The risk inherent in the price fluctuations of bonds has many dimensions. These include default risk, inflation risk, and call risk. The most important single source of risk, particularly for government and high-grade corporate bonds, is basis-risk price fluctuations caused by shifts in interest rates. For a given shift in the yield curve, and holding other factors unchanged, longer term-to-maturity bonds generally suffer greater price changes than shorter maturity bonds. This characterization is not exact because high coupon bonds are less volatile than low coupon bonds. Intuition says that this is to be expected because, other things being equal, high coupon bonds have a greater percentage of their value due to the interim coupons and, hence, have a shorter “effective” maturity. Duration may be interpreted as an attempt to quantify this qualitative statement through the use of a single, numerical measure intended to be used in place of maturity.

Much of the literature on the adequacy of bank capital is concerned with the role of such factors as default risk and faulty management. These factors are important but they neglect the role that purely stochastic elements can play in affecting the capital of a well-managed bank, even if it is free of default risk. Because banks raise funds by issuing liabilities with different maturities than the assets they acquire, changes in the interest rates paid on these liabilities relative to the interest rates on assets will affect earnings and, hence, bank capital.

In recent years, academicians and practitioners have been using the concept of duration more frequently in the analysis of debt securities. Although the use of duration has greatly expanded our insights into the behavior of bond prices and bond risk, it has given rise to a considerable degree of confusion and misunderstanding. The purpose of this review paper is twofold: (1) to clarify the record on what duration is and is not and what it can do and cannot do, and (2) to discuss the appropriate uses of duration in the analysis of security portfolios.

The world is still recovering from the shock of radically higher energy prices triggered by the October 1973 war in the Mideast. In the months following the oil embargo and the quadrupled price of petroleum, there seemed to be a very real possibility that the strains imposed on world markets and institutions, and indeed on national economies, would cause a fracture in one or another part of the complex linkages that make up the world economic system.

Dynamic policies for corporate finance have mostly been studied under conditions of certainty. Financial optimal control models (Davis [3], Krouse [5], Inselbag [4], and Senchack [7]) are characterized by time-varying, state-dependent policy formulations: when and to what extent should earnings retention, borrowing, and debt repayment, new stock issues, and capital investment be varied over an extended planning horizon. Optimal policies generated by these (and other) dynamic deterministic models tend to exhibit a bang-bang phenomenon: switching instantaneously from one extreme to another in a managerially unpalatable way. Dividends are either nonexistent or all of net earnings; borrowing is either absent or at the limit of what banks and the bond market will allow. This sort of policy behavior is acceptable only in a completely deterministic world. Investors would tolerate such extremes since they know that their share, when it finally comes and even after discounting, would still be larger than by any other policy. However, with uncertainty, a balance between dividends now and capital gains later must be struck which will better satisfy investor preferences.

The striking and powerful conclusions of the capital asset pricing model (CAPM) [13,8] arise from imposing the requirement that optimal individual portfolio decisions must be consistent with a market equilibrium for securities. That simple requirement–of market balance–produces the strong results that have been the centerpiece of research in finance in the last fifteen years. But despite the huge payoffs to imposing equilibrium requirements on financial markets, the CAP model remains a partial equilibrium result. The risks which are attributed to securities are strictly exogenous. Securities are risky because their prices fluctuate, but the cause of those price fluctuations is rarely specified. The literature seems to associate “market risk” with the business cycle and individual security risk with either random technological change or demand uncertainty. But whatever attribution is made, such risk remains outside of the model itself. Since the keystone of the CAPM is its important distinction between “real” or nondiversifiable risk and purely financial uncertainty, it is disconcerting to recognize that it is a model in which real quantities do not appear at all.

In recent years the cost of fuel to operate power plants for electric utilities has increased much faster than many utility executives and regulators have anticipated. In the presence of substantial regulatory lag in adjusting rates, stockholders have had to absorb the difference between revenues and unanticipated increases in fuel expenses. In an effort to shorten the time required for increased costs to be reflected in increased prices to consumers, many firms have been allowed to use an automatic fuel adjustment clause (FAC) to pass on increased costs to consumers as they occur. The FAC usually allows the firm to adjust the price of electricity when the price of fuel deviates from some fixed base price. Presently more than 40 of the 50 state regulatory commissions allow some type of FAC.

Since the first owner of a gold depository discovered that profits could be made by lending some of the gold deposited for safekeeping, there has been a concern for the “capital adequacy” of depository institutions. The idea is simple enough. If the value of an institution's assets may decline in the future, its deposits will generally be safer, the larger the current value of assets in relation to the value of deposits. Defining capital as the difference between assets and deposits, the larger the ratio of capital to assets (or the ratio of capital to deposits) the safer the deposits. At some level capital will be “adequate,” i. e., the deposits will be “safe enough.”

This paper is a pioneering effort in the examination of the workings of rationality and efficiency in capital markets. The central theme of the paper is the notion of informational efficiency in markets for durable assets. In its broadest terms this imposes a behavioral constraint on the intertemporal development of the asset markets; in a perfect market the development of the equilibrium over time must not be self-contradictory. Individual agents' anticipations of future developments determine their current actions and these, in turn, determine equilibrium prices. But, tomorrow the process will be repeated and it is at this second step that the possibility of conflict enters. The future development need not fulfill precisely people's previous anticipations, but in a perfectly functioning market it would be difficult to accept a blatant contradiction. To believe that prices are lognormally distributed, for example, and to have that belief generate the same equilibrium price period after period is such a contradiction.

Estimation and control of security risk are subjects of major theoretical and practical importance. Much of the literature in this area has focused on the risk associated with returns over a single holding period. Within this context, a great deal of attention has been devoted to estimation of security betas, which relate to coveriance with “the market,” since the well-known Capital Asset Pricing Model implies that expected returns will, in equilibrium, be related to such values. However, a number of papers [3, 7, 14] have considered “extra-market covariances,” i.e., covariances among security returns not due to common correlations with the market as a whole. Accurate estimates of such covariances are necessary for tailoring portfolios to account for differences in investors' circumstances (e.g., tax brackets) and, a fortiori, for active portfolio management designed to exploit any security mispricing.

These three papers deal with a common subject from three very different attitudes and perspectives. As a result, without challenging such restrictive conventions as the assumption that investor holding periods are fixed and knowable a priori or indeed disagreeing on anything of substance, the respective sets of authors sound three very different themes.