by 10.8 points and increased cash by one percentage point. The 19.7% weight in the hybrid stock/bond market timing asset indicates successful market timing. The increase in the R-squared to 48.3% from 81.4% tells us that adding the market timing asset explained 15.6% of the unexplained variance. [(84.3-81.4)/(100-81.4) = 15.6%] By adding the stock/bond market timing asset to the analysis, we were able to explain the source of the portfolio's alpha while at the same time explaining more of its variability of returns.
The third and fourth rows introduce the hybrid market-timing assets that return the better performance of stocks vs. cash and bonds vs. cash, respectively. They provide less explanatory power than does the hybrid stock/bond asset. The next three rows introduce the market-timing assets in pairs and the last row includes all three market-timing assets.
From these data you can see our TAA strategy successfully made the stock vs. bond call, but did not add incremental value by timing stocks vs. cash or bonds vs. cash. In all of the analyses, by adding the market-timing assets to the analysis, we were able to explain the portfolio's alpha while at the same time explaining more of its variability of returns than we were able to do using only stock, bond and cash indexes.
The analysis illustrates how one can gain additional insights into a portfolio's performance by introducing hybrid market timing assets into returns-based style analysis. The specific pattern of returns for each hybrid asset should be a function of the portfolio manager's investment process and the type of insights that one is attempting to gain.
If the weights on the market-timing assets are negative, it indicates perverse market timing. If the R-squared falls, it indicates market timing does not explain the portfolio's alpha.
