What’s in a correlation?

US equity indices have tended to go up with bond yields since the turn of the century. History suggests the correlation will remain predominantly positive until 10-year yields reach 5% and we are not convinced lower growth/inflation will change that. An analysis of the dividend yield gap gives the same answer.

We recently wrote about the Phillips curve and concluded that inflation and bond yields will likely move higher. Rising bond yields are bad news for holders of bonds but what about for holders of equities? It is commonly supposed that rising bond yields are associated with falling equity prices but in what follows we show that things are not that simple.

Anybody who works with dividend discount, Fed or yield gap models is implicitly assuming that equity yields should go up with bond yields. Put another way, when bond yields rise, equity prices should fall. Indeed, those of us starting our careers in the mid-1980s had plenty of empirical evidence to support this supposition. Any doubters were easily convinced by the events leading up to Black Monday (October 19, 1987), with US 10-year yields rising from 7.23% at end-December 1986 to 9.64% at end-September 1987 (and the rest, as they say, is history).

Indeed, Figure 1 shows that the correlation between the S&P 500 and 10-year treasury yields was predominantly negative during the 1970s, 1980s and 1990s (though interestingly, the run-up to Black Monday was a period in which the reverse was true – equities continued to rise despite the steep climb in bond yields). During those three decades it would have been unwise to hold equities when bond yields were rising.

However, something changed at around the turn of the century, since when the correlation has been mostly positive. Suddenly it became more sensible to hold equities when bond yields are rising, rather than falling. Our interpretation is that equity markets are now more driven by the economic “good news” that drives bond yields higher, than they are by the movement in bond yields themselves.

So far so good but, as we await further gains in bond yields over the coming year or so, can we count on a continuation of the positive correlation with equities? The fear is, of course, that as we approach the 3% barrier for 10-year yields, the equity-bond correlation regime will change. We hope not but, of course, an investment strategy has to be based on something more than hope … doesn’t it?

We have long suspected that the direction of that correlation is somehow linked to the level of bond yields. Figure 2 gives some support to that notion, showing that the correlation between the S&P 500 and 10-year yields tends to increase as bond yields decline. Admittedly, the relationship is not tight but it seems acceptable, with an r-squared of 0.42 (based on an exponential fit).

Using data since 1964, the chart suggests that a 10-year yield around 3% is more often than not associated with a positive correlation between bond yields and equity prices. Indeed, it has not been until the 10-year yield exceeds 5% that the correlation has become predominantly negative (equities falling as bond yields rise). Of course, the scatterplot displays a wide range around that trendline, so operating with such a degree of precision may be ill-advised.

Accepting that last caveat, it would be nice if we could understand why the correlation increases as bond yields decline. That way we could build some confidence about the level of yields above which the correlation regime may change (and whether that critical level is constant).

One obvious avenue of exploration is the link to inflation. However, when we construct a version of Figure 2 that uses core CPI (CPI ex-food and energy) in the place of bond yields, the trendline is still downward sloping but the relationship is not so good (the r-squared is only 0.30). So, inflation may have something to do with it but the bond yield appears to better explain changes in the correlation regime.

Growth may also play a role: surely, the equity market will be better able to withstand a rise in bond yields if economic/profit/dividend growth is high. This may be true from a cyclical perspective but what we are talking about here are secular shifts in correlation regimes. Further, it is hard to argue that the growth environment has been better this century than during the 1970-2000 period: there has been a noticeable slowdown in average annual real GDP growth from 3.3% in the 1970-1999 period to 1.9% in the 2000-2016 period.

Of course, GDP growth does not necessarily equate to corporate profit growth but we do find a similar pattern when looking at annualised earnings per share (EPS) growth, which went from 7.3% in the 1970-1999 period to 4.0% in 2000-2016 (or from 2.1% to 1.9%, respectively, in CPI-adjusted terms, all data based on Robert Shiller’s EPS series). Hence, growth seems an unlikely explanation for the shift in correlation regime (though we should point out that real dividend growth increased from an annualised 0.6% to 3.9% over those same periods). Further, given that we expect economic and profit growth to be permanently lowered by weaker demographics, we doubt there will be much improvement in the coming decades on the rate of growth delivered so far this century.

What about the gap between bond and equity yields? Could changes in this yield gap have anything to do with the correlation between equities and bonds. If so, the fact that 10-year yields have recently risen above the equity dividend yield could be a concern.

However, if we try to plot the relationship between the dividend yield gap (dividend yield minus 10-year bond yield) and the correlation between equities and bond yields (an alternative version of Figure 2), we have no more success than with core CPI inflation. The relationship is upward sloping (the greater the yield gap the higher the correlation between equities and bond yields) but the r-squared is less than 0.30.

According to our best fit, the correlation doesn’t normally switch sign until the yield gap falls to around -3.0. As the yield gap is currently around -0.7 (based on the dividend yield derived from Robert Shiller’s data), we conclude that bond yields would need to rise another two percentage points before the correlation regime changes (if we assume no change in dividend yield and that history repeats itself). This is almost identical to the conclusion we drew when using the bond yield by itself (that yields need to rise to 5%).

So, having examined the possibility that lower growth/inflation could reduce the bond yield at which the equity/bond correlation regime changes, we remain to be convinced. Our analysis suggests the best explanation for movements in that correlation is the bond yield itself. Even the dividend yield gap (which statistically explains less of the variation in correlation) gives a very similar result to the bond yield by itself; namely, that 10-year yields need to rise to closer to 5% before the correlation regime will change (if history is a guide).

Hence, as bond yields trend higher (as we think they will), we would expect further advances in broad equity indices. As ever, there are caveats: first, we believe the US equity market is very expensive (the Shiller PE was close to 34 at the end of January and has been higher only 2% of the time since January 1881) and suspect this will limit the upside for this market (thankfully, the same does not apply to other major indices); second, bond yields and equity markets will not move up in a straight line and further disappointments such as January’s US retail sales and manufacturing production data could see both moving lower.

In conclusion, we do not believe the correlation regime between stocks and bonds is about to change. We believe that US and global economies are strong enough to continue the normalisation of bond yields and wouldn’t be surprised to see yields go above “normal” at some stage during this cycle (we believe “normal” for the US 10-year yield is 3.0%-3.5%). Luckily, historical evidence suggests equity markets will continue to rise along with bond yields until 10-year yields are closer to 5%. Naturally, yields and equity indices will not rise in a straight line and disappointing economic data (as is common during Q2) could provoke a temporary sell-off. However, we would not expect the equity bull market to end until the economy turns down in a meaningful cyclical, rather than seasonal, sense.

Paul Jackson – Head of Multi-Asset Research – Invesco PowerShares
András Vig – Multi-Asset Strategist – Invesco PowerShares