The “Fed-model” and the changing correlation of stock and bond returns: An equilibrium approach Henrik Hasseltoft Stockholm School of Economics & The Institute for Financial Research-SIFR June 6, 2009

Introduction Objective: Provide an economic understanding of two “puzzling” features of data: 1.The positive correlation between dividend yields and nominal yields - “Fed-model” 2.The time-varying correlation between stock and bond returns Several statistical papers but few economic models I take a consumption-based approach

1. The “Fed-model”

1. Why is it puzzling ? Historically, changes in inflation and bond risk premiums have been main drivers of nominal yields Drivers of dividend yields, Gordon growth formula: Inflation illusion (e.g., Modigliani and Cohn, 1979, Campbell and Vuolteenaho, 2004) Bekaert and Engstrom (2008): Rational mechanisms are at work. High correlation between inflation and the equity risk premium

2. The time-varying correlation of stock and bond returns

Possible channels: Changes in real rates – Positive correlation Dividend growth – Wedge between stocks and bonds Changes in risk premiums – Positive correlation if both assets are risky Empirically, higher short rates, steeper yield curve, higher inflation, higher inflation uncertainty & volatility predict correlations positively E.g., Li (2002), Viceira (2007), David and Veronesi (2008), Yang et. al (2009)

Main Results Model provides rational explanation of the Fed-model and the time-varying correlation of returns Key mechanism US data - inflation has signalled low future consumption growth Investors dislike positive inflation shocks Equity and nominal bonds are poor inflation hedges Implications Equity/bond risk premiums are positively correlated Corr(Dividend yields, nominal yields) > 0 Corr t (stock ret, bond ret) move positively with macro volatility

Model Builds on Bansal and Yaron (2004), Piazzesi and Schneider (2006) Recursive preferences of Epstein-Zin (1989) and Weil (1989) Dynamics: Specification I and II Interaction between real variables and inflation Log pc,pd-ratio,bond prices: Linear function of state variables

Asset prices Log asset prices linear functions of state variables (homoscedastic case): Dividend growth drives a wedge between stocks and bonds Compare to Bansal and Yaron 2004 and Piazzesi and Schneider 2006

Model Implications Quarterly US data 1952 – 2007: Expected and unexpected inflation signal lower future consumption growth Innovation to pricing kernel (homoscedastic case) Given elasticity of intertemporal substitution > 1: Investors’ dislike positive inflation shocks Investors’ dislike positive shocks to macro volatility PD-ratios negatively related to inflation, macro volatility as in data. Power utility gives opposite implications

The equity risk premium Positive inflation shocks lower both investors’ well-being and real stock returns → positive risk premium Higher macroeconomic volatility raises risk premiums, in particular inflation volatility Positive covariance between dividend growth and inflation lowers risk premiums. Important in late 1990s

The inflation risk premium on bonds Decompose nominal short rate The inflation risk premium: Bonds have low payoffs in bad times positive risk premium Inflation volatility plays key role (again) →

Conditional volatilities Consumption growth Inflation

Conditional covariances Dividend growth and inflation Consumption growth and inflation

Explaining the Fed-model Positive unconditional correlation between equity and bond risk premiums due to common exposure to macroeconomic volatility Turning off risk premium channel yields a correlation of 0.17

Explaining the time-varying correlation of stock and bond returns Recall: Higher macroeconomic volatility increases both equity and bond risk premiums positive covariance of returns Covariance is increasing in the volatility of consumption growth and inflation Covariance is decreasing in covariance between inflation and dividend growth Recall: Dividend growth drives a wedge between stocks and bonds

Predicting realized correlations

Realized correlations 1970s-early 1980s: High macro volatility Early 1980s-2000: “ The Great Moderation ” Late 1990s: Low volatility + positive covariance of dividend growth and inflation

Conclusion 1.Risk premiums on equity and nominal bonds comove positively through changes in macroeconomic volatility. 2.Positive correlation of risk premiums explain the Fed-model, which stands in contrast to the inflation illusion argument 3.Conditional correlation of stock and bond returns loads positively on macroeconomic volatility 4.Low macro volatility + pos correlation between dividend growth and inflation = negative stock-bond correlation 5.Model suggests that inflation volatility is key driver of both equity and bond risk premia Key : inflation has real effects + recursive preferences

Extra Slides

Estimating homoscedastic case Maximum likelihood Both expected and unexpected inflation signal low future consumption growth

Asset prices Risk aversion = 10, EIS = 1.5, discount factor = 0.997

Asset prices Valuation ratios are negatively related to expected inflation in data