A model of intertemporal discount rates in the presence of real and inflationary autocorrelations

Article Abstract:

This paper discusses the pricing of assets in an intertemporal rational-expectations model when real production and inflation evolve according to first-order autocorrelated processes. The focus is on the structure of the various intertemporal discount rates (yields) exhibited by this economy. Yield curves are identified for consumption claims, indexed bonds, and nominally riskless bonds and can be extended to any claim that can be approximated by a (finite) linear combination of such securities. The model demonstrates that, if the average term structure for nominally riskless securities is upward sloping, then the yield curve for consumption (market) claims is downward sloping, suggesting that conventional methods for computing long-term discount rates err by not accounting for maturity factors. The paper also explores the relationship between the intertemporal equilibrium and its embedded single-period equilibria. The single-period risk measures in this economy are derived and shown to be (generally) functions of maturity. A model of nominal bond betas is constructed along these lines. It is shown that bond betas that are increasing functions of maturity do not necessarily imply an upward-sloping term structure. (Reprinted by permission of the publisher.)

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R(2)

Article Abstract:

Even with hindsight, the ability to explain stock price changes is modest. R(2)s were calculated for the returns of large stocks as explained by systematic economic influences, by the returns on other stocks in the same industry, and by public firm-specific news events. The average adjusted R(2) is only about .35 with monthly data and .20 with daily data. There is little relation between explanatory power and either the firm's size or its industry. There is little improvement in R(2) from eliminating all dates surrounding news reports in the financial press. However, the sample kurtosis is quite different when such news events are eliminated, thereby revealing a mixture of return distributions. Non-news dates also indicate the presence of a distributional mixture, perhaps due to traders acting on private information. (Reprinted by permission of the publisher.)

Corporations

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Estimation bias induced by discrete security prices

Article Abstract:

Commonly, equilibrium security prices are modeled by continuous-state stochastic processes, while observed prices are rounded into discrete units. This paper models the rounding mechanism and examines the probabilistic structure of the resultant rounded process. We provide accurate and simple estimates of the inflation in estimated variance and kurtosis induced by ignoring rounding. In particular, the maximum-likelihood estimate of security price volatility using rounded prices is developed, and a simulation analysis is performed to examine the small-sample properties of this estimator. For many practical applications, a simple correction for rounding becomes available. (Reprinted by permission of the publisher.)

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