Much effort has been recently devoted to investigating and expounding the properties of the measure called “duration.” Two properties claimed for duration are (1) that it is a good indicator of the average life of a payments stream and (2) that it measures the elasticity of the present value of such a stream with respect to the discount rate. Unfortunately the theoretical justifications of the second, more important, property have been based upon the analysis of either a change in a discount rate constant for all future time periods, or, more generally, a parallel shift in the term structure of interest rates.

The asset and liability portfolios of financial institutions generate patterns of future cash flows that must conform to many restrictions in order to assure solvency and profitability. Many institutions, including insurance companies and pension funds, have definite and certain future commitments of funds. These institutions may wish to invest funds now so that their cash inflows (investment with accumulated earnings) will match their future commitments. In principle, the simplest way to meet future commitments exactly is to purchase single payment notes (or zero coupon bonds) which mature on the commitment dates. For long-term commitments, such instruments are not readily obtainable, at least in the United States. Most available bonds promise coupon payments over time so that these payments would have to be reinvested at unknown future interest rates in order to realize an accumulated sum at any future date when a commitment must be discharged. Since future interest rates are unknown at the initial moment of investment, it is not certain what accumulated earnings will be at future dates. In the absence of default, the risk of not meeting future commitments may be minimized by adopting investment strategies based on the concept of duration. Duration is a measure of the average maturity of an income stream; it is a weighted average of the dates at which the income payments are received, where the weights add to unity and are related to the present value of the income stream. Dating from the initial work of Macaulay [9] and Hicks [6], duration has been shown to be important in constructing portfolios that are hedged or ‘immunized’ from the possible ravages of interest rate uncertainty.

The empirical distributions of price changes for speculative assets (e.g., common stocks, bonds, etc.) measured over calendar time yield a higher frequency of observations near the mean and at the tails than would be expected for a normal distribution. The sample kurtosis is almost always greater than 3—the value expected for a normal distribution—and the distributions are commonly characterized as fat-tailed and peaked (i.e., leptokurtic).

In recent years a substantial number of empirical studies have been conducted concerning aggregate commercial bank behavior [2, 8, 11, 14, 15, 17, 18]. Although the scope of these studies has varied widely, none has included an adequate treatment of the relationship between commercial bank liability management and earning asset adjustments. The importance of the relationship between liability management and commercial bank asset behavior has been alluded to in the literature [3, 5, 6, 13, 18]; but there has been very little empirical investigation of the subject. Moreover, little is known about which assets and liabilities are primarily involved. By increasing or decreasing earning assets, the commercial banking system can create or eliminate deposits, thus affecting the supply of both money and bank credit. Since liability management and asset behavior are very closely related, it seems that an adequate understanding of this relationship is essential to understanding the money supply process.

If the “smart money” was out of Franklin before its financial difficulties became public knowledge, just what elements of Franklin's balance sheet were the sagacious analysts reading and why weren't the banking authorities aware of this information? The purpose of this paper is to determine what balance-sheet and income-statement figures, if any, could have been arrayed in an ex post early-warning system to spotlight Franklin's developing problems.

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.

The general framework employed in analyzing diversification among securities involves the mean-variance theory of portfolio selection described by Markowitz [8]. Observation of the securities comprising the efficient set indicates which financial sssets possess attributes (i.e., expected return and covariances) making them worthwhile components of an optimally diversified portfolio. This paper will be concerned with forming an efficient set from four security classes—common stocks, preferred stocks, corporate bonds, and U.S. government bonds (hereafter denoted CS, PS, CB, and GB, respectively). The first objective will be to derive and analyze an efficient set from a sample of these securities in order to determine which securities have potential benefits for diversification.

This paper examines the stationarity of beta coefficients, especially in regard to recent, major stock market trends. In addition to the usual correlation tests for stationarity, this paper describes a more direct method for testing the stationarity of portfolio betas. The method involves the use of paired t-tests which show separately the degree of stationarity for each portfolio beta. In the process of testing for stationarity, the portfolio betas also are adjusted for measurement error using a formulation suggested by Blume [3].

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.

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.

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 ].

Prof. A. Carol examined a replacement problem in a paper published in the January 1972 issue of this journal.

The aim of the author seems to be to obtain a precise insight in the pattern of quantities to be considered to take a rational decision.