The Fed-model puzzle

Myron Gordon at the University of Toronto in 1982

For the last 13 years and until recently (see Bonds/Equity Positive Correlation: For How Long?) correlation between US stock and bond returns have been negative.

As presented by Hasseltoft (2009), the correlation between US stock and bond returns has varied substantially over time (puzzle 1), reaching highly positive levels in the late 1970s and early 1980s while turning negative in the late 1990s.

 

US strock and bond returns correlation Henrik Hasseltoft 2010

Several statistical models have been put forward to model the time variation but little work has been done on explaining the phenomenon within an equilibrium model. A second feature (puzzle 2) of data that has been considered puzzling is the highly positive correlation between US dividend yields and nominal interest rates, a relation often referred to as the Fed-model. From the Gordon (1962) growth formula, dividend yields are given by the real discount rate on equity minus the real dividend growth rate:

D/P= R – G,

where D is the dividend yield, P is the stock price, R is the real discount rate on equities  and G is the real dividend growth rate. R can itself be decomposed as the sum of the risk free rate R_f and the equity Risk Premium RP_e: R = R_f + RP_e.

Since changes in expected inflation E(p) and bond risk premiums RP_b, have been the main source of variation in nominal yields y^$, e.g. Campbell and Ammer (1993),

y^$ = R_f + E(p) + RP_b,

the positive correlation observed in data implies that one or both of these components must either be positively associated with real discount rates or negatively associated with real dividend growth rates.

           

However in the literature, it has been considered implausible for inflation to have rational effects on any of these two real components of dividend yields. Instead, a behavioral explanation in the form of inflation illusion, e.g., Modigliani and Cohn (1979), and Campbell and Vuolteenaho (2004) has been put forward.

Hasseltoft’s model was inspired by Bekaert and Engstrom (2009) empirical work; it underlines some key mechanisms such as:

• Investors dislike inflation shocks and demand positive risk premiums for holding assets that are poor inflation hedges, such as equity (which can be a hedge against inflation only in a limited number of cases – see Are Equities A Good Inflation Hedge?) and nominal bonds,
• Stagflation (high inflation with slow economic growth) feature of US data induces a common risk premium channel for stocks and bonds.

One powerful aspect of Hasseltoft's model is its ability to bring explanations of the following facts:

• Both equity and bond risk premiums load positively on macroeconomic volatility – in particular inflation volatility,
•  High inflation volatility together with stagflation induces a strong comovement between dividend yields and nominal yields,
• The Great Moderation led to lower correlations.

Bekaert, Geert, and Eric Engstrom (2009). "Inflation and the Stock Market: Understanding the Fed Model," NBER Working Papers 15024. National Bureau of Economic Research, Inc.

Campbell, John Y & Ammer, John, (1993). What Moves the Stock and Bond Markets? A Variance Decomposition for Long-Term Asset Returns, Journal of Finance, American Finance Association, vol. 48(1), pages 3-37, March.

Gordon, Myron J. (1962). The Investment, Financing, and Valuation of the Corporation. Homewood, IL, Irwin.

Hasseltoft, Henrik (2009), The 'Fed Model' and the Changing Correlation of Stock and Bond Returns: An Equilibrium Approach (January 17, 2009). Available at SSRN: http://ssrn.com/abstract=1361489  or http://dx.doi.org/10.2139/ssrn.1361489

Modigliani, Franco and Cohn, Richard A (1979).  Inflation, Rational Valuation and the Market

Financial Analysts Journal. Vol. 35, No. 2 (Mar. - Apr), pp. 24-44.

Campbell, John Y. and Tuomo Vuolteenaho (2004). Inflation Illusion And Stock Prices, American Economic Review, vol 94 (May), 19-23.