Beyond Risk Parity
Gaining edge by forecasting volatility and correlations
By: Dan Rasmussen, Chris Satterthwaite, and Lionel Smoler Schatz
Passive investing has been taking share from active management for years. And, in some ways, the evidence is clear that low-fee passive index funds outperform high-fee active approaches with a high degree of consistency.
Eugene Fama predicted this outcome in 1965, arguing that security prices follow a random walk, that markets efficiently priced in all available information, and that “chartist” approaches to investing as well as individual stock picking were likely fool’s errands.
Yet even if we believe in the efficient markets hypothesis (“EMH”), we are left with the problem of picking indices, a challenge made more difficult by the fact there are now more indices than there are individual equities. In his 1965 paper, Fama called this the challenge of portfolio analysis: the investor needs to determine his risk and return preferences, classify securities according to riskiness, and then “determine how securities from different risk classes combine to form portfolios with various combinations of risk and return.” Essentially, investors must do mean-variance optimization to find the efficient frontier and choose the portfolio on the frontier that best matches risk preferences.
The problem is that this still requires investors to forecast the expected returns of different asset classes and sub-asset classes, diagnose the risk of those asset classes, and then combine those asset classes in an optimal way based on their correlations. This problem seems equally, if not more daunting than individual security selection.
Ray Dalio came up with a novel answer to Fama’s problem of portfolio analysis with the launch of his All Weather fund in 1996. Dalio observed that, as we wrote about recently, while CAPM fails to hold within asset classes, it does appear to hold across asset classes.
Figure 1: CAPM across Asset Classes
Source: Capital IQ, FRED, Ken French Data Library, MacroTrends, Fidelity, Verdad analysis
We have a rough—and roughly reliable—sense of expected returns, volatility, and correlations for the major asset classes. Dalio’s insight was that you could then lever up each asset to the same volatility and, if Sharpe ratios are the same across asset classes, the same expected return. By doing so, you’d have a portfolio that was more diversified than an all-equity or 60/40 portfolio. He pointed out that, in the classic 60/40 portfolio, 60% of the portfolio is allocated to equities by dollar amount, but equities actually account for 90% of the risk, since equities are three to four times more volatile than bonds.
But let’s push this logic one step further. We believe there should be two theoretical ways to improve results within the framework of EMH: improve our forecasts of volatility, or improve our forecasts of the correlations between assets. And this is important because volatility and correlations, much like returns, all vary over time. The below charts, for example, show the trailing one-month returns, volatility, and correlation with US Treasurys for the S&P 500 Index.
Figure 2: Autocorrelation of Returns, Volatility, and Correlation
Source: Verdad analysis
As shown above, returns exhibit very little autocorrelation, as Fama suggested. However, both volatility and correlations exhibit sustained periods above and below their long-term averages. Given this autocorrelation, it seems like both volatility and correlations should be somewhat predictable. To test this, we regressed future returns on trailing returns, future volatility on trailing volatility, and future correlations on trailing correlations (all to US Treasurys). The below chart shows the R-squared of these regressions for the S&P 500, US Treasurys, oil, and gold.
Figure 3: Regressing FWD 1M Returns, Volatility, and Correlations on Trailing 1M Returns, Volatility, and Correlations (1992-2023)
Source: Verdad analysis
These regressions show that volatility and correlations can be predictable based on trailing data, whereas expected returns, across all the asset classes, follow Fama’s random walk. Simple autocorrelations appear to provide an edge in predicting future volatility and future correlations, but no edge in forecasting expected returns.
The key question then is whether having an edge in predicting volatility and an edge in predicting correlations offers a path to better long-term returns, lower risk, and a higher Sharpe ratio.
The best equity-biased investors have figured out that volatility poses a great challenge to staying the course, and they’ve learned to ignore volatility in pursuit of the long-term compounding of equity markets. But that good lesson does not mean that we can’t use volatility forecasting to improve returns. To understand how knowing volatility can improve outcomes, consider two assets with the same expected return of 5%. If the first asset goes up 10%, then down 10%, that asset is now down 1%. If the same asset had double the volatility and went up 20% and then down 20%, it would be down 4%. This is captured in the Sharpe ratio, which would be higher for the asset with lower volatility (0.5 versus 0.25) and could be leveraged to a target risk level (e.g., comparable to the S&P 500) to achieve a higher return.
