Time series techniques based on autocovariance and spectral analysis methods have often been used for statistical analyses of commodity and stock prices, with the usual conclusion that the prices, zt, are best described by a random walk:

where the errors, ut (alternatively called shocks or residuals), have zero expectation and form a sequence of independent random variables [5 and 8 ].

In recent years intensive work has been done applying the Sharpe-Lintner-Mossin Capital Asset Pricing Model to the multiperiod investment decision under uncertainty. The purpose of this paper is to develop a practical working procedure for use by the financial manager. We first develop the multiperiod capital budgeting decision criterion in a form that lends itself to application. Second, we propose a method of implementation, one that we have made operational in computer programs currently on the Columbia University computer system. This makes it possible to extend the evaluation to encompass typical capital budgeting problems which, until now, have been discussed only under certainty. In particular we deal with the case of capital rationing. We employ programming techniques for this analysis and interpret the meanings of the dual variables.

The rationality of compensating balance requirements has been widely debated in the literature and among participants in the market for loanable funds. Rationality in this context refers to a net gain in interest income for the lending bank in the transaction without, at the same time, an increase in interest cost to the borrowing firm; or, conversely, a decrease in interest expense to the borrower without, simultaneously, a decrease in income derived from interest on the transaction by the bank. The lack of consensus as to whether or not compensating balance requirements are rational is based on the absence of uniform assumptions regarding the imposition of these requirements as well as by their restrictive, if not unrealistic, nature. Thus, Davis and Guttentag [2] and Hodgman [9] come to the conclusion that compensating balance requirements (hereinafter also known as c.b.) are indeed rational. However, this conclusion is based on the assumption that the borrowing firm maintains voluntary demand deposits in the lending bank or in another bank (i.e., balances that the firm employs for transaction and/or precautionary purposes which do not serve to satisfy c.b. for any loan or service performed by either bank) and that these deposits are sufficient in quantity to meet c.b. On the other hand, Hellweg [8] finds the use of c.b. irrational inasmuch as he assumes a lack of voluntary balances in either bank. In between these two extremes, Gibson [7], Shapiro and Baxter [11], and Wrightsman [13] suggest that c.b. may either be rational or irrational depending on the proportion of these balances satisfied through the voluntary holdings of the borrowing firm.