A Case of Empirical Reverse Engineering: Estimation of the Pricing Kernel
65 Pages Posted: 30 Sep 2000
Date Written: March 2000
We revisit the Roll (1977) critique regarding the unobservability of the market portfolio in the framework of the CAPM. It is equivalent to the unobservability of the pricing kernel (also known as the stochastic discount factor) in the language of the modern asset pricing theory. We advocate an econometric procedure which allows the estimation of the pricing kernel without either any assumptions about the investors preferences or the use of the consumption data. We propose a model of equity price dynamics, which allows for (i) simultaneous consideration of multiple stock prices, (ii) analytical formulas for derivatives such as futures, options and bonds, and (iii) a realistic description of all of these assets. The analytical specification of the model allows us to infer the dynamics of the pricing kernel. The model, calibrated to a comprehensive dataset including the S&P 500 index, individual equities, T-bills and gold futures, yields the conditional filter of the unobservable pricing kernel. As a result we obtain the estimate of the kernel, which is positive almost surely (i.e. precludes arbitrage), consistent with the equity risk premium, the risk-free discounting, and with the observed asset prices by construction. We find that the S&P 500 index contains virtually zero idiosyncratic volatility. The pricing kernel filter involves a highly nonlinear function of the contemporaneous and lagged returns on the index. This contradicts typical implementations of CAPM, which use a linear function of the market proxy return as the pricing kernel. Hence, the S&P 500 index does not have to coincide with the market portfolio if it is used in conjuction with nonlinear asset pricing models.
Keywords: Pricing kernel, risk-neutral valuation, simulated method of moments, reprojection
JEL Classification: G12, G13; C14, C52, C53
Suggested Citation: Suggested Citation