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.

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 e____ffect 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__. 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.**investment shock**becomes the dominating force for generating the stock-bond return and consumption-inflation correlations__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 *

*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**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.*