Much effort has been recently devoted to investigating and expounding the properties of the measure called “duration.” Two properties claimed for duration are (1) that it is a good indicator of the average life of a payments stream and (2) that it measures the elasticity of the present value of such a stream with respect to the discount rate. Unfortunately the theoretical justifications of the second, more important, property have been based upon the analysis of either a change in a discount rate constant for all future time periods, or, more generally, a parallel shift in the term structure of interest rates.

This paper applies the technique for valuing compound options to the risky coupon, bond problem. A formula is derived which contains n-dimensional multivariate normal intecjrals. It is shown that, for some compound option problems, the special correlation structure allows an application of an integral reduction which may simplify the numerical evaluation. The effects of various indenture restrictions on the formula are discussed, and a new formula for evaluating subordinated debt is presented.

The net monetary position of a firm, defined as the nominal value of its monetary assets minus the nominal value of its monetary liabilities, partly determines the wealth transferred to (or from) the firm's owners when unanticipated price level change occurs. Price level change (a random variable) is defined as unanticipated when assessments of (the moments of) its probability distribution are systematically incorrect or biased. During unanticipated inflation, which conventionally means an underestimate of the expected value of the distribution of price level change, the real dollar returns of net monetary debtor firms are enhanced—the unforeseen honoring of debt contracts in dollars of lower purchasing power is a wealth transfer to the firm's owners from the firm's creditors. Conversely, real returns of net monetary creditor firms suffer during unanticipated inflation and gain during unanticipated deflation.

The inception of modern portfolio theory dates from Markowitz's pioneering article [7] and subsequent book [8]. Yet despite the early development of a full theory of portfolio management, this theory has rarely been implemented. One problem arises from the difficulty in generating inputs to the general portfolio model. Index models and simple structures for correlation relationships, which go a long way towards solving this problem, have been developed. Yet the time and cost of solving actual portfolio problems (involving the solution of a quadratic programming problem) and more importantly the difficulty of educating portfolio managers to relate to risk return trade-offs in terms of covariances has virtually brought the application of portfolio theory to a halt.

An important maintained hypothesis in financial economics states that the average interest rate on a firm's debt is positively related to its leverage. This hypothesis has a long history going back at least to the work of Kalecki [4] where it was used to derive a determinate size for the competitive firm when the production function is homogeneous of degree one. The upward sloping interest rate-leverage relationship has also played an important role in the theory of finance. In this connection, it is somewhat interesting to find both Modigliani-Miller [5] and their many critics in complete agreement on the nature of this relationship. In particular, their statement on this subject conveys the impression that this relationship is governed by an unalterable law when they write: “Economic theory and market experience both suggest that the yields demanded by lenders tend to increase with the debt-equity ratio of the borrowing firm” [5, p. 273].

Corporate taxes and default risk are relevant to an understanding of the effect of financial leverage on the total market value of the firm. Recently, Kraus and Litzenberger [6] have examined the implications of taxes and default risk for capital structure decisions in a state preference valuation model. A parameter preference model as distinct from a state preference model may be applied to continuous probability distributions. As the most familiar parameter preference approach, the capital asset pricing model is an obvious alternative approach to incorporate the effects of leverage in a world of taxes and default risks. Given the analysis by Hamada [4] of the effects of taxes in absence of default risk and by Stiglitz [16] of the effects of default risk in absence of corporate taxes, such an exercise would superficially appear to be a trivial extension of their studies. However, this paper presents a “reduction ad absurdum” argument that, in an economy where corporate interest charges are tax deductible and firms issue risky debt, the total market value of a levered firm using the capital asset pricing model is misspecified.

Looking back over the last two decades, financial economists can find considerable cause for pride and self-congratulation in the development of their discipline. From the earliest steps toward a rigorous theory of capital budgeting, through the Modigliani-Miller theorems on corporate financing and cost of capital, to the development of the capital asset pricing theory, the field of finance has garnered a well-deserved reputation for rigor, analytic sophistication, and pace of intellectual growth.

A set of theorems was derived based on the following set of axioms: (1) financial management seeks to maximize the wealth of existing shareholders; (2) all projects being considered at period 0 are of one period duration and possess the attribute that their adoption or rejection by the firm will not affect the business risk of the firm's asset portfolio; and (3) the ratio of debt to total book capital is given as α, and r and k reflect the firm's business and financial risk however perceived by investors.

