In this edition of The Edge, the first in a multi-part miniseries, we present a novel yet simple alternative for measuring the correlation between asset classes.
After the poor performance of both bonds and equities in 2022, a flurry of papers pulled into question the persistence of the negative correlation between them. In October 2020, we wrote a piece investigating this relationship, showing that a steady negative correlation is only a very recent feature of their relationship, and that expectation of an inflationary environment was a strong indicator for the correlation becoming more positive.[1] Unsurprising then what happened in 2022…
Measuring correlations can be a tricky affair and is complicated by certain stylised facts. Returns in financial markets are mostly ‘fat-tailed’. This means that an overall correlation coefficient could be driven by ‘outliers’ (the ‘tails’), introducing uncertainty or error to a measurement based on a small number of large events. For example, the correlation between the S&P 500 and US 10-year treasury since 1990 is negative ~20%. However, after capping outliers beyond 3 standard deviations, the correlation decreases to negative ~15%.[2] The choice of return update frequency also impacts results – the correlation between the S&P 500 and the US 10-year since 1990 (tails not removed) is -20%, -15% and -0.07% for daily, weekly, and monthly returns, respectively.
The exercise of measuring the variation of correlation between two (or more) assets requires the a priori choice of not only frequency of returns, the type of correlation measure, but also the size and shape of the look-back window. Different combinations of these inputs can yield different results which then raises questions regarding the robustness of the conclusion.
To sidestep some of the pitfalls, we do the following:
We take the sign of bond and equity returns (either +1 for positive returns, or -1 for negative returns) and multiply their signs for each time step concomitantly.[3] If returns for the asset classes are of opposite sign (+1 and -1), the multiplicative product is negative. Conversely, for returns of the same sign (+1 and +1 / -1 and -1), the multiplicative product is positive. This yields a time series of +1s and -1s. We then take the cumulative sum of this multiplicative product time series, yielding a ‘correlation P&L’ which is upward (downward) sloping if the two asset classes move in the same (opposite) direction.
For the purposes of this post, we will look at the result of this measure using the S&P 500 and US 10-year treasury.[4]
So, what’s the point? We have provided a similar result to that using standard correlation measures -the correlation P&L shows a distinct turn around the end of the 1990s, analogous with a rolling correlation measure; a steady negative correlation since; and correlation from 2020 onwards having become less negative (even positive).
However, this approach negates many of the a priori choices needed for say a classic rolling correlation measure, and is as such not subject to a lag baked into the choice of backward-looking window. Moreover, this approach is agnostic to the magnitude of returns, so outliers are not able to bias the result. The structure of the bond equity correlation through time is confirmed to be stable and robust!
The reason we care about correlation is because of its importance in building diversified portfolios. Portfolio construction techniques generally tend to take correlation as a given without too much thought as to how to measure it. For maximising risk-adjusted returns the correlation of interest is that in the heart of the return distributions (although tail correlations are nice to know, especially for tail hedge strategies, but are notoriously difficult to measure!) and therefore most portfolio managers are more concerned about the optimal blend of assets within a portfolio to maximize long-term results.
Our robust indicator presented herein is worth consideration as a complementary and visual aid for gauging correlations and identifying regime shifts.
[1] ‘Bond equity correlations: are the times a-changin’?’ available for download on our website here .
[2] We use for the purposes of this piece, the S&P 500 and S&P US 10-year total return indices (SPXT Index and SPBDU1BT Index) as proxies.
[3] Returns for both the S&P 500 and S&P US 10-year indices are normalised by their historical standard deviations after having removed the daily mean returns.
[4] We applied the same procedure on various other geographies and found comparable results, albeit with some idiosyncratic and unique features across regions.
Disclaimer
ANY DESCRIPTION OR INFORMATION INVOLVING MODELS, INVESTMENT PROCESSES OR ALLOCATIONS IS PROVIDED FOR ILLUSTRATIVE PURPOSES ONLY. ANY STATEMENTS REGARDING CORRELATIONS OR MODES OR OTHER SIMILAR BEHAVIORS CONSTITUTE ONLY SUBJECTIVE VIEWS, ARE BASED UPON REASONABLE EXPECTATIONS OR BELIEFS, AND SHOULD NOT BE RELIED ON. ALL STATEMENTS HEREIN ARE SUBJECT TO CHANGE DUE TO A VARIETY OF FACTORS INCLUDING FLUCTUATING MARKET CONDITIONS AND INVOLVE INHERENT RISKS AND UNCERTAINTIES BOTH GENERIC AND SPECIFIC, MANY OF WHICH CANNOT BE PREDICTED OR QUANTIFIED AND ARE BEYOND CFM’S CONTROL. FUTURE EVIDENCE AND ACTUAL RESULTS OR PERFORMANCE COULD DIFFER MATERIALLY FROM THE INFORMATION SET FORTH IN, CONTEMPLATED BY OR UNDERLYING THE STATEMENTS HEREIN.
