In part 1 of this miniseries, we proposed an alternative for measuring the co-movement between bonds and equities.
Here, in part 2, we investigate the correlation of bonds with equity sectors.1 We again deploy our approach as in part 1, but here calculate the ‘product of sign of sector returns’ with the US 10-year treasury. We use sectors as per the GICS classification system, i.e., the eleven Level 1 sectors.2 This yields sectorial time series of +1 and -1 of which we take a cumulative sum. The result of this operation is presented in figure 1 below.3
The evolution of the sectorial correlation P&Ls follows largely a similar trajectory to that of the benchmark S&P 500 (the ‘market’), bar a few idiosyncratic exceptions (notably Utilities). All stocks share common risk factors, the overall market being the predominant factor. That also seems to apply to baskets of stocks, in this case, sectors.
It is therefore essential, with a view to better understanding the correlation dynamics of individual sectors, to account for and remove this factor. We thus calculate the residual returns of each sector individually in respect to the market, the S&P 500 (i.e., removing the market factor).4 We repeat our correlation P&L procedure as above but now use the residual returns of each sector. The result of this procedure is shown in figure 2 below.
Notable is how the relationship of each sector with bonds – once we have accounted for the market factor – appears stable through time, as is observable in the nearly linear correlation P&Ls. If one zooms into time slices of the plot, some of the wiggles might be quite large shifts locally, but, nonetheless, seem to revert to previous trends. One observes a wide spread from positive to negative residual correlations across the sectors through time.
Given this stable residual correlation structure of each sector, and since we observe a constantly changing covariance between the benchmark S&P 500 and US 10-year, one can conclude that the time-varying changes in the bond-equity correlation are dominated by exposure to the market and not wholly determined by the idiosyncrasies of the underlying sectors.
The performance of portfolios made up of bonds and equities is sensitive to shifts in the correlation between the two asset classes (as was painfully experienced in 2022, and again of late). Because this dynamic is driven by the market, it is not easily mitigated by a reshuffling of asset allocations across sectors.
In contrast, a beta-neutral strategy eliminates that uncertainty. After residualisation to the market, sector correlations and exposures to bonds are easier to anticipate – and therefore easier to manage. In this way, hedging out the market factors negates at least one large macro concern for an investor – i.e., the time-varying correlation structure between bonds and equities. For a long-only investor in both asset classes, however, this risk is unavoidable!
1 As in part 1, we use the S&P 500 total return (SPXT Index), i.e., the market-cap weighted version, and the US 10-year treasury total return (SPBDU1BT Index) indices. We also use the individual GICS Level 1 sector total returns from Bloomberg.
2 We excluded the Real Estate sector due to a lack of comparable historical data.
3 Consistent with the procedure in part 1, we first remove the long-term daily mean return from all the time series before normalising by the standard deviation.
4 As a reminder, residual return is the return of each sector independent of the benchmark, or the ‘market’ (the S&P 500 TR Index in this case). More specifically, the residual return is the fraction of the returns (for each sector independently) that cannot be accounted for by its benchmark (the S&P 500). This residual return can be both positive or negative and is the amount the sector has returned once the market exposure has been subtracted.
Residual returns (Rr) are calculated as follows:
Rr = Rs – (Rb* β)
Rs = Returns of each sector
Rb = Returns of the benchmark
β = (Covariance (Rs, Rb)) / Variance(Rb)
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