It was shown that the NPV of any project satisfying the above conditions could be evaluated for accept-reject purposes with a CC involving book weights. This CC yielded an NPV numerically equal to the NPV using market value weights under special circumstances, namely, when k = r (1 − λ) or when M0/V0 = 1 − α, a special case of which is M0 = (1 −α)c0, i.e., if the firm were at its investment margin. After determining the book value CC, which is denoted as β, it was shown that it can be applied repeatedly for testing period 0 projects satisfying our axioms, even if these projects are unknown to management at the outset of the period. A market value CC, denoted as γ, was derived which gives identical accept-reject signals as the procedure.

The asset and liability portfolios of financial institutions generate patterns of future cash flows that must conform to many restrictions in order to assure solvency and profitability. Many institutions, including insurance companies and pension funds, have definite and certain future commitments of funds. These institutions may wish to invest funds now so that their cash inflows (investment with accumulated earnings) will match their future commitments. In principle, the simplest way to meet future commitments exactly is to purchase single payment notes (or zero coupon bonds) which mature on the commitment dates. For long-term commitments, such instruments are not readily obtainable, at least in the United States. Most available bonds promise coupon payments over time so that these payments would have to be reinvested at unknown future interest rates in order to realize an accumulated sum at any future date when a commitment must be discharged. Since future interest rates are unknown at the initial moment of investment, it is not certain what accumulated earnings will be at future dates. In the absence of default, the risk of not meeting future commitments may be minimized by adopting investment strategies based on the concept of duration. Duration is a measure of the average maturity of an income stream; it is a weighted average of the dates at which the income payments are received, where the weights add to unity and are related to the present value of the income stream. Dating from the initial work of Macaulay [9] and Hicks [6], duration has been shown to be important in constructing portfolios that are hedged or ‘immunized’ from the possible ravages of interest rate uncertainty.

In derivations of the mean-variance model of portfolio selection, authors from Markowitz [6 and 7] and Tobin [11] to Merton [8] and Black [1] rely on the inverse of the matrix of variances and covariances for the returns on risky securities. Unfortunately, as is shown in this paper, such an inverse does not exist when risk-free combinations can be formed from the risky securities. Accordingly, the general validity of the mean-variance model is challenged by the existence of opportunities for hedging, including those fostered by short sales and the rapidly expanding markets for warrants, options, and futures. Fortunately, the mean-variance model is tractable even when the conventional methods for deriving it fail. Alternative solution procedures presented in this paper are valid with or without riskless securities and with either singular or nonsingular variance-covariance matrices. The important properties of the mean-variance model are shown to extend for the previously omitted cases. In particular, the frontier of mean-variance combinations is always well-defined, is always strictly convex, and (the efficient portion of the frontier) is always positively sloped. In addition, the frontier of mean-variance combinations always can be expressed in terms of a pair of mutual funds which are determined on purely technical grounds.

Since its inception the single-index market model has been the subject of a large body of theoretical and empirical research. This study deals with the very difficult issue surrounding the practical implementation of the model in portfolio analysis where significant, nonmarket sources of covariation in security returns are believed to be present.

Consider a productive investment project (or financial security), which would yield a stream of cash flows, positive and negative, over time. A major index of the acceptability of such a project is its internal rate of return, i.e., that rate of interest which discounts all the cash flows from the project to a present worth of zero. Soper [8] has developed a sufficient condition for the internal rate to be unique in the interval, (−1,∞), along the real line. Then, if the project requires an initial outlay, if Soper's condition holds, and if the unique internal rate exceeds the market rate of interest in each period of the project's life, the project's present worth is positive, and hence, other things being equal, it is worth undertaking.

The empirical distributions of price changes for speculative assets (e.g., common stocks, bonds, etc.) measured over calendar time yield a higher frequency of observations near the mean and at the tails than would be expected for a normal distribution. The sample kurtosis is almost always greater than 3—the value expected for a normal distribution—and the distributions are commonly characterized as fat-tailed and peaked (i.e., leptokurtic).

In a world where individuals are assumed to receive new information about an asset in random and sequential order, the volume of trading for a given message is a random variable. If the probabilities of trading events can be specified, it is possible to develop closed form expressions for the expected number of trades and the variance of trading. The result is a theory of trading which relates the number of trades to the characteristics of the message and to the number of participants in the market for an asset.

The purpose of this paper has been to empirically test Stone's Two-Index Model. The results are mixed, but generally favor the model. Adding a bond index term for the bank sample only marginally improves the model's explanatory power although the index is more important than the equity index. The lack of importance of the bond index for banks is not surprising upon further consideration, however. Banks and their earnings should be more sensitive to short-term rather than long-term rates, and the index reflects primarily long-term rates. To the extent that short- and long-term rates moved in different directions during the sample period, negative correlation is introduced between bank's returns and the index.

