Knowledge that Transforms

What policy should a corporation adopt concerning the funding of a defined-benefit pension plan and the investment of the assets held in trust for the plan? Until recently, pension plans did not have to be insured, and some risk could be borne by intended beneficiaries. Federal legislation has now mandated such coverage. This paper analyzes corporate policy under three conditions which correspond, roughly, to the earlier situation (‘uninsure’ loans), the current situation (‘partially insured’ loans), and the situation required by law to be implemented in the future (‘completely insured’ plans). We show that if insurance premiums are set correctly, corporate policy in this area may not matter; otherwise the optimal policy may simply be that which maximizes the difference between the value of the insurance and its cost.

Using the option pricing methods developed by Black and Scholes as a general technique for contingent claims analysis, this paper examines a class of mutual funds known as Dual Purpose Funds. By constructing a simplified model for these funds under the ‘perfect hedge’ conditions of Black and Scholes, it is demonstrated that the asset value of the fund will always exceed the market value and that it is not inconsistent with market equilibrium or efficiency for the capital shares to sell at a discount. The simple model predicts price fluctuations in the seven dual funds studied quite well; however, there is a persistent downward bias in the predicted price level. Finally, refinements to the model are examined to determine the nature of the misspecification causing this bias.

This paper considers the equilibrium pricing of equity-linked life insurance policies with an asset value guarantee; such policies provide for benefits which depend upon the performance of a reference portfolio subject to a minimum guaranteed benefit. The benefit is decomposed into a sure amount and an immediately exercisable call option on the reference portfolio. A numerical procedure for determining the value of the call option is presented and the risk minimizing investment strategy to be followed by the issuer of the policy is derived.

This paper examines the structure of option valuation problems and develops a new technique for their solution. It also introduces several jump and diffusion processes which have not been used in previous models. The technique is applied to these processes to find explicit option valuation formulas, and solutions to some previously unsolved problems involving the pricing of securities with payouts and potential bankruptcy.

In this paper we present evidence on the existence of seasonality in monthly rates of return on the New York Stock Exchange from 1904–1974. With the exception of the 1929–1940 period, there are statistically significant differences in mean returns among months due primarily to large January returns. Dispersion measures reveal no consistent seasonal patterns and the characteristic exponent seems invariant among months. We also explore possible implications of the observed seasonality for the capital asset pricing model and other research.

Numerical approximations are presented for the expected utility of wealth over a single time period for a small investor who proportions her or his available capital between a risk-free asset and a risky stock. The stock price is assumed to be a log-stable random variable. The utility functional is logarithmic or isoeleastic (yaq, q extless 0). Analytic results are presented for special choices of model parameters, and for large and small time periods.

The contract price on a forward contract stays fixed for the life of the contract, while a futures contract is rewritten every day. The value of a futures contract is zero at the start of each day. The expected change in the futures price satisfies a formula like the capital asset pricing model. If changes in the futures price are independent of the return on the market, the futures price is the expected spot price. The futures market is not unique in its ability to shift risk, since corporations can do that too. The futures market is unique in the guidance it provides for producers, distributors, and users of commodities. Using assumptions like those used in deriving the original option formula, we find formulas for the values of forward contracts and commodity options in terms of the futures price and other variables.