While working at the Norwegian sovereign wealth fund, we (like so many others) had to think in-depth about the correlation between equities and bonds — one of the main factors to consider when evaluating the overall equity share of the portfolio.
At that time, two decades of negative correlations between stocks and bonds were the anchor point for the discussion. Whether the correlation is negative, zero, or positive, has huge implications for multi-asset investors. As a result, there have been countless research articles trying to assess whether the correlation has changed.
The debate remains very much alive. Nowadays, investors are asking whether a negative correlation may be a thing of the past — and whether the foundations of classic allocations such as the 60/40 mix are much weaker. However, this article has a provocative idea: negative correlations were only ever relevant for a short-horizon, and we should think of stocks and bonds as being positively correlated for long-term allocation decisions.
Short-term Correlations, Long-term Investments?
For long-term investors, there are always tensions between the prevalence of short-term correlation statistics and the potentially multi-decade horizons attached to strategic allocations. How should allocators reconcile taking a long-term perspective while gauging market outcomes through risk and correlations over short windows? The discussions at the Norwegian fund included a chart similar to the one below, showing cumulative equity and fixed income returns for the US market over a long time window (in logs, for readability).
A comment on the chart was that both lines are going up, so aren't stocks and bonds positively correlated in the long-term? This observation was both relevant and unprovable: we were looking at a single 'long-term' historical observation for stocks and bonds. Basic statistics tell us that we can't establish correlations from one data point.
On this basis, we might have to be agnostic about long-term correlations. But this is hardly satisfactory given the importance of long-term asset allocation decisions. Of course, historical data alone give us very limited independent observations when using long horizon windows. Some studies - such as this one - might examine very long histories. But they still look at correlations measured over relatively short horizons. For long-term investors, is there anything else we can do to understand returns and risk measured over long periods?
Simulating Long-term Returns
Over recent years, we have developed frameworks for understanding markets and asset returns that are specifically designed to capture long-term risks in markets. An important ingredient is to carefully model the evolution of slow-moving variables into the long-term – for example, expectations of long-term growth, long-term real rates, and inflation expectations.
This simulation technology forms the basis of market/macro simulations, from which we build simulated return paths for a wide range of asset classes and underlying macro-variables (out to 30 years). From this, it turns out we might be able to learn more about long-term correlations. We have an alternative to historical correlations, where we can measure correlations over long-horizons many times over across simulated paths.
When carefully modelling expected returns and how they behave through time, one of the surprising features of simulated equity and government bond returns is that their correlations tend to increase when measured over long horizons.
Even if correlations are calibrated to be negative at first, as the return horizon extends, the correlation increases. The underlying driver of this is the compounding of expected returns over long-horizons. We have all heard how compounding returns is an increasingly powerful force over the long-term. It seems this matters a lot also for thinking about risk. In past research, we have shown that the compounding effects drive the variance of long-horizon bond returns, and this intuition also applies to correlations.
From a correlation perspective, the question becomes whether expected returns co-move positively or negatively across asset classes. Compounded returns mean that even modest common drivers of expected returns lead to returns cumulating in the same direction. This is likely the case if we think of expected returns on equities comprising risk-free and risky components, at the very least sharing a risk-free component with government bonds.
One extra check - while still warning heavily against the use of historical data for getting long-term statistics – we can try to get some handle on this idea empirically. The chart shows rough-and-ready correlation estimates extracting what little we can gather from even ultra-long samples for the US. The correlation profile resembles the simulated version, where correlations increase with return horizons in the data as well. The confidence band around the correlations will be very large in this case, but at least we get some cross-check against the simulations.
Implications for Investors and Portfolios
All of this matters for portfolios. If correlations drift upward over long horizons, long-term investors that rely on negative correlation assumptions may under-estimate portfolio risk and over-state diversification benefits.
A key aspect to all this is to what extent you are actually a long-term investor. Our analysis is assuming you can hold equity and bond portfolios for a decade or more. Any fund outflows probably mean a reduction in your investment horizon. Without clarity on your actual horizon, it is difficult to judge whether short-window correlations, long-run dynamics, or something in between should drive portfolio design.
One caveat when thinking about asset performance over long horizons is that uncertainty is very high. Investors need to think about the biggest issues relating to geopolitics, political systems, transformative technologies, and environment change, which can't be captured through a correlation statistic only.
Going back to the Norwegian story, in the end we included scenarios for zero and positive correlations across stocks and bonds. This seemed a relatively good call given how things later played out, but perhaps we should have been leaning more heavily toward a positive correlation as a long-term investor.
More generally, we shouldn't be confining this long-horizon thinking to stocks vs. bonds only. For long-term investors, there might well be a completely different risk-return trade-off to have in mind based on expected returns and correlations measured over long windows. At the least, we might need to be even more sceptical of Sharpe ratios and correlation matrices than we were before. We will write more about this in the future.