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Understanding the correlation of equity and bond returns

The correlation of equity and high grade sovereign bond returns is a powerful driver of portfolio construction and the term premia of interest rates. This correlation has turned from positive in the 1970s-1990s to negative in the 2000s-2010s, on the back of similar shifts in the correlation between inflation and economic growth and between inflation and real interest rates. The structural correlation flip has given rise to a risk parity investment boom and contributed to the compression in long-term yields. Both theoretical and empirical analysis suggests that negative equity-bond correlation is due largely to pro-cyclical inflation, i.e. higher inflation coinciding with better economic performance, as opposed counter-cyclical inflation or stagflation. Inflation is more likely to be pro-cyclical if it is low or in deflation (view post here) and driven by demand rather than supply shocks.

Pericoli , Marcello (2018), “Macroeconomics determinants of the correlation between stocks and bonds”,  Banca d’Italia, Working papers,  No 1198 – November 2018

The post ties in with SRSV’s summary lecture on implicit subsidies.
The below are quotes from the paper. Emphasis and cursive text have been added.

The importance of bond-equity correlation

“Forecasting stock-bond correlation using macroeconomic factors helps to improve investors’ asset allocation decisions…A negative correlation implies that bonds can hedge stock portfolio when the economy is in a bad state and this increases the room for portfolio immunization….From the investor’s point of view, the new regime [of negative stock-bond return correlation], observed [over the past 20 years] is extremely beneficial since diversification opportunities are available, making portfolio immunization more effective [unlike] the 1980s and the 1990s.”

“The correlation between stock and bond prices…is also a driver of long-term government bond prices and of their term premia…An increased hedging demand for bonds can explain the extremely low level of bond term premia we have observed since around 2005.”

The historical facts

In advanced economies, the correlation, which was positive until the end of the 1990s, changed sign at the turn of the century; since the late 1990s stock and bond prices have been moving in opposite directions…The change in the sign of the stock/bond correlation has been a global phenomenon….During both of the two most recent global recessions, in 2001 and 2007-09…government bonds performed well.
[The figure below] presents the time-varying correlations for the US, the UK, Germany, France and Italy since data availability. The correlation recorded positive figures until the late 1990s and dropped into negative territory just before 2000. Only in Italy has the correlation remained negative for a few years.

Inflation has played a role in driving the correlation…We show this…[by] computing the correlation and the covariance between returns on stocks and index-linked government bonds, securities whose payoff is computed net of realized inflation….The standard and real correlation coefficients moved together…until the global financial crisis in 2008-09 and moved in opposite directions thereafter; the stock/real-bond correlation and covariance was negative from 2000 to 2008 and positive thereafter, while the standard correlation and covariance has remained negative.”

Economic variables and their interlinkages play a…role in driving the correlation between stocks and government bonds. We can see that the change in the sign of the correlation coincides with a change in the sign of the correlation between real interest rates, inflation and growth…[While] the correlation between…the rate of growth of GDP…and real interest rates is negative in the two periods [1990-1999 and 2000-2017]… the correlation coefficients dividend/inflation and real-interest-rate/inflation change considerably. The dividend/inflation relation moves from negative to positive…The real-interest-rate/inflation relation moves from positive to negative…Since 2000 an increase in inflation causes a decrease in the real interest rate.”

The connection between bond and equity returns

“The literature agrees that long-term bond prices are determined by the inflation rate, real interest rates, the term premium, and the corresponding shocks to inflation and real interest rates. Stocks share with bonds two of their factors (namely inflation and real interest rates) and two of their shocks (namely to inflation and real interest rates) but they are also affected by distributed earnings (i.e. dividends) and by shocks to them.”

“A standard no-arbitrage [asset pricing] model suggests that the correlation between bond yields and stock returns can be decomposed into the uncertainty about inflation, real interest rates [and] the covariance between inflation, real interest rates and dividend yields.”

“For a given level of inflation, a negative shock to the real interest rate will push bond and stock prices higher…Inflation impacts bonds negatively, since their payoff is in nominal terms, and stocks positively or neutrally, since dividends and stock payoffs may change with respect to variations in inflation.”

The empirical findings

“The literature separates the period up to the late 1990s from the subsequent period; in the first period, the cycle in advanced economies was characterized by supply shocks, which induced a countercyclical response of inflation to growth. Conversely, since 2000, the cycle has been characterized by demand shocks, both monetary and …fiscal, and thus inflation has behaved in a pro-cyclical manner, showing a positive correlation with output growth.”

“We test empirically this decomposition [of the correlation between bond yields and stock returns] by regressing a time-varying measure of the stock/bond correlation on variables that approximates…measures of uncertainty.”

“Results support the role of inflation across the business cycle in determining the sign of the stock/bond correlation. A key mechanism…is time-variation in the conditional correlation between expected inflation and expected aggregate cash flows to equity. Macroeconomic dynamics swing from periods of countercyclical expected inflation, stagflation, to periods of pro-cyclical expected inflation. During stagflation, good (bad) news about future cash flows tends to be accompanied by news of lower (higher) expected inflation…Such a pattern is consistent with what happened from the 1970s to the late 1990s. Pro-cyclical shocks to expected inflation generate the opposite correlation, such as in the Great Recession.”


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