Knowledge that Transforms

In this paper, we analyze the behavior of equilibrium real interest rates in an identical consumer economy in which the preferences are represented by time additive logarithmic utility functions and production technologies are Cobb-Douglas with stochastic constant returns to scale. The following main results are established. (i) When there is no relative price uncertainty, it is shown that the equilibrium interest rate exhibits a mean reverting tendency. A nontrivial steady state distribution is found to exist for the equilibrium interest rate. The properties of the equilibrium interest rate are also derived and discussed. (ii) In a multigood economy, even with additive preferences across goods, the equilibrium interest rates depend explicitly on relative prices. The substitution possibilities in production technologies induce this result. This is in contrast to the findings of Richard and Sundaresan 11 who show that the analytical general equilibrium term structure of interest rates formula of Cox, Ingersoll, and Ross 5 is unaffected by the introduction of relative price uncertainty when the technologies are linear and hence involve no substitution. Furthermore, we relate our results to those of Cox, Ingersoll, and Ross 5, Breeden 3, and Richard and Sundaresan 11 with special emphasis on stochastic production and realtive price uncertainty.

Under conditions consistent with the Black-Scholes formula, a simple formula is developed for the expected rate of return of an option over a finite holding period possibly less than the time to expiration of the option. Under these conditions, surprisingly, the expected future value of a European option, even prior to expiration, is shown equal to the current Black-Scholes value of the option, except that the expected future value of the stock at the end of the holding period replaces the current stock price in the Black-Scholes formula and the future value of a riskless invesment of the striking price replaces the striking price. An extension of this result is used to approximate moments of the distribution of returns from an option portfolio.

With a short sales restriction, there may be switching points along the mean variance frontier corresponding to changes in the set of assets held. Traditional wisdom holds that each switching point corresponds to a kink, while Ross has claimed that kinks never occur. This paper shows that the truth lies between the two views, since the efficient frontier may or may not be kinked at a switching point. There is some indication that kinks are rare, since a kink corresponds to a portfolio in which all assets have the same expected return.

Robert A. Eisenbeis, Robert S. Harris, Josef Lakonishok, Benefits of Bank Diversification: The Evidence from Shareholder Returns, The Journal of Finance, Vol. 39, No. 3, Papers and Proceedings, Forty-Second Annual Meeting, American Finance Association, San Francisco, CA, December 28-30, 1983 (Jul., 1984), pp. 881-892