Knowledge that Transforms

In the world of practical finance, the management of working capital—cash, marketable securities, receivables, and inventories is, perhaps, the most pressing and most frequently encountered problem for financial managers. Yet, in the realm of theoretical finance, and even at the level of “textbook” finance, working capital is given minimal attention.

The original Black-Scholes (BS) [2] European call option pricing model does not take account of divided payments on the underlying stock and does not allow for the possibility of early exercise that may be optimal when the stock pays dividends. Black [1] has suggested that the original BS model can be modified to take account of dividends and Sharpe [14] predicts that this modified or pseudo-American BS approach, “while not exact, is probably sufficient for many listed options.”

The question of whether security return distributions have a finite or an infinite variance has been debated for many years. The possibility that the security return-generating process actually has an infinite variance is particularly vexing since it implies that all statistical techniques and theoretical frameworks utilizing the second (or higher) moment are invalid. While this is clearly not a disaster—alternatives do exist—much of the work which has been done in the field of finance has assumed the existence of the second moment. It is, therefore, important to determine whether or not the security return distribution actually has a finite variance.

Numerous studies in recent years have emphasized the importance of accounting properly for abandoment value in capital budgeting (see [1], [4], [7], [10], and [11]). For a variety of reasons, a project need be neither physically exhausted nor have negative cash flows to be abandoned. Robichek and Van Home [10] suggested that a project should be abandoned in any period in which the present value of future cash flows does not exceed its abandonment value. In a modification of this rule, Dyl and Long [4] proposed that the firm give consideration to all possible future abandonment opportunities. They argued that abandonment need not occur at the earliest possible date that the abandonment condition is satisfied, but rather at the date that yields the highest NPV over all future abandonment possibilities. A generalization of these models was offered by Bonini [1], who developed a dynamic programming model to analyze investment projects with abandonment possibilities and uncertain cash flows. More recently, Gaumnitz and Emery [7] compared the abandonment decision to the like-for-like replacement decision and noted that the correct model for a particular case depends on the suitability of the assumptions.

A number of recent papers have shown that it is possible for an investor to immunize a portfolio of default and option-free coupon bonds so that the return realized over a given planning period will never be less than that promised at the time the bonds were purchased. In this way, a future fixed dollar liability may be discharged with certainty by acquiring an asset portfolio with a market value equal to the present value of the liability and setting its appropriate duration equal to the time remaining to the date of discharge. However, most investors have more than one liability to discharge. In his seminal article in 1952, F. M. Redington showed that a stream of liabilities may be immunized if an asset portfolio having the same present value as the liabilities is selected so that:1. its duration is equal to the duration of the liabilities; and2. “the spread of the value of asset-proceeds about the mean term (duration) should be greater than the spread of the value of the liability” ([16], p. 191).

Financial analysts have been intrigued by bond ratings since John Moody first started publishing them in 1909. Bond ratings are assigned by three agencies (Moody's, Standard and Poor's (S&P), and Fitch); these ratings are widely publicized and are, therefore, critically important. A bond's rating affects investors' purchase decisions and, consequently, the issuing firm's cost of debt and, indirectly, its cost of equity.

John D. Martin, J. William Petty, An Analysis of the Performance of Publicly Traded Venture Capital Companies, The Journal of Financial and Quantitative Analysis, Vol. 18, No. 3 (Sep., 1983), pp. 401-410

This paper provides a closed-form, preference-free means of valuing a European call option written on a default-free pure discount bond. Investors may not agree upon a theory of the term structure, but they will necessarily agree on equilibrium option values. Further, these equilibrium option values may be obtained without recourse to numerical approximation.Default-free pure discount bond prices were posited to follow a non-standardized transformed Brownian bridge process. This specification implicitly incorporates the terminal constraint that the price of a default-free pure discount bond equal its face value at maturity.Contingent claim valuation necessarily involves consideration of terminal constraints on the value of financial securities. The Brownian bridge specification permits an appropriate means of incorporating a number of such constraints. Therefore, while this paper has considered only the application of the Brownian bridge process to the valuation of debt options, the introduction of this process may provide for many further financial applications.

In 1959, Henry Lataná [2] proposed an approximation to the geometric mean that was a simple function of the arithmetic mean and variance, thereby indicating a mathematical relationship between the risky investment choice model of Bernoulli and the Markowitz mean-variance model. In 1969, Young and Trent [4] presented empirical test results of the Latané approximation, as well as a set of other approximations to the geometric mean based on moments, and concluded that the Latane formula yielded a quite accurate approximation to the geometric mean. In Jean's 1980 paper [1] relating the geometric mean model to stochastic dominance models, the infinite series representation of the geometric mean used suggests a more accurate approximation with moments of the geometric mean than that contained in the earlier papers may be possible. Various forms of that series expressed in alternate-origin moments are tested empirically below, and the results confirm that this later series does yield the greatest accuracy of the three approaches.

J. D. Jobson, Bob Korkie, Statistical Inference in Two-Parameter Portfolio Theory with Multiple Regression Software, The Journal of Financial and Quantitative Analysis, Vol. 18, No. 2 (Jun., 1983), pp. 189-197