Estimation and Test of a Simple Model of Intertemporal Capital Asset Pricing

Abstract

A simple valuation model that allows for time variation in investment opportunities is developed and estimated. The model assumes that the investment opportunity set is completely described by two state variables, the real interest rate and the maximum Sharpe ratio, which follow correlated Ornstein-Uhlenbeck processes. The model parameters and time series of the state variables are estimated using data on US Treasury bond yields and inflation for the period January 1952 to December 2000. The estimated state variables are shown to be related to the equity premium and to the level of stock prices as measured by the dividend yield. Innovations in the estimated state variables are shown to be related to the returns on the Fama-French arbitrage portfolios, HML and SMB, providing a possible explanation for the risk premia on these portfolios. When tracking portfolios for the state variable innovations are constructed using returns on 6 size and book-to market equity sorted portfolios, the tracking portfolios explain the risk premia on HML and SMB, and these state variable tracking portfolios perform about as well as HML and SMB in explaining the cross-section of returns on the 25 size and book-to market equity sorted value weighted portfolios. An additional test of the ICAPM using returns on 30 industrial portfolios does not reject the model while the CAPM and the Fama-French 3 factor model are rejected using the same data.

Monetary Policy and Corporate Bond Returns

“…Specifically, firm riskiness can increase, in response to an unexpected increase in the FFR, through a rise in the interest burden and the weakening of balance sheets, which can also translate into an increase in the credit spread. 8 This risk-based explanation is consistent with asset pricing models in which the (innovation) in a short-term interest rate (and specifically, the innovation in F F R) is a priced risk factor that helps to explain cross-sectional equity risk premia (Brennan et al, 2004;Petkova, 2006;Lioui and Maio, 2014;Maio and Santa-Clara, 2017). In these multifactor models, the interest rate factor earns a negative price of risk, and thus stocks that have negative interest rate factor loading (that is, negative return responses against positive changes in interest rates) earn a higher risk premium, which translates into higher expected stock returns, relative to stocks that are uncorrelated with short-term interest rates.…”

The cross-section and time series of stock and bond returns

“…Ang and Bekaert (2007) find some predictability of nominal short rates for future aggregate stock returns. Brennan, Wang, and Xia (2004) write down an intertemporal-CAPM model where the real rate, expected inflation, and the Sharpe ratio move around the investment opportunity set. They show that this model prices the cross-section of stocks.…”

A model of asset pricing under country risk

“…The nominal risk-free interest rate and the maximum Sharpe Ratio are respectively r ¼ 0.0547 and l ¼ 0.70, equal to the long-run averages in Brennan et al (2004). These authors set the long-run real interest rate to 0.0162 and the long-run inflation to 0.0385, which adds up to 0.0547.…”

“…These authors estimate that the real growth trend of US aggregate earnings from 1947 to 2005 is 0.0343, which results in a nominal growth rate of 0.0728 after adding the 0.0385 long-term inflation rate in Brennan et al (2004). After the hostile renegotiation of foreign debt and associated regime change, the nominal growth trend drops to m x ¼ 0:0410.…”