To sum up, Emery and Cogger [5] have raised several interesting questions concerning the derivation of the safety index (as well as the related risk of ruin) and the interpretation of that index which needed to be addressed. While the potential limitations discussed are theoretically possible, closer examination reveals that most of the concerns raised are unlikely to occur in practical applications, although certain of the procedures utilized were in need of further explanation. Several of these issues also provide extensions of the present work to make the estimation of the risk of ruin an even more robust measure of the potential for corporate failure.

Recently, there has been an increased interest in the role that bankruptcy or ruin plays in the valuation process. Several authors have discussed this subject (Gordon [17], Quirk [27], and Smith [35]) and some have constructed theoretical models attempting to show how the probability or risk of ruin introduces an element of risk into valuation (for example, Bierman [5], Borch [8], Tinsely [37]). The question of corporate survival is, therefore, central to the financial considerations of the firm. None, however, has attempted empirical tests of the role of such a probability in valuation.

This paper develops an exact theoretical test of the presence or absence of a filter effect for a portfolio of securities and a general number of different filter sizes. It is a natural development from Praetz [8], which obtained exact expressions for the mean and variance of rates of return of the investment strategies under filter tests assuming the underlying stochastic process is a random walk. These expressions showed that expected returns from filter strategies are, in fact, less than the return from a buy-andhold alternative with which filter returns are usually compared.

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.

I was interested to read Meyer and Kim [5], where I learned a little about sugar futures, but regret to say that I found the attempted Box-Jenkins analysis singularly lacking in expertise. It is my intention, here, to discuss a few of its most obvious shortcomings. My list will not be exhaustive, but will include just five points.

Numerous empirical studies have appeared in recent years concerning the behavior of stock market prices. Cootner's book [2] presents an excellent summary of pre-1964 efforts, while Fama's paper [5] discusses some of the more recent work. While a few writers believe that certain price trends and patterns exist which enable the investor to make better predictions of the expected value of future stock price changes, the majority of these studies conclude that past price data alone cannot form the basis for the prediction of the expected value of price movements in the stock market.

Jack Clack Francis' paper is a most interesting and provocative one, because it is the first to present empirical evidence questioning the importance of a distribution's skewness parameter in the investor's decision process. In particular, Francis claims his evidence demonstrates that stock market investors do not consider skewness in choosing among alternative investments.

The relationship between capital market equilibrium and firm financial policy has received extensive attention in recent years. Until recently, accepted theory was generally consistent in its view that the diversification effect of new investment on firm earnings is a necessary consideration in project selection. In arguing this position, no distinction was made between the perfect market situation exemplified by the models of Modigliani and Miller (M-M) [9, 10, 11] and those of Sharpe [19], Lintner [6, 7] and Mossin [12] (LSM model) and the traditional case in which firm value is not independent of debt policy, e.g., as might be the case if individual investors cannot lever on terms comparable to those available to firms. In a recent article, Mossin [13] examines the implications of the former case of perfect markets. Using a single period model with riskless rate borrowing and lending by individuals and firms, homogeneous expectations, mean-variance portfolio selection, and no taxes, Mossin shows that the effect on the investing firm's value of a new project is independent of the stochastic properties of the other income earned by the firm. This conclusion and the M-M [10] Proposition I follow from the statistical property of Mossin's model that any income stream has the same value regardless of how that stream is divided into the equity or debt streams of one or more firms; or, equivalently, firm value and financial structure are independent. Schall [18] presents a general proof that firm value and financial structure are independent and that firm investment diversification effects are irrelevant in perfect capital markets.

The purpose of this study is to analyze the behavior of the cost of equity capital in the commercial banks by looking at whether there exists an optimal composition of the bank “fund structure” that would maximize bank earnings through the minimization of its cost of funds. The analysis should give an approximate cut-off point for testing such projects as “checking plus, ” checkless payment systems, etc.