A capital asset-pricing model which relates risk and return under conditions of changing price levels has been developed in this paper. The resulting model implies that price-level changes do not affect the expected real returns on individual assets except through their impact on the return of the market portfolio. If real market returns are independent of price-level movements, the model is very much like the standard capital asset-pricing model expressed in real returns. This version of the capital asset-pricing model does not, however, resolve all the difficulties associated with changing price levels, since we have assumed that the nominal default-free rate is determined outside the model and that relative prices do not change. These limitations, however, also apply to all other single-period capital asset-pricing models.

In addition, the model was converted into nominal returns by assuming that price-level changes and the real market returns are uncorrelated. The resulting equation illustrates the difficulty involved in using nominal returns to test a model expressed in real returns. The same equation also provides a possible explanation for the noted discrepancies between the empirical' evidence found by Black, Jensen, and Scholes [3] and the prediction of the traditional capital asset-pricing model.

We have been concerned with investigating the structure of rate-of-return comovements among major international equity markets. Working with 12 such markets we have analyzed the structural features of the configurations over alternative time periods (one-, three-, five- and ten-year periods) and the intertemporal stability of the configurations.

On the issue of intertemporal stability we found considerable one-year and three-year stability, but somewhat weaker stability in the five-year case. As a measure of stability we used cophenetic correlation coefficients between successive (in time) dendrograms. This technique was described in the methodology section.

We uncovered several interesting structural features. There seems to be a core of international markets that have higher degrees of similarity than the other markets. Furthermore, these markets (the United States, Canada, the Netherlands, Switzerland, West Germany and to a lesser extent, Belgium) may be generally described as relatively well developed and open to international capital flows. There is also an obviously strong tie between the United States and Canadian markets. There are less strong, but identifiable ties between France and Belgium, Germany and the Netherlands, and England and Australia. Many of these results parallel Ripley's [14] findings. We also noticed some countries that tend to be least similar to most other countries: Austria and Italy. Ten-year results corroborated these findings.

This study is only descriptive. We have only attempted to identify international equity market structure and structural change. A logical subsequent research area is to explain observed structural properties and the causes of structural change. We hope that our research will help provide some basis for this further analysis.

1. This paper presents and tests a model of dealer inventory response. The estimated inventory responsiveness coefficient is statistically significant and its magnitude is consistent with reasonable values of underlying variables which, it is hypothesized, determine the coefficient.

2. The sign of the inventory responsiveness coefficient indicates that dealers tend to be passive and acquire shares when prices fall and sell shares when prices rise. This type of behavior is sometimes termed “stabilizing.”

3. Dealer inventories tend to increase on days prior to price declines and tend to decrease on days prior to price increases; that is, inventory changes tend to be “destabilizing” with respect to future price changes. This implies that a fraction of the public trades on superior information and that dealers tend to lose money to such information traders.

4. There is a strong tendency for dealer inventory levels to return to normal, presumably zero. The implied typical inventory holding period is about 8 to 10 trading days.

5. Comparison of NASDAQ dealers and NYSE specialists shows that the pattern of inventory responsiveness is very much the same for the two. This suggests that both act in accordance with the underlying economic model and that differential regulation has little effect on typical inventory responsiveness.

6. This finding does not obviate the possibility that individual dealers or specialists behave in atypical or undersirable ways, and that the extent of such atypical behavior might depend on the degree of public regulation of dealer activities. An exhaustive comparative study of deviations from normal behavior was not possible. However, it was possible to compare the frequency of nonstabilizing transactions in which price change and inventory change on a given day are in the same, rather than opposite, direction. One could not conclude that NASDAQ dealers had more nonstabilizing activity than NYSE specialists.

I welcome the oppostunity to second the analysis of Davies and Ronning [4]. The considerations they raise crop up repeatedly in various contexts of uncertainty analysis and prompt the following remarks dealing with various tonics described in ray title.

The U. S. National Bank was declared bankrupt in October of 1973. Just a few days short of a year later the Franklin National Bank failed. These were the largest bank failures ever experienced in the United States and they occurred against a backdrop of extensive bank regulatory operations first to prevent them and then to reduce the effect of these failures upon bank depositors and the banking public. The objective of this study was to determine the effects of these two large bank failures upon the structural relationship of risk and return of equity investments in other large commercial banks. Using historical hindsight, it can be seen that these large bank failures were isolated and noncumulative, but it should be remembered that the investors in bank equities at that time did not know that these failures would not precipitate other bank failures. This worry or apprehension.should have.been reflected in the equity prices of other large bank stocks. Did these failures substantially affect the perceived risk of failure in other large commercial banks? Did these failures result in a substantial increase in the required rate of return on bank equity? Under the efficient markets hypothesis it is assumed that all current prices reflect all knowledge and thus equity prices should adjust quickly to the presence of new information contained in a bank failure. Therefore, in order to determine the influence of these banking failures upon the structural relationships of risk and return of bank equities, the market model was used to relate the weekly holding period returns on 19 large commercial bank common shares to the weekly holding period returns on the S & P 500 index over the past four and one half years.

This study found that there was a lengthy period of structural stability when the realized returns on large bank stocks were compared with the realized returns on the market portfolio. Further, the study found that the U. S. National failure had no structural effect upon the relationships of risk cognizance and required return in that there were no resulting significiant changes in the parameters of the market model before and after the failure. On the other hand, the failure of the Franklin National had a significant structural effect upon risk cognizance. The perceived level of unsystematic risk significantly increased above that of a base period established before the Franklin failure. There was no structural change found in either the intercept term or the measure of systematic risk after the Franklin demise, only a change in unsystematic risk. The most significant change occurred just after the closing of the Franklin and subsided completely during the first and second quarter of 1975.

