In a recent article in this journal [6], Clement G. Krouse and Wayne Y. Lee (hereafter K-L) presented a model of optimal equity financing of a corporation based on Pontryagin's maximum principle. In this note the basic assumption of a constant internal rate of return of the K-L model is relaxed. As a result, the financial implications of the K-L results remain essentially unchanged, but their applicability is extended considerably, and some undesirable solution characteristics are eliminated.

Three important methods exist for the treatment of risk in capital budgeting problems: the certainty equivalent method (CE), the risk-adjusted discount method (RAD), and the probability distribution or Hillier-Hertz approach (PD, based on [4]). Each one of these methods evaluates the multiperiod stream of risky returns generated by an investment for given distributions of the returns in each period. A common assumption for all three methods is the certainty of the occurrence of a given risky cash inflow (defined by its distribution) in a given time period. This assumption is probably derived from accounting practices. In references [8] and [9] the PD approach was generalized by removing the certain timing assumption. This paper examines the implications of random timing of cash returns within the framework of the better known CE method.

Le texte intégral de ce document de travail n'est pas disponible en ligne. Une copie papier est disponible à l'Annexe de la bibliothéque. Effectuez une recherche par titre dans le catalogue pour réserver le document. // The full text of this working paper is not available online. A print copy is available in the Library Annex. Search by title in the catalogue to request the paper.

Le texte intégral de ce document de travail n'est pas disponible en ligne. Une copie papier est disponible à l'Annexe de la bibliothéque. Effectuez une recherche par titre dans le catalogue pour réserver le document. // The full text of this working paper is not available online. A print copy is available in the Library Annex. Search by title in the catalogue to request the paper.

Abstract We derive equilibrium restrictions on the range of the transaction prices of American options on the stock market index and index futures. Trading over the lifetime of the options is accounted for, in contrast to earlier single-period results. The bounds on the reservation purchase price of American puts and the reservation write price of American calls are tight. We allow the market to be incomplete and imperfect due to the presence of proportional transaction costs in trading the underlying security and due to bid-ask spreads in option prices. The bounds may be derived for any given probability distribution of the return of the underlying security and admit price jumps and stochastic volatility. We assume that at least some of the traders maximize a time- separable utility function. The bounds are derived by applying the weak notion of stochastic dominance and are independent of a trader's particular utility function and initial portfolio position.

In a series of recent articles ([2], [3], [4], [5]) R. B. Porter and his associates have conducted empirical comparisons of the Mean-Variance (EV) and Stochastic Dominance portfolio choice criteria. The basic methodology of all these studies was first to compute the set of EV-efficient portfolios by an optimizing algorithm, then to find through heuristic methods “stochastically dominant” portfolios, and finally to compare the two. A major finding of these studies was that most EV-efficient portfolios survived the second-degree stochastic dominance (SSD) test against the randomly generated portfolios. The purpose of this note is to show that, for all cases of practical interest, a portion of the EV frontier is a subset of the SSD-efficient set. In other words, we offer here an exact theoretical justification of some empirical results of the aforementioned studies.

This paper examines the decision to enter into a sector dominated by a monopoly if demand is random at entry time. Given a two-period world, the monopolist enters initially and enjoys an uncontested monopoly for one period, while the entrant may enter and compete during the second period. Demand is random one period earlier and independently distributed in both periods and entry corresponds to an irreversible capacity choice, made under certain demand. All other production decisions take place after demand has been revealed. Risk-neutrality is assumed on both sides. If entry occurs then there is a Cournot duopoly in the second period. It is shown that concurrently with this Cournot production game, there is a separate Stackelberg-type game with capacities as decision variables. Entry-deterrence conditions are derived under general demand and cost assumptions. It is shown that demand uncertainty changes several of the results of similar certain demand models.

[Widespread violations of stochastic dominance by 1-month S&P 500 index call options over 1986-2006 imply that a trader can improve expected utility by engaging in a zero-net-cost trade net of transaction costs and bid-ask spread. Although precrash option prices conform to the Black-Scholes-Merton model reasonably well, they are incorrectly priced if the distribution of the index return is estimated from time-series data. Substantial violations by postcrash OTM calls contradict the notion that the problem lies primarily with the left-hand tail of the index return distribution and that the smile is too steep. The decrease in violations over the postcrash period of 1988-1995 is followed by a substantial increase over 1997-2006, which may be due to the lower quality of the data but, in any case, does not provide evidence that the options market is becoming more rational over time.]