Introduction, 283. — I. The portfolio manager's preference for current income and capital gains, 284. — II. Bank preferences and market yields, 289. — III. The values of zi and b derived from market yields, 292. — IV. The values of zj and b derived from a present value analysis, 294. — Conclusion, 301. — Appendix, 301.

THE purpose of this paper is (1) to determine whether corporations' decisions to borrow in the public or private corporate bond markets are significantly influenced by yield differentials between the two markets and (2) whether the sensitivity of corporations to yield differentials increases with the relative ease with which they can borrow in either market. In recent years, the influence of interest rates on corporation financing decisions has received considerable attention in studies which have sought to identify the determinants of corporate external financing and the maturity composition of corporations' liabilities.' In none of these studies, however, can the signs of the interest rate variables in the regression equations be predicted. This is because the expectations hypothesis of the term structure of interest rates which these studies accept posits that interest costs will be equalized regardless of the maturity financing strategy a borrower adopts. As a result the credibility of the findings of these studies concerning the influence of interest rates on financing decisions must be questioned even when this influence was found to be significant.2 In contrast, yield differentials between the public and private corporate bond markets have a predictable effect on the distribution decisions of borrowers. Since nominal rates typically are higher in the private market, a decrease (increase) in yield differentials should encourage (discourage) the sale of private placements. In the aggregate, then, the percentage of corporate debt sold privately should be negatively related to yield differentials between the two markets. In section II, the variables which influence the supply of and demand for funds in the public and private markets -are identified, and supply and demand equations are formulated. Differences in the distribution process in the two markets as well as marketing constraints, limit the ability of some corporations to borrow in both markets, as described in section III. For the purpose of measuring the influence of yield differentials on distribution decisions, then, corporations are divided into three groups, based on their ability to borrow in both markets. The regression results are discussed in section IV. Only the demand equation is estimated since appropriate data on the supply of funds to the corporate market is not available. The estimation of demand by itself, however, produces biased estimates of the coefficient of yield differentials between the public and private markets. The direction of this bias is considered in section V. The major findings are that yield differentials have exerted a significant influence on the distribution decisions of most of the groups studied. Moreover, the sensitivity of corporations to yield differentials is an increasing function of the relative ease with which they can borrow in both the public and private markets. Finally, if supply and demand had been estimated simultaneously, yield differentials most likely would have exerted a stronger influence on the distribution decisions of borrowers. Received for publication November 29, 1972. Revision accepted for publication May 22, 1973. * This paper is based in part on a study of the private placement market by Shapiro and Wolf (1972). In Shapiro and Wolf (chapter 5), the variables influencing the supply and demand for public and private financing are discussed and the distribution patterns of different borrower categories are compared. This paper extends this analysis by estimating a demand equation for public and private financing and by measuring the sensitivity of different borrower groups to yield differentials between the two markets. T am indebted to Professors John Keith, Richard Rippe and Maurice Wilkinson of the Columbia Business School and to Professors Robert Glauber and John Lintner of the Harvard Business School for their helpful comments. This study was supported by faculty research funds of the Columbia Business School. 1 Cragg and Baxter (1970) attempted to determine the factors which influenced the timing and the size of bond financings of 129 industrial companies using a probit analysis. Bosworth (1971) and White (unpublished) explained the maturity composition of total corporate borrowing using the Federal Reserve's Flow-of-Funds data. 2 Only in White's study was the fraction of long-term-tototal debt issues significantly (and negatively) related to the relative cost of long-term financing.

T HE object of this paper is to formulate a normative model for selecting a bank's Government security portfolio. Two major problems arise in constructing a model of bank portfolio selection. First, the model must handle uncertainty. This includes not only uncertain future events but also the decision maker's preferences for the outcomes associated with these events. Second, it must recognize the intertemporal or multi-period character of the decision making process. This means that a decision made in one period will influence subsequent decisions and hence, that subsequent decisions must be considered in arriving at the present one. The present paper applies Bayesian and sequential decision theory to handle both the expectationally stochastic and the dynamic aspects of this important decision problem simultaneously and consistently. No previous model of commercial bank portfolio selection handles either or both problems satisfactorily. Porter's model of bank asset selection recognizes uncertainty by treating future cash flows and security prices as random variables, but it is only one period in length. Moreover, it does not consider the decision maker's preferences.' Since the objective function is linear, the model produces a portfolio diversified between securities and loans only through the selection of distribution functions describing the random variables. These transform the function into a nonlinear one upon integration. Cheng's model of bank security portfolio selection is, in effect, a one period formulation also.2 It incorporates uncertainty and the decision maker's preferences through Markowitz's efficient portfolio concept.3 An efficient portfolio is one which maximizes expected return for a given variance of return (or minimizes the variance of return for a given expected return). As Tobin points out, however, this criterion assumes, quite restrictively, that either the variable return is normally distributed or that the decision maker has a quadratic utility function.4 Cheng also makes the highly unrealistic assumption that securities are held to maturity. Multi-period bank portfolio selection models are all based on the assumption that future events are known with certainty. One such model formulated by Chambers and Charnes attempts to reflect the risk inherent in different portfolio configurations by including the Federal Reserve's capital adequacy formula as a constraint.5 Used in the supervision of banks, the capital adequacy formula allocates a bank's capital to designated asset categories on a fractional basis. The values of the fractions are designed to measure the percent by which the different asset categories would decline in market value if they had to be liquidated quickly.6 The choice of these values is somewhat arbitrary. Moreover, the formula itself implicitly assumes a particular preference structure and a certain probabilistic occurrence of future events. Neither assumption is likely to represent accurately either the decision maker's preferences or expectations.7