Numerous studies have already examined the investment performance of mutual fund management with data from the 1950s and 1960s. Although the previous studies differed in the time period and evaluation method, they generally agreed that mutual funds, on the average, had failed to outperform the market over time. Thus they rendered a strong support to the efficient market hypothesis. Yet there is a need for an investigation of the data of the past several years. This study evaluates the quarterly investment performance of mutual funds in the period 1969–1975, using the weighted index benchmark portfolio approach.

An important aggregation problem is the derivation of equilibrium security prices which are independent of the allocation of initial wealth among investors. The problem is of interest because, if investors are conceived as being endowed with initial holdings of securities, it is clear that the initial wealth allocation which depends on security prices is endogenous to the model. Although he addresses a differently defined objective, Rubinstein [8] has shown that sufficient conditions for the solution of the problem described above are conditions that permit construction of “composite” (representative) investors whose resources, beliefs, and tastes depend on the exogenous specifications of the economy (viz., the beliefs and tastes of all investors and production conditions) but not on the initial allocation of securities.

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.

Ever since Markowitz introduced the concept of portfolio theory in 1952, one of the questions predominant in the minds of financial theorists has been the constituency of the investor's optimal asset portfolio. Research into this area, which became known as capital market theory, attempted to analyze the equilibrium relationships between assets. One of the products of this research was the widely accepted Capital Asset Pricing Model (CAPM) of Sharpe and Lintner.

Since the seminal article by Black and Scholes on the pricing of corporate liabilities, the importance in finance of contingent claims has become widely recognized. The key to the valuation of such claims has been found to lie in the solution to certain partial differential equations. The best known of these was derived by Black and Scholes, in their original article, from the assumption that the value of the asset underlying the contingent claim follows a geometric Brownian motion.

The finance literature has devoted considerable attention to the study of yields, yield spreads, and rating classification for fixed income securities. In the corporate market, authors such as Hickman [6], Johnson [7], Sloane [9], and Van Home [12] have investigated the behavior of yields and yield spreads over time. Johnson found that the yield differential, defined as the corporate yield minus the equal maturity Treasury rate, was unrelated to maturity. Van Home found that this differential widened during recessionary periods; he interpreted this to reflect either a higher default probability or greater investor risk aversion. In his important paper published in 1959, Lawrence Fisher [4] employed cross-sectional data at five points in time to relate corporate yield spreads to four key variables which serve as proxies for default and marketability risks. Pogue and Soldofsky [8] extended Fisher's approach to explain not corporate bond yield spreads but rather bond ratings. As explanatory variables, Pogue and Soldofsky chose several measures of the firm's income and debt capacity.

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.

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.

In recent years, a number of studies have been published evaluating alternative bond portfolio strategies. These studies basically simulate risk-return characteristics for a variety of strategies designed for use by financial institutions. Typical strategies considered include portfolios of bonds that have laddered or barbell (dumbbell) maturity structures. In laddered strategies, bonds are spaced evenly among a number of consecutive maturities, while in barbell strategies, bonds are concentrated in short and long maturities. The results of these studies tend to differ and conflict. For example, in a recent article in this journal, Fogler, Groves, and Richardson (FGR) conclude that “dumbbell portfolio strategies are not as efficient as indicated by previous analyses.” Among the previous studies to which they refer is one by Watson, who concluded that “portfolios split between a spaced group of short maturity bonds and a longer investment security” (barbell portfolios) are most efficient. Similar results are reported by Wolf and by Bradley and Crane.

The commercial banking industry has been buffeted by a variety of forces in recent years. Alternating periods of intense monetary restraint and the severity of the 1973–74 economic contraction (especially as it affected the real estate industry), huge losses on loan portfolios, a heavy commitment of funds to less developed countries on the part of a few major banks, and the failures of a number of individual banks have created considerable discussion about the stability of the banking system. Questions have been raised about the risk involved in committing funds to the securities of banking organizations. Moreover, the importance of these questions has been underscored for bank management by the necessity for many banking organizations to raise substantial amounts of external funds to prevent further depletion of existing capital ratios.

Many writers believe that minority-owned financial institutions can and should play an important role in aiding the economic development of minority communities. Indeed, economic theory describes a major role of financial institutions as gathering many relatively small deposits of households and other economic units, and combining these to support capital formation through lending for business and housing capital investment. The service which minority financial institutions can play may be magnified by the much-discussed inability of minority communities to obtain financing from nonminority financial institutions for business capital investment and–of more recent concern–for housing capital investment. The concept of pooling the savings of ghetto residents and putting the savings to work in financing the development of the inner city community may be sound in theory, but what does the empirical evidence indicate about its practical implementation?

In an earlier note in this Journal Strangways and Yandle (S-Y) [2] reported the results of a series of statistical tests on the effects of state usury laws on housing starts in 1966. Using cross sectional analysis, they focused on both the absolute level of single family housing starts in 1966 and the change in housing starts from 1965 to 1966.

It is widely accepted that percentage price changes in lower coupon (“deep discount”) bonds will exceed those of issues with higher coupons [see, e. g., 8 and 9 ]. Cramer and Hawk's recent article in this journal [5], in fact, utilized this assumption although no exact empirical verification was sought. In an efficient market, the existence of such capital gains opportunities would be expected to attract investors and thereby reduce any risk-adjusted advantage to these bonds. Indeed, Conard and Frankena found that exactly this riskadjustment phenomenon seems to occur [4, pp. 162–163]. Thus, the purpose of this note is to address the question: Have the deepest discount bonds actually provided the greatest capital gains opportunities during periods of falling interest rates? In doing so, the paper does not question the validity of the mathematical “linkage” between price and coupon; rather, it seeks to determine if market structure (e. g., investor preferences) leads to a breakdown in the assumed (traditional) price volatility-coupon level relationship.

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 a recent paper published in this journal [1], Bierman and Hass (BH) developed a model in which the risk differential that an investor would require to compensate him for the risk of default is stated as a function of the following variables: the probability of default on annual interest payments, (1-P1); the probability of default on the principal payment at the end of the maturity of the bond, (1-P2); the default-free rate, i, and the maturity, N.

In a recent issue of JFQA, Aucamp and Eckardt [1] (henceforth referred to as AE), developed a new sufficient condition for the existence of a unique (and simple) nonnegative internal rate of return (IRR), which includes the one previously formulated by Norstrøm [8] as a particular case. As pointed out by the former authors, their new procedure is appealing since it is easier to apply than the rather involved Sturm-Kaplan [6] method, while being a refinement of Norstrøm's result.

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.