Several years ago Sharpe suggested a measure for the evaluation of portfolio performance. The measure was conceptually simple, easily calculated, and applicable to an entire investment portfolio, in contrast to the measures of Treynor and Jensen which measure only the undiversifiable risk in a portfolio. Sharpe's measure is still a frequently recommended tool for measuring portfolio performance. The measure is, however, biased. It is the purpose of this note to demonstrate the existence of the bias, indicate its size, and provide a means of correcting it.

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.

Indexes are frequently used for a basis of comparison of the performance of different types of assets, such as mutual funds and common stocks. Sharpe [6] studied the performance of mutual funds over the period 1944 to 1963 and compared their performance to the Dow-Jones Industrial Average (DJIA) using the capital-asset pricing model. For this period he concluded that mutual funds were relatively inferior investments. Joy and Porter [2], using the stochastic dominance approach, reached conclusions similar to those of Sharpe for the 1954–1963 period.

The stated purpose of this review paper by Professors Bierwag, Kaufman, and Khang is (1) to clarify the record on what duration is and is not, and (2) to discuss its usefulness in the analysis of security portfolios. However, the implied, the more important, purpose is to focus the attention of the academic community on a subject that seems to warrant more attention than it has received. Indeed, it seems to me that the whole purpose of this session, which not incidentally is being chaired by coauthor Kaufman, is simply that: to show what can and cannot be done with the concept of duration.

In the applications of mathematical programming to the “pure capital rationing” problem, much of the attention has been focused on the search for an appropriate discount rate to account for the time value of money. The essential difficulty was first observed by Hirshleifer [10] in the classical economics context: “The discount rate to be used for calculating present values…cannot be discovered until the solution is attained, and so is of no assistance in reaching the solution.” Baumol and Quandt [1] showed that this problem persists in the Lorie and Savage [11] and Weingartner [15, Chap. 3] mathematical programming formulation and concluded that: “If there is capital rationing and external rates of interest are irrelevant, we cannot simultaneously insist on a present value formulation of the objective function and have the relevant discount rates determined internally by our program.” They then went on to propose an alternative utility formulation of the objective function.

After Markowitz [14, p. 100] and Sharpe [19, 20] suggested estimating the beta systematic risk coefficient for market assets, finance professors, stock brokers, investment managers, and others began expending large quantities of resources each year on estimating betas. Unfortunately however, it appears that the ordinary least-squares (OLS) regressions used in nearly every instance may be inappropriate. This paper suggests that many stocks' beta coefficients move randomly through time rather than remain stable as the OLS model presumes.

The purpose of this paper is to show that the internal rate of return (IRR) even when unique and real may nevertheless be an incorrect measure of the return on investment, and to prove that all projects characterized by negative flows occurring only at the beginning and end will be mixed investments for which the IRR, whether unique and real or not, is not a correct measure of investment return.

The certainty-equivalent method of evaluating risky investments has been widely discussed in the literature ([2], [5], [14, p. 356], [19], [20]) and consists of applying a multiplicative factor, αt, to each period's expected cash flow, μt, to produce a certainty-equivalent flow, αtμt. The certainty-equivalent flow is then discounted with the riskless rate of interest, αtμt/(l + i)t. Although there has been much discussion of αt, researchers have not derived explicit expressions for αt, relying instead on ad hoc graphs [24, p. 328] or arguments involving mean-variance indifference curves [2] which may not even exist ([4], [12], [22], [23]). In this paper, I will (1) provide a rigorous definition of αt, (2) derive formal expressions for a for αt three special cases, (3) discuss relationships between αt and σt, the standard deviation of the period t cash flow, (4) formally derive the period t risk-adjusted discount rate, kt, from assumptions concerning the decision maker's (d. m.'s) risk preferences and cash flow distribution, and (5) apply the preceding results to a specific problem involving calculation of the risk-adjusted present value of an uncertain cash flow stream.

As part of an overall investigation of risk and capital adequacy in banks, we have examined the magnitudes by which Interest rate movements may alter reported rates of costs and returns for a typical commercial bank. At the same time, we have attempted to measure the manner in which banks adjust their loans and costs over time in reaction to shifting markets and rates.

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.

Short interest is the number of shares of a stock borrowed for sale (and not yet replaced) by investors who anticipate a decline in the stock's price. After its price falls, the stock is purchased to replace the borrowed shares, the selling price being higher than the purchase price whence the profit. The New York and American Stock Exchanges disclose the current outstanding short interest for the market as a whole and for selected stocks around the 15th of each month.

Diversification and capital market theory in conjunction with investors' desire to quantify risk have caused the beta coefficient to receive considerable attention in recent finance literature. Results of empirical investigations of the stationarity of beta over time have been reported by Altman, Jacquillat, and Levasseur [1], Baesel [2], Blume [3], Levitz [5], and Levy [6]. Blume examined the longer-term stability of the beta coefficient, using monthly prices and successive seven-year periods, concluding that portfolio betas are very stable but individual security betas are highly unstable. Levy reported similar conclusions using weekly data and shorter-term estimates of beta; 52-week base periods; and 52-, 26-, and 13-week subsequent periods. Levitz also found portfolio betas to be stable using three-year base periods and one-year subsequent periods.

Since the first owner of a gold depository discovered that profits could be made by lending some of the gold deposited for safekeeping, there has been a concern for the “capital adequacy” of depository institutions. The idea is simple enough. If the value of an institution's assets may decline in the future, its deposits will generally be safer, the larger the current value of assets in relation to the value of deposits. Defining capital as the difference between assets and deposits, the larger the ratio of capital to assets (or the ratio of capital to deposits) the safer the deposits. At some level capital will be “adequate,” i. e., the deposits will be “safe enough.”

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?

Much of the applied work in finance, for instance the literature on capital budgeting, assumes that a firm's management has an accurate estimate of the firm's beta. This estimate is presumably derived by running a regression of the form:

where:

Ri = rate of return on equity for firm i,

Rf = the risk-free rate, and

u = a white noise random variable.

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.

Much of the literature on the adequacy of bank capital is concerned with the role of such factors as default risk and faulty management. These factors are important but they neglect the role that purely stochastic elements can play in affecting the capital of a well-managed bank, even if it is free of default risk. Because banks raise funds by issuing liabilities with different maturities than the assets they acquire, changes in the interest rates paid on these liabilities relative to the interest rates on assets will affect earnings and, hence, bank capital.

This paper is concerned with empirical measurement, analysis, and comparison of the returns expected by investors in U. S., German, French and Japanese equity markets. The expedited return to equity is a pivotal concept in capital market theory because of the concern of this theory with analyzing relationships between expected returns to the general market and expected returns to individual securities. Because the expected equity returns are not directly observable, the approach almost uniformly taken in the empirical testing of capital market theory is to make additional behavioral assumptions beyond those contained in the basic theory that enable it to be translated into an analysis of market relationships among ex-post returns. Empirical tests then become tests of both the basic theory and the appended assumptions. A new approach to the empirical testing of capital market relationships is to develop empirical approximations to the returns expected in the equity market, and to employ these expectational measures to directly test capital market relationships. This paper formulates and examines this approach. Empirical approximations of the expected equity return for a representative group of major international stock exchanges are formulated, estimated, and analyzed, leading to a direct test of the International Asset Pricing model in its original form.