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.

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.

In [1, p. 999] I wrongly stated that “the solution locus generated by the chance-constrained problem is efficient (for the class of utility function implied by the expected wealth-probability of ruin criterion) if the assets follow a multinomial distribution with means above the survival level.” In support of this statement footnote 6 of [1] attempted to establish the quasiconcavity of the expected utility function

in the (μ, σ) plane, where F is the normal distribution, z = (s-μ)/σ < 0, s is the survival level, μ is the mean of the portfolio, σ is the standard deviation, and c is a positive constant. The condition

was claimed to hold for any two assets (μ1., σ1) and (μ2., σ2) on any given indifference curve of (1), where zi. = (s-μi.)/σi., i = 1,2, and zγ = (s−μγ)/σγ corresponds to the convex combination μγ = γμ1 + (1−γ) μ2, σγ = γσ1+ (1−γ) σ2, in the (μ, σ) plane. (Note that this is not the same as asserting that F(z) is a convex function of μ and σ, which it is not as an examination of its Hessian determinant would readily show.)

For decision makers, we emphasize that it is feasible to consider multiple subjective criteria in a capital budgeting problem. The applicability of the procedures outlined is enhanced by the limited data base necessary to obtain subjective rankings, remembering that here we are only concerned with side criteria.

In this paper, we have formulated the capital investment problem in a graph theoretic framework. We characterized the problem as being composed of a set of finite alternatives, a set of subjective criteria, and a set of resource constraints. This formulation leads to an integer programming problem in which the rankings of sets of alternatives on the multiple subjective criteria are aggregated into a single index. It is stressed that we used a single budgetary constraint in the example but that the procedure can accommodate additional constraints. We also assumed that management has specific side criteria and that it is possible for the decision makers to rank all alternatives for each of those criteria.

The application of the above procedure to any problem involves three steps:

1) From the decision maker, or groups of decision makers,

the agreement matrix π is developed. This involves:

a) defining the alternatives,

b) defining the side criteria,

c) asking management to rank each alternative under each criterion, and

d) if appropriate, asking management to weigh the relative importance of each of the side criteria.

2) From the technical considerations of the problem, determine the resource constraints. In our example, this included the investment requirements of each alternative and the total resources available.

3) Solve the problem as posed above as a group of m integer programming problems.

Studies of returns on common stocks have observed positive market index autocorrelation (see Fisher [10] and Dimson [6]), negative autocorrelation of market model residuals (see Fisher [10] and Fama, Fisher, Jensen, and Roll [9]), and a deterioration in the market model R2 as the returns measurement period is shortened (see Pogue and Solnik [17], Altman, Jacquillat, and Levasseur [1], and Schwartz and Whitcomb [19]). We present further evidence on the strength of these findings and show that they are concurrent events. That is, common factors can explain both positive index and negative residual autocorrelation, and these correlation patterns in turn cause R2 to fall as the differencing interval is shortened.

Since we now have a data base approaching five years of more or less fluctuating exchange rates, there undoubtedly are numerous empirical studies under way comparing the movements of exchange rates with each other and with all sorts of other economic variables. A rather subtle problem with such activities is that the analysis is sensitive to which currency of an exchange rate one chooses to make the numeraire. Specifically, a time series of, say, dollars per pound sterling is not the same thing mathematically as a time series of pounds per dollar although the information content is the same. In particular it can be shown that

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.

We began this paper by posing four questions about the characteristics of optimal geometric mean portfolios. Tentative answers to these questions were obtained from an examination of the solutions to a relatively large number of geometric mean portfolio problems generated from a Monte Carlo simulation of ex-ante security return data. The results of this examination can be summarized as follows. First, the number of risky securities contained in an optimal geometric mean portfolio depends on one's expectations concerning future market conditions and on the conditions under which borrowing is permitted. If all capital must be invested, the investor who believes the market will fall should invest in just one security, he who believes the market will remain unchanged should diversify among two securities, while he who believes the market will rise should diversify among four to seven securities. In the event that some capital must be withheld from investment, the investor who believes the market will rise and who can borrow on reasonable terms will again diversify among four to seven securities, choosing the same securities in the same relative proportions as in the preceding situation. Should the investor be permitted neither to borrow nor to invest all his capital, his best portfolio consists of two to four securities, assuming he expects the market to rise.

The problem of bond portfolio selection may be viewed as consisting of two parts. The first is concerned with the maturity profile of the total cash flows (the after-tax coupons and principal repayments) which the investor requires; in general there will be many portfolios of bonds which provide the desired cash flow profile. Accordingly, the second problem is the choice of a particular portfolio of bonds which provides these cash flows in some optimal fashion. If bonds are default free, future taxes are known, and differences in marketability and callability among issues can be ignored, then price is the only relevant criterion in choosing among alternative portfolios. This paper describes a simple linear programming model for this last problem of selecting the portfolio which provides a given pattern of cash flows at minimum cost. This provides a method for improving any initial portfolio, where such improvement is possible, by increasing its yield without reducing any future after-tax cash flows.

Stable distributions are becoming increasingly popular as appropriate models for stock price changes and other economic phenomena. As a result, there is an expanding body of literature on inferential procedures for this family of distributions. Computationally simple estimators for the parameters of symmetric stable distributions have been provided by Fama and Roll. Little attention, though, has been given to goodness-of-fit tests for members of this family other than the normal.

It is the purpose of this paper to discuss simple goodness-of-fit hypothesis tests using kurtosis, b2, to distinguish among members of the stable family. The b2 tests of hypothesis comprise: 1) a null normal versus a nonnormal symmetric stable alternative; 2) a null nonnormal symmetric stable versus a normal alternative; and 3) a null nonnormal stable versus another nonnormal stable alternative. Tables that give the percentage points of b2 and that are necessary for these tests of hypothesis are given. Apart from providing critical values for the tests, the tables allow the researcher to calculate the power. It will be seen that the b2 test exhibits excellent power.

It is then hoped that computational convenience will make b2 an important tool for researchers and practitioners in finance. It is also hoped that the procedures we provide will aid these researchers and practitioners in the construction of appropriate financial models.

In a recent paper Joy and Porter [4] used the concept of stochastic dominance to address the question of whether or not mutual funds outperform the Dow Jones Industrial Average (DJIA). Since that time Meyer [5] has proven a theorem in the area of stochastic dominance which allows one to make further application of stochastic dominance to this question. The major purpose of this paper is to demonstrate the power and relevance of the recently developed stochastic dominance theorem in ordering investments for groups of investors. In doing so, some evidence is presented concerning mutual funds and the DJIA.

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.