By Jean-Jacques Ohana, CFA and Dr. Christian Witt, 18th December 2017.
The dependency of an equity portfolio to sovereign bonds is an important issue for investors in several ways. One is to use the bond sensitivity of equities to explain excess return coming from bond duration. Another one is to play the direction of interest rates indirectly through equities. Another application would be to immunize an equity portfolio against interest rate moves.
To assess the degree to which different equity investment styles or equity sectors depend on bonds, we propose to regress their daily returns on the changes of two different benchmarks:
The local global equity factor, i.e. the Stoxx 600 Europe for Europe or the S&P 500 for the US;
The local sovereign bond factor, i.e. the Germany Bund for Europe or the US 10-year T-Notes for the US.
The econometric framework we use is flexible least squares regression (FLS). This method has been specifically developed to estimate variable regression betas in order to explore their dynamic nature. The model allows us to see how different equity portfolios respond to variation in sovereign bond yields over time. The FLS model strikes a balance between fitting to the independent variable and the variability of regression betas. It ensures a variation of the regression betas akin to a Kalman filter, but does not infer any state model for the random beta variables.
Our key results over the period 2010-2017 are presented in the tables below:
As shown in figure 1, the sensitivity of a low volatility equity portfolio to the sovereign bond yield has steadily increased since 2012 in the US and since 2015 in Europe. The average beta is around 20% for both indices, i.e. a modified duration around 1.6 given that the duration of both sovereign benchmarks (10 years) is around 8. The low beta property of this low volatility-type portfolio is of course confirmed with a beta to global equities of around 75%. Therefore, low volatility equity portfolios may be synthesized as a combination of global equities and bonds with respective weights of 75% and 20%.
The duration of value stocks, unsurprisingly, is tilted to the negative side, although the pattern is more pronounced in the US.
When repeating the same exercise for equity sectors (and not by style), we find the following ranking ordered from highest to lowest dependency on sovereign bonds:
Table 2-a: Most dependent sectors to sovereign bonds in Europe
Table 2-b: Most dependent sectors to sovereign bonds in the US
Real Estate is among the most exposed sectors to bond yields in both regions whereas Banks display a strong negative exposure to bonds. In this respect, Banks appear to be a leveraged beta play with a high beta to stocks (above 1) and strong negative duration at the same time. US equity sectors also display stronger dependency to bonds than the European market, i.e. higher positive (lower negative) factor loadings. Our model suggests the modified duration of an equity portfolio may reach +/- 7 years in the US vs a maximum of +/- 4 years in Europe. In addition, defensive sectors displaying positive dependency to bonds have some common features both in the US and in Europe: Real Estate, Utilities (where the leveraged nature of their businesses appear clearly in the betas), Consumer Staples. On the other hand, Financials are clearly a highly cyclical bet upon the recovery of the global economy. Health Care, another defensive sector, does not show significant dependence on bonds.
To sum up, our study enables us to identify investment styles or sectors with a strong connection to bonds. Once the Modified Duration of equity portfolios is assessed, this information may be exploited by mixing equity and bond exposures (long or short) or alternatively by hedging the specific sensitivity of any given equity portfolio to sovereign bonds.
Figure 1: Dynamic Betas in the FLS model regressing Minimum Volatility Indices against Global Benchmark and Sovereign Bonds Market.
Figure 1-a: Europe
Figure 1-b: USA
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