Swedroe: Correlations Can Be Predictive

October 23, 2015

Academic researchers have presented theory, as well as empirical evidence, suggesting certain linkages between equity risk and the Treasury bond market, a relationship that clearly has important implications for investors’ understanding of markets and portfolio design.

Studies, for example, have found that greater economic uncertainty leads both to higher equity volatility and increased motives for precautionary savings that can depress interest rates. Moreover, links between the stock and bond markets have been attributed to flight-to-quality (FTQ) or flight-from-quality (FFQ) as some investors move between riskier stocks and safer Treasurys due to changing perceptions of risk.

A Recap

Recent contributors to the literature on this subject are Naresh Bansal, Robert Connolly and Chris Stivers, authors of the paper “Equity Volatility as a Determinant of Future Term-Structure Volatility,” which appeared in the September 2015 issue of the Journal of Financial Markets.

As I mentioned earlier this week, the authors found that: “With linkages between the economic state and stock volatility, a higher stock volatility this month is likely to be associated both with more extreme stock price movements over the next month (volatility clustering), and with higher economic uncertainty and volatility in that uncertainty (stock volatility tending to be higher in stressful economic times with greater economic-state uncertainty). If a higher stock-return volatility and a higher time series variability in economic uncertainty are likely following months with a high realized stock volatility, then the likelihood of FTQ/FFQ pricing influences over the subsequent month is presumably much greater.”

The authors went on to note: “Equity-risk dynamics and flight-to-quality pricing influences may be particularly important for understanding bond market dynamics over the post-1997 period since this period features a predominantly negative stock-bond-return correlation, a low inflation-risk environment, and several episodes of high and volatile equity risk.”

Among the key findings from Bansal, Connolly and Stivers’ study, which covered the period October 1997 through June 2013, were that:

  • Relatively high realized stock volatility in the previous month is reliably associated with higher subsequent stock volatility over the ensuing month. In other words, volatility clusters.
  • The conditional volatility of Treasury returns is dependent on whether the prior month’s stock volatility was extremely high or low. Treasury return volatilities following high stock volatility have a mean about twice the comparable values for observations that follow low stock volatility, with FTQ/FFQ dynamics being a key contributor to the relationship between stock and bond market volatility. There’s a much stronger relationship in stressful, uncertain economic times (such as around recessions) when bond prices are likely to appreciate with heightened economic uncertainty as the result of a precautionary savings effect.

Supporting Research

Liu Xinyi and Hua Fan—authors of a 2014 paper, “Stock-Bond Correlation and Duration Risk Allocation,” which covered the period Jan. 11, 1985 through Sept. 6, 2013—further contributed to our understanding of how stock and bond markets interact.

Their results are consistent with those of Bansal, Connolly and Stivers. Following is a summary of the authors’ findings:

  • Stock/bond correlations are highly persistent in the short to intermediate term.
  • A lower (more negative) stock/bond correlation forecasts falling 10-year Treasury interest rates over the following weeks. It also forecasts falling one-year Treasury interest rates over the next year.
  • The reverse is true when the stock/bond correlation is higher (more positive).
  • The 10-year bond underperforms exceptionally in the bottom deciles (when stock/bond correlations are highest). For example, in the tenth decile, annualized 10-year bond returns are -13 percent in week one, and -2 percent a week on average from week two to week eight. On the other hand, the 10-year bond outperforms considerably in the top deciles. For example, in the first decile, where correlations are the most negative, the annualized 10-year bond returns were 19 percent for week one (outperforming the tenth decile by 32 percentage points, with a t-stat of 3.5) and 11 percent for week two through week eight (outperforming the tenth decile by 13 percentage points, with a t-stat of 1.7, which is not quite statistically significant at the 5 percent level).
  • Expected returns for the 10-year Treasury bond are more sensitive to the stock/bond correlation when they are already low (markets underreact to the safe-haven status of 10-year Treasurys).
  • The yield curve (the 10-year yield minus the one-year yield) tends to steepen over the following year when correlations are low (negative) and flatten when correlations are high (positive). In the first decile, the curve steepens on average from 0.70 percent to 1.49 percent, while in the tenth decile, it flattens on average from 1.39 percent to 0.82 percent.

The authors posit that the short-lived outperformance of the 10-year Treasury bond in the first decile is related to the aforementioned and well-documented “flight to safety” phenomenon. The effect on the 1-year Treasury may be more moderate, but it’s long-lasting.

The authors found that the outperformance of the first decile relative to the tenth decile persisted through a full year, producing a 1.4 percent annualized return per week (with a t-stat of 3.7), which is sizable given that the annualized volatility of the one-year bond is just 0.8 percent. The strategy also produced a high Sharpe ratio—0.83.

Explaining Predictive Powers

The authors then go on to propose two possible explanations for this predictive power: “(1) the markets and/or policymakers’ under-reaction to the changing economic conditions implied by the stock-bond correlation; and (2) the markets’ initial under-reaction to the long-term bonds’ safe-haven status.”

They also explain the time-varying nature of the stock/bond correlation. They hypothesize: “Bond and stock prices are driven by two economic drivers—expected growth and inflation.” As such, stock/bond correlations are driven by the following:

  • Sensitivities to economic drivers. Higher expected inflation drives both bond and stock prices down; higher expected economic growth drives bond price down but drives stock price up.
  • The relative volatility of the expected inflation and growth. Stock/bond correlation is low when the uncertainty of growth dominates the inflation uncertainty.
  • Growth-inflation correlation. Stock/bond correlation is low at times when growth and inflation are positively correlated. Since the 1990s, demand shocks make bond returns largely countercyclical.

The authors concluded: “A lower stock-bond correlation implies higher impact of growth uncertainties relative to inflation uncertainties … Therefore, a lower stock/bond correlation implies that the central bank may ease the policy rate, because resisting a recession becomes the paramount policy priority instead of resisting higher inflation.”

They hypothesize: “The term structure of short-term interest rates may not ‘immediately’ reflect the economic conditions implied by the stock-bond correlation, but probably with a lag. It is either because the policy rate reacts to the implied economic conditions with a lag, or the markets react to the future policy rates with a lag.”

The bottom line is that the evidence demonstrates time-varying asset correlations do provide information on macroeconomic conditions from an interesting perspective.

The evidence also supports the view that quality bonds play an important role in downside protection of equity risk, and their impact increases in importance at exactly the right time. Ten-year Treasury bonds not only have higher returns in the weeks following equity crashes, but they become less risky, if we define their risk in terms of their equity market beta.


Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.

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