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The macro forces behind equity-bond price correlation

Since the late 1990s, the negative price correlation of equity and high-grade bonds has reduced the volatility of balanced portfolios and boosted Sharpe ratios of leveraged “long-long” equity-bond strategies. However, this correlation is not structurally stable. Over the past 150 years, equity-bond correlation has changed repeatedly. A structural economic model helps to explain and predict these changes. The key factor is the dominant macro policy. In an active monetary policy regime, where central bank rates respond disproportionately to inflation changes, the influence of technology (supply) shocks dominates markets and the correlation turns positive. In a fiscal policy regime, where governments use debt financing to manage the economy, the influence of investment (financial) shocks dominates and the correlation turns negative. In a world with low inflation and real interest rates, the fiscal regime is typically more prevalent.

Li, Erica, Tao Zha, Ji Zhang, and Hao Zhou (2020), “Stock-bond Return Correlation, Bond Risk Premium Fundamentals, and Fiscal-Monetary Policy Regime”, Federal Reserve Bank of Atlanta, Working Paper 2020-19, October 2020.

The below post is based mainly on quotes from the above paper. Other sources that have been used are linked after the respective quotes.

This post ties in with this site’s summary on macro trends.

The importance of bond-equity correlation

“Effective diversification by managers is reliant on the returns of ‘broad’ asset classes, primarily equities and bonds, moving independently (or even better, in opposing directions)…Negative correlation between equities and bonds…has allowed managers to use fixed-income assets…as protection in periods of high market stress. It has largely been the mainstay of asset managers’ playbooks for decades.” [CFM]

“The volatility of a balanced…equities and fixed income…portfolio increases dramatically if the correlation between these primary assets moves from negative to positive, particularly for those strategies that use leverage to augment returns from fixed income (see graph below). Sharpe ratios deteriorate, implying that the potential rewards no longer match the risks taken, and to maintain acceptable levels of portfolio volatility, investors are forced to de-lever, or find alternative ways to reduce risk.” [Sibley, 2020]

Key stylized facts

“Empirical studies have documented the time-varying correlation between returns on the market portfolio of stocks and those on long-term (5-10 years) nominal Treasury bonds. This correlation was positive before 2000 but turned negative afterwards (see chart below). At the same time, the correlation between consumption growth and inflation also changed sign around 2000 from negative to positive.”

“Key facts are…

  • The annual correlation between [daily] returns on the stock market, proxied by the stock market index, and returns on nominal (zero-coupon) Treasury bonds of 5-year maturity was 0.28 in 1971-2000 and −0.32 after 2000…
  • The annual correlation between consumption growth rate and inflation was −0.32 in 1971-200 and 0.16 in the post-2000 period… Real consumption growth is computed with quarterly real personal consumption expenditures per capita, and inflation is the change of quarterly GDP deflator. To obtain accurate annual correlations, we calculate the consumption-inflation correlation of year t using the data within the 5-year window…
  • Both the stock market index and nominal Treasury bonds of 5-year maturity earned positive risk premiums before and after 2000, even though the CAPM beta of the Treasury bonds, which has the same sign as the stock-bond return correlation, turned negative after 2000.”

“Using data going back to the mid-19th century, it is clear that the correlation between equities and bonds has been mostly positive, making the recent, and consistent stretch of negative correlation the anomaly, rather than the rule.” [CFM]

“The correlation between the returns of government bonds and equities is one of the most important metrics in asset allocation…We have shown, however, that this critical relationship depends on whether shocks occur in the equity or bond market. When shocks emanate from the equity market, the correlation is typically negative, but shocks to the bond market correspond to a positive relationship between stock and bond returns.” [PIMCO]

Distinguishing fiscal and monetary policy regimes

“To account for the sign changes observed in both the financial market [bond-equity correlation] and the real economy [consumption-inflation correlation], we develop a general equilibrium framework that incorporates a regime switching from the monetary regime to the fiscal regime. We…model the monetary regime as active monetary policy and passive fiscal policy and the fiscal regime as active fiscal policy and passive monetary policy.

  • Monetary policy is modelled as a simple Taylor rule, in which the short-term nominal interest rate reacts to inflation and output gap positively. The policy rate reacts to inflation more than one-for-one under active monetary policy, while less than one-for-one under passive monetary policy.
  • We…model fiscal policy as a lump-sum tax rule that reacts to government outstanding debt and output. Under passive fiscal policy, lump-sum taxes increase proportionately (in the present value) with government spending to satisfy the government budget constraint. Under active fiscal policy… taxes do not increase sufficiently to finance government spending; as a result, prices increase with government deficits to reduce the real debt burden… Passive fiscal policy does not influence macroeconomic fluctuations except for through the level of outstanding government debt, while active fiscal policy influences the price level, which in turn affects other macroeconomic variables.
    From mid 1950s through the Kennedy tax cut of 1964 into the second half of the 1960s, [U.S.] fiscal policy was active, paying little attention to the government debt. Another prolonged period of active fiscal policy began with President Bush’s tax cuts in 2002 and 2003, followed by drastically increased government spending and tax cuts enabled by the Economic Stimulus Act of 2008 and the American Recovery and Reinvestment Act of early 2009 around global financial crisis.”

