This statement presents the usual perception of bond risk. It is striking in that it does not discuss what is, from a portfolio theoretic view, the risk of a bond––the covariance of its return with the returns of other assets. This is in contrast to the typical discussion of the riskiness of common stocks, where we find some discussion of systematic risk and the role it plays in determining equilibrium expected security returns.

The form of the Pareto optimal general insurance contract has been investigated by Borch [5], Arrow [3], and Raviv [16]. This paper extends their work to the consideration of the optimal investment portfolio insurance contract. This is a contract whose payoff depends upon the investment performance of some specified portfolio of common stocks. Portfolio insurance differs from general insurance in two important ways. First, investment portfolio insurance lacks the property of stochastic independence between losses on different contracts which is characteristic of general insurance, and this has led some actuaries to question whether portfolio insurance contracts should be sold in view of the risks they pose for the solvency of insurance companies. Recent developments in the theory of option pricing suggest, however, that under certain assumptions an insurance company will be able to eliminate the risks associated with portfolio insurance contracts by following an appropriately defined investment strategy. Secondly, there exists a market for the pricing of investment risks, the securities market; and, under appropriate assumptions, the equilibrium price of portfolio insurance contracts may be determined without specification of the preferences of insurance companies. This permits consideration of insurance company preference functions to be dispensed with, in marked contrast to the earlier literature concerned with general insurance, which treats insurance company preferences symmetrically with those of the insurance purchaser. In addition, since the characteristics of the insured portfolio are known to the insurer, and the performance of the portfolio is beyond the control of the insured, portfolio insurance is not prone to the problems of adverse selection and moral hazard which are liable to arise in general insurance.

Cash concentration is the task of moving funds from depository banks into the central cash pool. It is useful to structure cash concentration by dividing it into two major problems––management and design. Management is the day-to-day operation of the cash concentration system once it is designed. Design is specifying the structure of the cash concentration system.

Over the past decade, a number of papers [1, 2, 3, 6, 7, 9] have explored the relative merits of negotiation versus competitive bidding in the underwriting of corporate bonds, particularly bonds issued by public utilities. Interest in this subject has been stimulated principally by an important public policy issue—namely, the SEC's posture vis a vis its Rule U–50. Originally promulgated in 1940, this rule required competitive bidding on certain classes of utility bonds. In 1974, however, it was “temporarily” suspended on the grounds that chaotic conditions in the market for these securities called for more flexibility in the way issues could be underwritten. While this suspension continues in effect, Rule U–50 could be reinstated at any time by the SEC.

In an efficient capital market, prices fully reflect available information and adjust to new information in a rapid and unbiased fashion. As a result, prices provide unbiased estimates of the underlying values. No known trading rule or security selection strategy which uses only publicly available information would provide an investor with the ability to earn, on average, positive “abnormal” returns in a market that is efficient in the semi-strong sense. Thus, a finding that common stocks selected, using a readily available, widely disseminated set of rules which requires only publicly available information for decision-making purposes, earn, on average, positive abnormal returns represents strong contradictory evidence regarding the semi-strong form of the efficient markets hypothesis.

The mean-variance model is precisely consistent with the expected utility hypothesis only in the special cases of normally distributed security returns or quadratic utility functions. There is little evidence, however, that security returns follow normal distributions (see [13] for references) and quadratic preferences can be shown to generate implausible results, exhibiting increasing absolute risk aversion in the Pratt [ll]–Arrow [1, 2] sense and displaying negative marginal utility after some finite wealth level. In addition, Hakansson [4] has shown that single–period, mean-variance-efficient portfolios can have disastrous consequences over time—even when return distributions are stationary. Such criticisms of the mean-variance approach within the Von Neumann-Morgenstern framework have prompted several writers to suggest that investors maximize the expected value of utility functions with more “realistic” properties, while others have criticized the single-period focus of the model. One popular alternative utility function is the logarithmic function which exhibits decreasing absolute risk aversion and (conveniently) leads to myopic decision processes through time (i.e., investors treat each period as if it were the last, basing investment decisions on that period's wealth and return distributions only [8, 4]). (Other utility functions with constant relative risk aversion—such as the power function—also imply myopic decision rules within a multiperiod setting.)

Boquist, Racette, and Schlarbaum [3] and Livingston [6] show that a security systematic risk may be expressed as a function of its duration. These results have led to research examining the role of duration in explaining systematic risk, but Lanstein and Sharpe [5] indicate that Livingston's expression relies on the implicit assumption that extra-market covariances between securities are insignificant. Lanstein and Sharpe argue that such an assumption is unwarranted. They find a significant negative relationship between extra-market covariances and differences in duration between paired samples of common stock. Their paper suggests that duration may be associated with unsystematic risk and that any relation between duration and systematic risk is more complex than implied in [3] and [6].

The algorithm leading to a solution of the above question has been known at least since Kaplan's 1965 tutorial [5] on Sturm's theorem. The Sturm-Kaplan method has the power to count all zeros on the real axis between any two specified limits. A significant problem may arise, however, when one tries to generate the Sturmian functions which play a central part in the Sturm-Kaplan method. The rather arduous nature of the task derives from the necessity to perform several polynomial (synthetic) divisions. As the number of cash flows involved in the analysis increases, the time and effort required to determine the Sturmian functions increase as well.

The usual formulation of the portfolio selection problem through meanvariance analysis assumes that the variance-covariance matrix of the rate of returns on risky assets is non-singular. In view of the literature discussing the creation of riskless portfolio from carefully balanced quantities of risky securities (e.g., shares and warrants as in Black-Scholes [1]), the assumption of non-singularity may be challenged. Consequently, the proofs of the classical theorems of portfolio management may no longer be developed as originally presented. Buser [2] presents a means of using a singular variance-covariance matrix in the derivation of portfolio weights, which, although slightly flawed by a mathematical error, still provides some interesting insights about the efficient frontier. We present a corrected version of Buser's method in Section II; in Section III, we comment on some of the implications of his presentation and indicate some more precise results.

In “The Pricing of Premium Bonds,” Livingston [4] presents an erroneous analysis of the coupon effect on yield to maturity (YTM). This comment will present a correct analysis and briefly indicate Livingston's error. Following [4], we will assume no transaction costs, etc., and confine our analysis to N-period bonds (N = 2). The prices of premium bonds (P+) and discount bonds (P−) can be represented as:

where

TP = tax rate on income of marginal investors,

TG = capital gains tax rate of marginal investors,

A = market price of an untaxed N-period $1- annuity,

D = market price of an untaxed N-period $1 discounted note,

C = coupon,

F = “face” or principal amount of bond,

and PS, PA, PDS, and PD are the prices of the annuities and discounted notes implicitly in taxable bonds. Expressions (1) and (2) show equilibrium prices as functions of A, D, TP, and TG; cf. McCulloch [6], Caks [2], and Livingston [3, 4, 5].

My paper, “The Pricing of Premium Bonds [2],” is the first to show deductively that the taxation of premium bonds makes it possible for yield to maturity to reach a maximum at par. My paper also supports this analytical result with empirical examples.