The bond index improves in performance for the 30 Dow Jones firms and contributes to the explanatory power of the model in 80 percent of the cases. There is some instability in signs and, contrary to Stone's speculations, omission of the bond index does not bias the equity beta estimates.

Finally, we caution the reader against generalizing about the long-run value of the two-index model. The short time period used here does not allow us to say anything about the relationship between interest rate movements and the stability of beta. Moreover, during the 1969–1972 period the returns on the bond and equity indexes did not behave as Capital Market Theory would predict. The average monthly return on the bond portfolio was .5 percent and the average return on the equity portfolio was .2 percent. Our findings must, therefore, be interpreted with care, but overall the introduction of interest rate effects into the single-index model looks promising.

In recent financial literature a large volume of the articles dealt with asset leasing. This author and his colleagues [6] and others [7] developed the conditions under which asset leasing cannot increase the overall firm's value over normal debt leverage. Many others [2, 3, 11] analyzed the “lease-buy” decision using a variety of models and assumptions. None, however, considered the effect of asset leasing on the firm's capitalization rate. While asset leasing per se would not affect the firm's unlevered cost of capital, it should affect its estimation. This paper developed the adjustment factor to obtain the firm's corresponding unlevered cost of capital with leasing leverage. Basically, Modigliani and Miller's methodology [9] was adjusted for the different tax situation with asset leasing. The effective benefit of leasing on the firm's average cost of funds was shown to be not nearly as effective as an equivalent amount of ordinary debt.

This paper is an analytic treatment of the abandonment decision in capital investment analysis. It provides a methodology which has application in obtaining better estimates for project value and risk.

A common dilemma faced by investors and portfolio managers is the tradeoff preference between risk and return. The general consensus and convention in finance and economics is that, in the aggregate, investors do not seek risk for its own sake. If so, it is reasonable to assume that returns on individual common stocks vary according to their risk. However, it is not the purpose of this paper to examine the ex post risk and return experience of various financial assets. This and related work have been treated by Sharpe [22] and by others. While some of these are studies of individual common stocks, the majority involves the ex post risk-return relationships of portfolios managed by institutional or professional investors. Although the conclusions are not totally consistent concerning the shape of the risk-return function, there is agreement that a generally positive relationship exists between risk and expected return. To date, little empiricism has been directed specifically to the ex ante risk-return preferences of individual common-stock investors. This paper takes a step in this direction by analyzing the ex ante risk-return preferences and expectations of individual common-stock investors. The purpose is two-fold: (1) to provide positive (as opposed to normative) evidence on the nature of the relationship between acceptable risk levels and expected annual rates of return; and (2) to examine the nature of this relationship between risk and the components of total return, income from dividends and capital appreciation.

We have formulated the mean-variance models of portfolio selection with stochastic cash demand. The results of the general model have indicated that the characteristic of the investor's stochastic cash demand, the liquidity risks of assets (measured by the covariance between an asset's return and the cash demand), and the structure of transfer costs also play important roles in the determination of the investor's optimal portfolio. We have also shown that the model of portfolio selection with stochastic cash demand can be greatly simplified if the assumption of symmetric transfer costs is invoked. Furthermore, it has been shown that the simplified model can be reformulated and solved by the LP techniques. Thus, LP formulation of portfolio selection with stochastic cash demand should have practical usefulness.

Finally, along the line of works by Chen, Jen and Zionts [3, 4], Pogue [14, 15] and Stone and Reback [20], one can extend the analysis in this paper to the problem of dynamic portfolio management with stochastic cash demand and transfer costs.

In recent years a substantial number of empirical studies have been conducted concerning aggregate commercial bank behavior [2, 8, 11, 14, 15, 17, 18]. Although the scope of these studies has varied widely, none has included an adequate treatment of the relationship between commercial bank liability management and earning asset adjustments. The importance of the relationship between liability management and commercial bank asset behavior has been alluded to in the literature [3, 5, 6, 13, 18]; but there has been very little empirical investigation of the subject. Moreover, little is known about which assets and liabilities are primarily involved. By increasing or decreasing earning assets, the commercial banking system can create or eliminate deposits, thus affecting the supply of both money and bank credit. Since liability management and asset behavior are very closely related, it seems that an adequate understanding of this relationship is essential to understanding the money supply process.