Recent market events have once again piqued investor interest in the relationship between the returns of equities and government bonds. Between 26 January and 8 February, the S&P 500 fell dramatically, returning -10% over this short window. During this same period, the yield on 10-year government bonds increased from 2.6% to 2.8%. What happened to the reputation of bonds as “safe-haven” assets in times of crisis?
In our view, the recent rise in bond yields resulted largely from upside surprises in the January payroll and hourly earnings numbers, which led to a reassessment of investors’ inflation expectations. This, in turn, pushed bond yields higher. In other words, the shock emanated primarily from the bond market, rather than the equity market. And it turns out this is critical.
Our Quantitative Research and Analytics paper, “Stocks, Bonds and Causality,” shows that the relationship between stock and bond returns – whether they are positively or negatively related – depends largely on whether a shock starts in the stock market or the bond market. Equity market shocks are associated with flight-to-quality (FTQ) effects and a negative relationship, whereas bond market shocks – consistent with recent events – typically induce a positive stock-bond relationship. Regardless of any notion of causality, however, government bonds have been good performers in nearly all recessions over the past 60 years, providing a hedge to procyclical equity exposure when it is most needed.
As evidence, Exhibit 1 shows the rolling 12-month returns for bonds and equities. Equities (in blue) illustrate a clear pattern of poor performance both heading into and during a recession. No such pattern is observed for bond returns (in green).
Exhibit 2 shows detailed statistical data on excess equity and bond returns during recessions. Equities underperformed bonds considerably during the first half of recessions by an average 232 basis points (bps) per month, while during the second half of recessions, equities outperformed bonds by an average 90 bps per month. Importantly, excess bond returns have been positive in both the first and second halves of recessions, generating Sharpe ratios of 0.34 and 1.03, respectively. Even during the turbulent, inflation-driven 1970s, bonds experienced positive nominal returns in each recession.1 Hence, while equity returns are strongly related to the business cycle, U.S. government bonds have historically acted countercyclically, providing relatively stable returns during recessions.
While the countercyclical properties of government bonds are clearly of great significance to investors, it is important to understand the dynamics between these asset classes in non-recessionary periods as well. In the next section, we discuss the stock-bond relation more broadly.
GRAVITATIONAL PULL OF VALUATION
Much like the game “No Limit Texas Hold ‘em” understanding the basic equity valuation model takes a minute to learn and a lifetime to master. On the surface, deciphering the relationship between equity and bond yields seems almost trivially simple. From the basic Gordon dividend discount model, one can easily show (under certain assumptions) that the earnings yield on equities can be written as
where E/P is the equity earnings yield (earnings divided by price), r is the real “risk-free” rate of interest, and ERP is the equity risk premium, or the amount of additional return that investors require over the risk-free rate for bearing equity risk. This equation, however, masks the causal relationships as well as the complex array of feedback mechanisms between the variables, as they are all correlated with one another.
So how is one to make sense of such complexity? In “Stocks, Bonds and Causality” we have estimated a model that accounts for some of these causal relations. Furthermore, the model allows for the long-run impact of valuation on the forward-looking relationship between equity and bond yields. This turns out to be critically important.
In the model, valuation is defined by the ERP, or the difference between the stock and bond yields. Because the ERP changes over time (and, in fact, mean-reverts over long time intervals), valuation effectively acts as a “gravitational force,” bringing equity and bond yields closer together when markets are “cheap” (ERP is high) and further apart when they are “expensive” (ERP is low). We illustrate this concept in Exhibit 3: As the equity yield and bond yield move away from one another, long-term forces (ERP) ultimately bring both yields back to an equilibrium state.
CAUSALITY AND VALUATION
Let’s explore the concept of causality and then turn to the issue of valuation. Equity prices, of course, represent today’s value of a set of discounted future cash flows. Consistent with the earnings yield equation above, a shock to the real bond market has a direct impact on discount rates and hence higher real rates translate to lower stock prices, or equivalently, a higher equity yield. However, when there is a negative shock to the equity market (a flight-to-quality (FTQ) episode), investors tend to flock to the bond market, pushing down yields. Of course, if the earnings yield rises and the real yield falls, this naturally means that the ERP must increase. (As noted, all of the variables are correlated.)
Exhibit 4 shows the impact on equity and real yields, at three-month and 12-month horizons, from a shock to the earnings yield and real yield. A positive shock to equity yields (a decline in equity prices) tends to result in declining bond yields, while a positive shock to the real bond yield (a decline in bond prices) results in an increase in the earnings yield. This finding highlights the importance of causality in the stock-bond relation: Depending on the source of the market shock, equity and bond yields will respond differently to one another.
The analysis in Exhibit 4 was conducted under the assumption that valuations were “fair,” meaning that the ERP was at its long-run equilibrium level at the time of the shock. But what if markets are far from equilibrium at the time of an FTQ episode or bond market disturbance?
Exhibit 5 shows what is expected to happen to equity and real bond yields 12 months after the same set of shocks as in Exhibit 4, but allowing for the equity market to start out either cheap or expensive relative to the bond market. When markets are expensive, Exhibit 5 shows that the negative stock-bond relation is even more pronounced after a positive shock to the earnings yield. Effectively, when equity markets are frothy, stocks have further to fall (the earnings yield rises) and bonds have more room to rise (real yields fall). On the other hand, when markets are cheap, valuation acts as a buffer, resulting in little relationship between equity and bond returns.
In the cheap scenario, in fact, the earnings yield is actually lower and real yields higher 12 months after a negative equity shock – the exact opposite impact from when markets are expensive.
While real yield shocks result in a positive relationship in both fair and expensive markets, the relationship is negative when markets are cheap, again reflecting the long-run force of valuation on the yields of both asset classes. Hence, when markets are away from equilibrium, the forces of valuation may dominate transitory shocks to stock and bond yields.
Given today’s level of the equity risk premium, which is slightly rich relative to the long-run average of about 3%, we would generally anticipate the behavior of equity and bond yields to be somewhere between the “fair” and “expensive” scenarios shown in Exhibit 5. FTQ shocks are expected to be associated with a slightly more pronounced negative stock-bond relation and real yield shocks resulting in a positive correlation. However, equities are more susceptible to negative bond market shocks (a rise in bond yields) when markets are expensive and, therefore, a rapid rise in real bond yields is a tangible risk that investors should be aware of.
Furthermore, an inflationary surprise could lead to a positive stock-bond correlation. This would occur through two mechanisms: first, vis-à-vis the inflation surprise itself, which tends to induce a positive correlation and second, through the likelihood of Federal Reserve rate hikes. Additionally, historically high levels of household and government leverage globally could portend a simultaneous increase in bond yields and a fall in corporate earnings, leading to a contemporaneous decline in equity and bond prices.