“We focus on the economic mechanism with a mix of both active fiscal and active monetary policy that endogenously generates the time-varying correlations of both macroeconomic and financial variables.
We show that the mix of the monetary and fiscal regimes is essential to account for the [bond-equity and inflation-consumption] correlation patterns and risk premiums. Under the monetary regime, the effect of the technology shock on these two correlations dominates that of the investment shock; while the opposite is true under the fiscal regime, because the effect of the technology shock is largely muted by passive monetary policy. Narrative accounts of U.S. monetary-fiscal policy history as well as previous empirical studies indicate that the post-2000 period is consistent with the fiscal regime, while the 1971-2000 period is consistent with the monetary regime.”

How the policy regime shapes correlation

“Our general equilibrium framework is a new Keynesian model with four structural shocks: the technology shock defined as a shock to neutral technology, the investment shock defined as a shock to the marginal efficiency of investment, the monetary policy shock, and the fiscal policy shock.”

“The technology shock drives negative stock-bond correlations and positive consumption-inflation correlations under the fiscal regime, while the investment shock drives positive stock-bond correlations and negative consumption-inflation correlations under the monetary regime… Investment shocks…contribute significantly to business cycle fluctuations and economic growth [and] command significant risk premiums in financial markets.

  • A positive technology shock, as a positive supply shock, causes both output and consumption to increase while driving down prices. The resulting consumption-inflation correlation becomes negative. The rise in consumption and the persistent fall in the short-term nominal interest rate as a reaction to falling inflation lead to higher stock prices and higher prices of long-term nominal Treasury bonds. As a result, the stock-bond return correlation is positive in response to a technology shock.
    Under the monetary regime, the interest rate falls more than inflation and thus the real interest rate falls as well. A fall in the real interest rate further stimulates output and consumption. Active monetary policy amplifies the effect of the technology shock and makes this shock a dominating force behind both the negative consumption-inflation correlation and the positive stock-bond return correlation.
    On the contrary, under the fiscal regime, the nominal interest rate falls less than inflation due to passive monetary policy and as a result the real interest rate increases in response to a positive technology shock. Therefore, the stimulating effect of the technology shock is largely muted and this shock becomes unimportant for determining the correlations between consumption and inflation and between returns on stocks and on long-term bonds.
  • Under the fiscal regime, the investment shock becomes the dominating force for generating the stock-bond return and consumption-inflation correlations. A positive investment shock…makes a transformation of investment into capital more efficient. In response to this positive demand shock, both output and investment increases but consumption decreases in the short run as an intertemporal substitution for higher consumption in the long run. The dominating effect of decreased consumption in the short-run causes stock price to fall. An increase in output leads to an increase in tax income and a decrease in the debt-to-output ratio. With active fiscal policy, taxes do not respond to a fall of the debt-to-output ratio. Thus, a combination of higher output, higher tax income, and lower debt-to-output ratio reduces government deficits. It follows from the government budget constraint that the price level must fall to make the real value of government debt more valuable. The falling price level leads to a reduction in the nominal interest rate following the Taylor rule, and as a result, bond prices go up. Hence, under the fiscal regime, the investment shock causes negative stock-bond return correlation and positive consumption-inflation.”

“Consistent with the empirical observation, risk premiums of long-term Treasury bonds remain positive under the fiscal regime in the model while the stock-bond correlation is negative. The key to this result is that the dynamics of the pricing kernel, thus risk premiums, in the model are driven mainly by the technology shock, regardless of the policy regime. Since stock and bond risk premiums are both positive under the technology shock, positive bond risk premium and negative stock-bond correlation coexist in the fiscal regime.”

“We calibrate the model to match moments of key macroeconomic and financial variables and show that technology and investment shocks, not monetary and fiscal policy shocks, are the critical structural shocks in yielding the following key results:

  • Both the positive stock-bond return correlation and the negative consumption-inflation correlation are driven by the technology shock under the monetary regime.
  • Both the negative stock-bond return correlation and the positive consumption-inflation correlation are driven by the investment shock under the fiscal regime.
  • The negative stock-bond return correlation coincides with positive bond risk premiums under the fiscal regime.”

“All our results hold when the nominal interest rate is at the zero lower bound, which is an extreme case of the fiscal regime.”

Note: this model is consistent with other theoretical research that suggests that

  1. monetary policy has played a key role for the direction of equity-bond correlation and that in periods of restrictive monetary policy the correlation has been positive (view post here), and
  2. negative equity-bond correlation is due largely to pro-cyclical inflation (view post here), 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 and driven by demand rather than supply shocks.




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