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Calibration is commonly regarded as the process whereby the scale of a measuring instrument is determined or adjusted on the basis of an informative or ‘calibration’ experiment. For example, if we wish to calibrate an unsealed thermometer we might note the position x1 on the liquid scale when the thermometer is immersed in boiling water at atmospheric pressure, that is, corresponding to temperature t1 (= 100°C); and the position x2 when the immersion is in ice, say corresponding to temperature t2 (= 0°C). We might then divide the scale between x1 and x2 into 100 equal divisions so that, when the thermometer is immersed into some other substance, we are able to deduce very simply from the x-scale the corresponding temperature of the substance. In this example the use of the calibration experiment yielding trial records (t1, x1), (t2, x2) is straightforward since there is, or at least we are assuming that there is, a one-to-one correspondence between the x-scale and the temperature or t-scale. But the same type of problem arises commonly in a less simple form, for usually, as in the following examples, there is no unique x corresponding to a given t.
Example 10.1
Measuring water content of soil specimens. Two methods are available for obtaining the water content in soil specimens. The first method, performed in the laboratory, is very accurate but is expensive and tedious to operate. The second method, which can be performed on site, is much quicker and cheaper, but is less accurate.
Most textbooks in finance are apparently embarrassed by the Modigliani-Miller (MM) theorem on capital structure. The intense controversy it has provoked in academic circles over the past sixteen years makes it hard to ignore, and yet many textbook writers seem to be unable to distill anything from it that might be of interest to their readers. A typical example might begin by laying out the economist's conventional perfect market assumptions and showing that the theorem may be derived deductively from these assumptions. It is then observed that markets are not perfect and it is implied that perfect market theorems, while perhaps interesting to ivory-tower academics, are of no use to a businessman who has to act in imperfect real-world markets. (For example, Weston and Brigham [16], in their appendix to Chapter 11, on p. 339 state: “Given their assumptions, their theoretical arguments were quite correct. However, their assumptions have been questioned extensively, and very few authorities today accept the MM position.”) We are then returned rather uneasily to the traditional world of U-shaped cost of capital curves, in which managers are required to examine such holy relics as financial break-even charts (Van Home [15, p. 231]) or to exercise judgment about the stockholders' utility preferences (Weston and Brigham [16, p. 258]) in order to make their debt/equity decision.
In the process of managing a financial institution there are decisions that require special considerations beyond those in other firms. In this paper dividend disbursal practices in the banking firms will be analyzed. The central issue is what part of profits should be distributed and what part should be retained within firms as an addition to the banks' net worth.
Among the risks inherent in international business operations the exchange rate risk represents one of the important considerations for the managers of multinational firms. Three techniques are well known as effective methods against the erosion of value due to the exchange rate fluctuation. These are (1) use of a forward market, (2) use of monetary balance, and (3) use of foreign currency swap arrangements. While the use of a forward market represents an effective tool against the exchange rate loss in ordinary transactions, the other two are designed for different purposes. The use of monetary balance is a protective device against the erosion of the value of the assets due to the exchange rate fluctuation, whereas the foreign currency swap is a device primarily to protect the value of the investment in countries whose currencies are “soft” in that the likelihood devaluation is so high that forward markets do not even exist.
Prior to the recent experience with relatively flexible exchange rates, there was much concern that a high degree of exchange-rate flexibility might somehow overburden the institutions of the foreign-exchange market, particularly the forward market, with disruptive consequences for international commerce. While seldom clearly stated, the reasoning underlying this concern usually proceeded along the following lines. Substantial exchange-rate flexibility would lead business management to expect greater exchange-rate variations, with the result that businesses would seek to cover much more of their foreign-exchange exposure (i.e., would seek to “insure” against the greater exchange-rate risk) by purchasing or selling foreign currency forward. However, foreign-exchange traders either could not accommodate this greatly increased demand for their services, or could accommodate it only at substantially higher cost. Consequently, business firms would significantly reduce the volume of their international transactions.
During the last 15 years, the Eurodollar deposit market has grown from perhaps $1 billion to a level now estimated to exceed $200 billion. This growth has prompted numerous arguments and investigations as to its cause [cf. 14, 22, 27], factors influencing it [cf. 24, 28, 29, 32], its import for U.S. banking and monetary policy [cf. 2, 38], its role in international financial market integration [cf. 1, 9, 39], and its impact on the internationalization of U.S. monetary policy [cf. 18, 23]. Over this same period of time, an increasing empirical interest has developed in the term structure of interest rates. Yet most empirical studies of the Eurodollar market [cf. 2, 28, 29, 32] have employed the 90-day Eurodollar CD rate as though it were “the rate of interest” in this market. This tendency has resulted more from the empirical ease of computing covered interest differentials in conjunction with the three–month forward exchange rate than from theoretical considerations [cf. 32, p. 7].
The normative theory of portfolio selection has, since Markowitz, proceeded for the most part on the assumption that there are no costs of transacting in securities markets. Exceptions to this generalization are the work of Pogue who proposes a quadratic programming solution to the portfolio selection problem with variable transactions costs, and, in a multiperiod context, the ad hoc portfolio revision models of Smith, and the more rigorous, though computationally burdensome dynamic programming models of Chen et al. All of these models focus exclusively on the variable costs of transacting. Mao deals implicitly with the fixed costs of purchasing securities and the limited diversification which these will imply. However, his model both lacks an explicit optimization criterion for determining the number of securities to include in the portfolio and assumes a homogeneous security universe; this latter assumption is relaxed when he later considers the problem of which securities should be included in the portfolio. Clearly an ideal solution to the problem must consider simultaneously both how many and which securities to include. More recently, Jacob has developed some simplified models for selecting optimal portfolios, given a constraint on the number of securities which may be included in the portfolio. While her models are superior to Mao's in taking account of the residual risk of the securities as well as their systematic risk, they do not contain any explicit procedure for determining the optimal number of securities to include in the portfolio.
In the evaluation of investment opportunities risk is often a primary consideration. Risk is usually not a factor of such importance, however, in the evaluation of borrowing opportunities. But when the borrowing opportunities include the borrowing of foreign currencies, then the possibility of exchange rate fluctuations during the loan period may introduce a significant component of risk. It is our purpose to develop a method for evaluating and selecting international borrowing sources in the face of exchange rate uncertainties.
The literature on security selection and evaluation is quite extensive-Aside from the chart readers, however, there is little or no theoretical framework on the optimal trading price. The theories of technical analysts have been almost completely debunked by the evidence on the random walk nature of price performance. This state of affairs leaves the investor, who has decided to buy or sell a particular security, with very little insight as to the optimum price to trade. The random nature of price performance suggests that both higher and lower prices are likely to be obtainable in the near future. Thus, trading at the current market price may not be the best strategy. On the other hand, waiting for the stock to move decisively in the desired direction exposes one to the risk of an equally large movement in the opposite direction.