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.

D. J. Ashton, D. R. Atkins, Interactions in Corporate Financing and Investment Decisions--Implications for Capital Budgeting: A Further Comment, The Journal of Finance, Vol. 33, No. 5 (Dec., 1978), pp. 1447-1453

THE CHOW TEST is a widely used procedure for testing for the equality of sets of coefficients in two linear regression models. However, when the number of observations in one of the models is less than the number of regression coefficients, the Chow test is incapable of testing the hypothesis of equality against that of inequality. It can never be concluded from the Chow test itself that the two sets are equal, although at times it may be possible to conclude that they are unequal. This point is implicit in [1], but has not been specifically discussed heretofore. The indeterminacy of the Chow test results from the insufficient number of observations. The two linear regression models, each of which is assumed to satisfy the conditions of the standard normal linear regression model, can be written as

In this paper an explicit and computationally convenient expansion of the exact finite sample distribution function of a quasi-maximum likelihood spectral estimator is given. In the majority of practical situations it will be necessary to estimate certain nuisance parameters of the distribution. Therefore, a method of evaluating these parameters is suggested and some Monte-Carlo evidence concerning the practical implementation of the results is given. 1 INTRODUCTfON AN EXTENSIVE SET of asymptotic results relating complex statistical analysis to the problems that arise in estimating spectra from the discrete Fourier transforms of time series data has been well established; see, for example, Brillinger [3] and Goodman [6]; and Hannan [11] has recently extended these results to cover the modified Fourier coefficients, proposed by Bingham, Godfrey, and Tukey [1] and defined in (2.3) below. Unfortunately it seems likely that the sample sizes required for one to approach the asymptotic position will not be available when considering the analysis of many economic time series. In a recent article, however, Hatanaka [12] has shown that the elimination of leakage produced by the modified Fourier coefficients is effective for small finite realizations and that it may be possible to recover the loss of degrees of freedom associated with the familiar estimator obtained by averaging over the modified periodogram.2 The purpose of the present paper is to extend these results by using complex statistical analysis to derive expressions for both the form and exact finite sample distribution of a spectral estimator obtained from the modified Fourier coefficients. Thus in the following section a brief exposition of some basic theory is given and a quasi-maximum likelihood estimation procedure is suggested. In Section 3 an exact expression for the finite sample distribution of the proposed estimator is given and shown to incorporate an established distributional result as a particular special case. In the majority of practical situations it will be necessary to estimate certain nuisance parameters of this distribution if it is to be employed and a method of evaluating these parameters is also suggested. It is well known, however, that while the replacement of nuisance parameters by consistent estimates will generally leave asymptotic theory intact the consequences of estimating nuisance parameters are unlikely to be negligible in finite sample theory. Since it is not possible to determine analytically the effect that the estimation of these nuisance parameters will have, the results of some simple Monte-Carlo

Reviews the book "Public Budgeting Systems," 2nd ed., by Robert D. Lee and Ronald Johnson.

Reviews the book "C.P.A. Law Review," 5th ed., by Joseph L. Frascona.

Reviews the book "Introduction to Modern Accounting," 3rd ed., by Ronald J. Thacker.

Reviews the book "European Financial Reporting 1: West Germany," by J.H. Beeny.