## Maxim Ulrich

*Decomposing Equity Returns*

Coauthor(s): Andrew Ang.

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**Abstract:**

We have not agreed on an abstract, yet. The main idea of the paper is as follows: We derive an asset pricing model with (almost) only observable macroeconomic variables to price equity, inflation-indexed Government bonds and nominal Government bonds and learn how different macro factors affect the return on equity. The macro variables are the observable components of a forward looking Taylor rule, i.e., expected inflation, expected GDP growth and the Fed intervention factor which measures deviations of the actual fed funds rate from the Taylor rule implied one. Knowing the nominal short rate and its expected path under the pricing measure allows us to price nominal bonds.

We start out with that Taylor rule, specify an inflation process and derive the corresponding real interest rate. The real interest rate is endogenous and affected by all macro factors that affect also the standard forward looking Taylor rule for the fed funds rate. Knowing the real interest rate, we price inflation-indexed bonds.

We specify a dividend process which is allowed to depend on the macro variables. The price of the dividend stream coincides with the discounted expected value of future dividends, where the expectation is taken under the risk-neutral measure and the discount rate is the risk-free rate. Dividends are in real units, so we also use the real risk-free rate as the discount rate. All macro variables that affect the nominal Taylor rule do also affect the price of equity. The linearized dividend yield is affine in expected GDP growth, expected inflation, dividend growth and the Fed intervention factor.

We find that the model does a superb job in explaining the cross-section and time-series of bond yields, dividend yield and holding period returns of equity. The advantage of our model over competing models is that we can decompose the nominal return of equity into the equity premium, inflation risk premium, expected inflation, duration premium and real interest rate. All of these components are explained by the observable macro factors.

**Source:** *Working paper*

**Exact Citation:**

Ulrich, Maxim, and Andrew Ang. "Decomposing Equity Returns." Working paper, Columbia Business School, December 31, 2010.

**Date:**
31
12
2010