Formal models for portfolio analysis, such as Markowitz [13], are frequently based upon mean-variance analyses and involve the estimation of a mean vector and a variance-covariance matrix describing expected returns and variability of returns for all securities under consideration. These parameter estimates play a major role in the selection of a single, optimal portfolio. Kalymon [9] and Barry [1] have considered the effects of parameter uncertainty upon individual investors' inferences and decisions in the context of portfolio selection, and Barry and Winkler [2] have similarly considered the impact of nonstationary means upon portfolio selection decisions by individual investors.

Krouse and Lee [5] have formulated an optimal financing problem of a firm in the dynamic setting of optimal control theory. Specifically, the problem is to find a financing mix of retained earnings and external equity over time in a way that maximizes the present value of the entire future dividends stream accruing to the firm's initial stockholders subject to a given maximum allowable growth rate for the firm.

In a recent article, Modigliani and Pogue [2] raised the issue of “leverage bias” in portfolio performance measures. Specifically, they contended that the value of the Jensen's alpha (α) could be affected by borrowing or lending at the risk-free rate, while the Treynor index (TI) does not suffer from this shortcoming. They illustrated this effect through the use of a graphical example similar to the one in Exhibit I where A and B are two unlevered portfolios with the same α's but different TI's. Modigliani and Pogue argued that by leveraging, i.e., borrowing at Rf, the portfolio with the greater slope (TI), A, could attain a levered portfolio AL which clearly dominates portfolio B. In other L words, the line with the higher TI will dominate the line with a lower TI regardless of α values. This seems to imply that, in general, TI is a better measure of ex post portfolio performance, and that ranking based on TI's is consistent and invariant to the leverage effect, while ranking based on a's is not.

In [2], I gave a solution of an extended cash balance problem which disallows overdrafts and shortselling. This solution is incorrect. To show this, we produce a counterexample constructed by Carl Norstrøm. In the notation of the note [2], let x0 = 0, y0 = 3, d(t) = 0, α = 0, T = 10, M1 = M2 = ∞

and r2 (t) = .1. Applying the procedure in [2] to this problem, we obtain the policy of impulse-selling all the securities at t = 0. On the other hand, it is obvious by inspection that the optimal policy is to keep the securities until t = 5, at which time, turn them into cash by an impulse-sale. We note, in passing, that the solution by inspection in this case is possible because there is no bounds on the control variable.

One of the innovative and successful new markets developed in recent years has been the registered exchange for the trading of option contracts. Key innovations provided by the option exchanges include the standardization of some contractual terms and the creation of a central clearing corporation to serve as issuer and obligor of each option contract, thus severing the contractual link between a specific option writer and buyer. These changes have facilitated the trading of existing call options in the secondary market and have provided increased liquidity, continuous public reporting of prices, better information on trading volume and open positions, and reduced transaction costs.

Jay Gould's image is stamped heavily upon the picture historians have drawn of the “Gilded Age” of American economic development. Our lack of knowledge of the man, and our meager efforts to understand him, account in large measure for the fatuous traditional interpretation of the era. Professor Klein explains how the work of recent historians has made the hackneyed view of both the man and his age obsolete. He reviews the constructive role that Gould played in the rise of modern America, and offers an explanation of why the man was singled out for extraordinary condemnation in his own time.