In [1] the authors proved the following proposition.

Proposition 1: If the positive random variables are exchangeable and linearly independent and if u(x) is strictly concave and satisfies

then the unique optimal choice is given by .

This paper presented a stochastic discounted cash flow model with which mortgage companies can assess the value of a mortgage servicing contract. The model was illustrated with data provided by a group of eight MBC's. Simulation and sensitivity analysis showed the impact of different mortgage amounts, termination distributions, and expected rates of servicing cost increases on the value of a mortgage servicing portfolio. In general, because servicing contracts are long-term fixed revenue arrangements, high rates of servicing cost increases substantially reduce the value of an MBC's servicing portfolio. To the extent that mortgage prepayments are reduced by high inflation rates, the impact of high cost increases on the value of a servicing portfolio is compounded.

In a general equilibrium model of risky assets, prices would be determined by the interaction of the supply and demand. Unpredictable events would impact one or both sides of the asset market and thereby influence the return on assets. The probability distribution of returns would thus be endogenous. Since expectations as to subsequent asset returns influence asset demand, the probability distribution of returns is a crucial element in the general equilibrium system; it is the consequence of the demand and supply of assets and, at the same time, a central determinant of expectations and, hence, of the demand for assets. Nevertheless, it is possible to undertake a partial equilibrium analysis in which the behavior of asset demand, conditional upon a postulated probability distribution of returns, is examined. In such a limited context, it is natural to postulate a “convenient” probability distribution of returns, namely, one that facilitates the analysis of demand. A leading assumption has been that returns are serially independent and obey a stationary distribution.

In application of portfolio selection algorithms [3,4] and in tests of the effectiveness of these approaches [1,2], it is sometimes useful to know, a priori, the size of the set of possible portfolios that may be encountered. Given a set of linear restrictions such as that worked by Frankfurter, Phillips, and Seagle [1,2], the set of possible portfolios is finite. This note presents a simple algorithm for determining the size of this set. Only two inputs are required:

1. The size of the universe of securities under study, and

2. A functional relationship which acts as a constraint on the weights.

The following is a heuristic algorithm without a rigorous, generalized proof.

There appears to be growing interest in the development and estimation of simultaneous equation models for finance. Simkowitz and Jones [11] stimulated much of this concern in their observations on the need for these structures. Moreover, Simkowitz's application to the modeling of security returns with Logue [12] provides some support for these suggestions. Recently Lloyd [6] has argued that there may be significant problems in using two-stage least squares (hereafter 2SLS) with such models as a result of the potential for contemporaneous correlation in the structural errors across equations. The purpose of this note is to question several of Lloyd's conclusions and to provide some evidence that his findings may not be representative for the broad array of simultaneous models applicable to financial problems.

The weighted average cost of capital (Ko) is presented in virtually all textbooks in financial management and capital budgeting as a practical concept fundamental to the actual selection of optimal financial and investment alternatives. As often employed Ko can be defined as

where

Ko = the weighted average cost of capital,

Ks = the cost of equity capital,

Kb = the cost of debt capital,

S = the market value of the firm's equity,

B = the market value of the firm's debt, and

V = S + B, the total market value of the firm.

Whenever the firm must borrow funds, it must also decide maturity of the new debt. Yet, the decision models which have dealt with the debt maturity decision have done so almost incidentally, as an extension of the decision to exercise the call provision on outstanding bonds ([6], [10], [23]). There has been little direct examination of the corporate debt maturity decision. In an attempt to fill this gap, this paper is an exploration of the debt maturity decision for a firm which is concerned with minimizing the present value of the expected costs of borrowing. This paper develops a discrete dynamic programming model of the debt maturity decision, in a world where interest rates follow a finite Markov process, and where the yield curve is formed from expectations regarding the future course of interest rates. With this optimization model, the influence on the debt maturity strategy of variables such as flotation costs and liquidity premiums will be explored. There will be no consideration of the risks associated with alternative borrowing strategies.

This study tests whether a “portfolio effect” exists in a given branch bank; i.e., does the addition of branches reduce the variability of demand deposits for the bank? The approach taken is narrower than that in the usual portfolio selection model. The study measures risk by the intrayear coefficient of variation of average monthly demand deposits. The term “portfolio effect” was defined operationally as a reduction in the overall coefficient of variation of demand deposits through the addition of sets of branches. Relatively few portfolio effects were realized from the chronological addition of sets of branches. The absence of portfolio effects is largely attributable to (1) generally high positive correlations between deposits of the various sets of branches and the defined deposit base and (2) the small size of the sets of branches relative to the base deposits. Further, while the correlations were generally high and positive, they were also serially unstable which suggests they would be poor predictors of future correlations. Based on the experience of this bank, it does not appear that the reduction in demand deposit variability by adding branches is general or consistent enough to facilitate improved management of reserves or selection of branch locations. However, this conclusion does not necessarily imply that the bank should not have undertaken branch expansion. For example, this study does not include an analysis of branch profitability. While the results of this study based on a single branch bank cannot be generalized, they do suggest the need for a more comprehensive analysis of the impact of branching on the variability of demand deposits.