As to correlations, we’ve written enough recently about the changing correlations between stocks and bonds to make our views clear: there’s no reason to diversify into other asset classes if those asset classes don’t actually provide diversification. We believe being able to forecast correlations means we can effectively increase diversification, reduce volatility, and increase returns by increasing exposure to uncorrelated assets and decreasing exposure to correlated assets.
Predicting volatility and predicting correlations, which, as we’ve seen, is something we believe we can do decently well using only recent trailing data, should then, in theory, allow us to be better at Fama’s task of portfolio analysis.
We ran some simple risk parity backtests to empirically validate these intuitions using four major asset classes: the S&P 500, US Treasurys, oil, and gold. We then tested three different model improvements to evaluate the benefits of predicting variance and correlation.
As our reference model, we created a risk parity portfolio levered to the same volatility as the 60/40 portfolio that used static return, volatility, and correlation forecasts based on long-run historical averages (RP_BASE).
Next, we created a risk parity portfolio levered to the same volatility as the 60/40 portfolio but where we forecasted volatility based on trailing one-month volatility (RP_VOL).
Then, we created a risk parity portfolio levered to the same volatility as the 60/40 portfolio but where we varied our portfolios based on trailing one-month correlations (RP_CORR).
Finally, we created a portfolio that varied both volatility and correlation forecasts, with the same target volatility as the 60/40 portfolio (RP_VOL_CORR).
The below table shows the CAGR, standard deviation (volatility), max drawdown, and Sharpe ratio of each of these approaches as compared to a 60/40 portfolio and the S&P 500. The risk parity portfolios have been levered up to the same volatility as the 60/40 portfolio (note that the standard deviation is roughly the same across all of these approaches).
Figure 4: Risk Parity Backtest Results (1992-2023)
Source: Verdad Analysis
As you can see, the risk parity portfolios constructed above accomplish two key objectives. First, better compound returns than the 60/40, with RP_VOL and RP_VOL_CORR also beating the S&P 500. And second, less severe drawdowns than the 60/40 portfolio for all risk parity methods. This is the benefit of diversification across additional asset classes like oil and bonds, as well as managing volatility to increase the Sharpe ratio.
Returns and Sharpe ratios increase as we incorporate our simple one-month trailing volatility and correlation forecasts. By forecasting volatility and correlation more effectively, we can increase the Sharpe ratio and our returns by decreasing volatility and increasing leverage. Predicting correlations proved very useful in times like 2023, when stocks and bonds became more correlated (from 6/30/23 through 9/30/23, the dynamic correlation RP_CORR model outperformed the simple RP_BASE model by 2.1%). Volatility forecasting showed its peak usefulness in 2011 during the US debt ceiling and European sovereign debt crisis, when Treasury volatility spiked (the RP_VOL model outperformed the RP_BASE model by 3.7% over the six-month period from October 30, 2010, to April 30, 2011).
Taking advantage of the autocorrelation of volatility and correlation is entirely in keeping with EMH, a natural extension of Fama’s own thinking, and, in our minds, reflects a logical improvement to a more simplistic version of risk parity. Notably, we have demonstrated a logical path to improving investing outcomes without arguing that we have any edge at all in forecasting expected returns. Nor have we done anything particularly complex in our modeling of volatility or correlations.
But it doesn’t seem crazy to think that things like changes in the VIX might improve our volatility forecasting or that there might be information in, say, the term spread that would help in predicting stock-bond correlations. If we could layer in any edge in predicting expected returns in any asset class (e.g., What if some commodities trend? What if the yield curve and inflation nowcasts were to offer some insight into expected returns in Treasurys?) then this model could be improved yet further. This would, of course, risk crossing over from the safe ground of EMH into the risky territory of arguing that alpha can be derived from superior analysis. But in a weekly research piece to come in the next few weeks, we will argue for just such a heresy.