In a recent article appearing in this journal [2] Jonathan Ingersoll developed a normative multidimensional security pricing model for the individual investor in which he corrected errors in an earlier attempt by William Jean [3] [4] [5] at developing such a model. The purpose of this correction is to clarify and correct certain parts of Ingersoll's correction of Jean's work.

This study investigates the liquidity effects of reverse stock splits using bid-ask spread, trading volume, and the number of nontrading days as proxies for the liquidity of the stock. Results indicate a decrease in bid-ask spread and an increase in trading volume after reverse splits. More importantly, the number of nontrading days significantly declines following reverse splits. For the control group, however, no such changes are observed. These results suggest that reverse splits enhance the liquidity of the stock.

Andrew C. Thompson, Valuation of Path-Dependent Contingent Claims with Multiple Exercise Decisions over Time: The Case of Take-Or-Pay, The Journal of Financial and Quantitative Analysis, Vol. 30, No. 2 (Jun., 1995), pp. 271-293

This paper provides a closed form solution for the value of a multiple claim insurance contract that is subject to a deductible amount and/or an upper limit on claims. The solution is a time integral of European option prices. The model provides three important insights. First, systematic risk in insurance policies is altered in the presence of deductibles and maximum indemnity levels. Second, idiosyncratic risk affects policy valuation and the required rates of return on underwriting portfolios. Finally, contrary to traditional actuarial intuition, changes in the risk-free interest rate may either increase or reduce policy values.

An analysis of the dual problem described by Ronn (1987) reveals that it provides a powerful and easily interpretable test for the hypothesis of a single class of marginal investors, including models of equilibrium based on a “representative tax bracket.” When Ronn's empirical tests are interpreted via the dual, they lend additional support to his conclusions in providing a strong rejection of the representative tax bracket hypothesis. A valid dual LP used to test the hypothesis can be obtained with fewer assumptions than Ronn's primal; in addition, a minor error in Ronn's presentation of the dual is corrected.

The primary objective of this paper is to derive a multi-factor equilibrium model using a mean-variance approach. The results of this derivation provide greater insight into the nature of the resulting factors than does APT. There are several important implications for empirical tests of any a priori defined multi-factor model.

The advance of the theory of contingent claim pricing has made it possible to model and analyze very complex financial claims. When the value of the firm can be represented as a contingent claim, then the firm's optimal financial policy can be determined with only a slight modification in standard solution techniques for contingent claims. In this paper, stochastic control theory is used to determine a dynamic investment policy for the valuemaximizing firm. The value of future, stochastic economic rents (i.e., the net present value of the firm), and the firm's optimal investment policy must reflect a rational reaction on behalf of its competitors. A computationally efficient methodology is presented for solving the simultaneous investment-valuation problem for an n-firm game.

Edward C. Blomeyer, An Analytic Approximation for the American Put Price for Options on Stocks with Dividends, The Journal of Financial and Quantitative Analysis, Vol. 21, No. 2 (Jun., 1986), pp. 229-233

Changes in the Japanese financial system over the coming decade will play a significant role in the functioning of U.S. financial markets and, indeed, of the entire U.S. economy. From World War II through at least the mid–1970s, the United States was a major exporter of investment capital in the form of foreign direct and portfolio investment. More recently, low U.S. savings rates, recurring federal budget deficits, reduced sovereign lending by U.S. banks, and, possibly, high real returns on domestic investment have combined to make the United States a major importer of capital. At the same time, large trade surpluses and very high savings rates in Japan have more than offset increases in government borrowing to make Japan the world's principal capital exporter, a position it is likely to hold for some time. These are fundamental changes.

This paper demonstrates the strong linkages that exist between currency risk, represented by inflation risk and exchange rate changes, and relative price risk. These linkages affect the optional quantities of forward exchange contracts, nominal debt, and fixed price sales (purchase) contracts to use in hedging against these risks. It is shown that the existence of as many hedging mechanisms as there are forms of price risk allows for the precise targeting of specific price risks with specific hedging instruments. Moreover, even though each hedging mechanism specializes in protecting against a particular form of price risk, the optimal quantitiy of each influences and is influenced by the optimal quantities of the others.