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## Über dieses Buch

The recent introduction of two European index options on the FTSE Eurotrack 100 and the Eurotop 100 is evidence of a demand from investors to hedge pan-European risk. The FTSE Eurotrack 100 was designed to closely resemble the longer established and widely quoted Morgan Stanley European index. The Eurotrack 100 covers a hundred companies in eleven countries in continental Europe. The index is denominated in DM and' a breakdown by value into the different countries covered is given in figure 1. Capitalisation weights for Figure 1 FT-SE Eurotrack 100 Index Norway mark Germany Italy Switzerland France Netherlands Another recently introduced European index is the Eurotop 100 index denominated in EeUs, this index contains twenty two UK companies which represent 27% by value of this index. The attraction of investments in these indices is that they provide a basis for weighted exposure to Europe, investors can then build on this 240 basis by investment in individual countries. The multinational context of the universe of shares defined by this index raises some new questions for the selection of portfolios, whether the portfolios are chosen for absolute performance or to track the index. Various possible objectives of portfolio selection will be discussed, in all cases the crucial role of the covariance matrix of returns is clear. The extra source of risk present in a multinational portfolio is the combination of country risk coupled with foreign exchange risk. Two models of the return covariance matrix are proposed and examined.

## Inhaltsverzeichnis

### Modelling Reality

Abstract
Financial modelling takes many forms, as evidenced by the wide spread of topics covered in this volume. All the papers published herein were presented at either the 9th meeting, in Curaçao, or the 10th meeting, in London, of the EURO Working Group and subsequently independently refereed and in many cases revised. I would like to express my gratitude to all the referees for their work. I would especially like to thank Robin Hewins for co-organising the London meeting with me, and for helping in the production of this volume. The topics range from the simulation of a pension fund to the management of a swaps portfolio; from inventory evaluation to the pricing of contingent claim securities; from the behaviour of traders to the inclusion of subjective beliefs in forecasting.
Richard Flavell

### Economic Policy Determinants: Sensitivity Testing Based on the Mahalanobis Distance Statistic

Abstract
The objective of this paper is to argue for, and to demonstrate, the use of multivariate statistical modelling in order to detect potential periods of unusual behaviour by the unit under examination (for instance, a company). Apparently, exceptional periods as detected by this purely empirical test, may then be investigated using more specifically economic concepts. This paper mainly avoids the latter task.
Dirk-Emma Baestaens

### Time Dominance and I.R.R.

Abstract
Time dominance among cash flows leads, in a very simple way, to state inequalities among their present values evaluated with generic discount factors.
In particular it is shown how some well known theorems concerning the uniqueness of a non-negative I.R.R. represent special cases, requiring no proof, of the above argument.
Francesca Beccacece, Erio Castagnoli

### Linear Gears for Asset Pricing

Abstract
The purpose of this paper is to use a few simple results of linear algebra to derive some properties of a general asset pricing model. Since one can apply essentially the same techniques in both cases, we start by considering a traditional asset pricing model and then show how to extend the reasoning to a more general model. In order to present our results, we need to state several assumptions that are customarily made in the studies of finance. Unless explicit mention is made, we maintain these assumptions throughout this work although some of them could be relaxed with little effort.
Erio Castagnoli, Marco Li Calzi

### A Definitions and results from stochastic calculus

Abstract
In the discussion above, we have made extensive use of some definitions and results from the theory of stochastic calculus. To disecumber our discussion from these technicalities, we have confined those which are less known in this section. For a more complete treatment see for instance Protter [3], whose notation is followed here. Let (Ω, ℱ, P, {ℱ t }) be a filtered complete probability space satisfying the usual conditions (see [3]). Given a stochastic process X on (Ω, ℱ, P) we write X t instead of X(t, ω) and X t for lim s↑t X(s, ω). Moreover, we define ΔX t = X t X t to be the jump at t. Finally, we set X0− = 0 by convention; remark however that we do not require X0 = 0.
Richard Flavell

### Stochastic Behaviour of European Stock Markets Indices

Abstract
This paper is concerned with modelling return generating processes in several European stock markets. Distributional properties of daily stock returns play a crucial role in valuation of contingent claims and mean-variance asset pricing models, as well as in their empirical tests. A common assumption underlying a considerable body of finance literature is that the logarithm of stock price relatives are independent and identically distributed according to a normal distribution with constant variance, while little attention is paid to the empirical fit of the postulated process. For instance, the mean-variance asset pricing models of Sharpe (1964) and the option pricing model of Black and Scholes (1973) are based on the assumption of normally distributed returns. Moreover, the normality assumption and the parameter stability are necessary for most of statistical methods usually applied in empirical studies.

### Measuring Firm/Market Information Asymmetry: The Model of Myers and Majluf or the Importance of the Asset Structure of the Firm

Abstract
This paper shows that measures of information asymmetry ought to be event-specific and model-specific in order to design correct tests of alternative models of information asymmetry. It shows that the traditional measures: volatilities, or residual volatilities, are not necessarily correct. The paper presents a correct measure of information asymmetry for the analysis of the equity issue process in the context of Myers and Majluf’s model. This measure is a function of the asset structure of the firm, and captures the volatility of the assets in place only. Some empirical evidence suggests that the distinction can matter empirically.
Nathalie Dierkens

### The Construction of Smoothed Forward Rates

Abstract
The concept that money due at some time in the future is worth less than money received today is fundamental to most financial analyses. Before such analyses may be performed, it is necessary to estimate a discount δ function such that
$${{\text{c}}_{\text{t}}}\,*\,{\delta _{\text{t}}}\, = \,{{\text{c}}_{\text{0}}}\,\forall \,{\text{t}}\, \geqslant \,{\text{0}}$$
(1)
where ct is cash at time t and c0 its value at time 0. Associated with the concept of a discount function is that of forward rates, ie. what rate of interest should be applied to ct over a time period (t’−t) to estimate the worth of the cash at time t’? The forward rate may be easily constructed from the discount function, namely
$${{\text{f}}_{{\text{t,t'}}}}\, = \,\left( {{\delta _{\text{t}}}/{\delta _{{\text{t'}}}}} \right)\, - \,1\,\forall \,{\text{t'}}\, \geqslant \,{\text{t}}$$
(2)

### An Index of De-stability for Controlling Shareholders

Abstract
This paper presents an index of de-stability for firms’ control groups, based on a game-theoretical approach.
Gianfranco Gambarelli

### On Imitation

Abstract
The main focus of this paper is on the construction of a micro-model of stock-market speculator consistent with the assumptions on imitative behaviour used in Ferrari-Luciano-Peccati (1990)1. Our work is partially related to Grossman - Stiglitz (1980).
M. L. Gota, L. Peccati

### Financial Factors and the Dutch Stock Market: Some Empirical Results

Abstract
A financial security represents a prospect to future receipts. The expected value of these receipts will be surrounded with risk. Hence, a financial security can be viewed as a claim on a specific but uncertain pattern of future cash flows, or equivalently as a particular distribution of risky future returns. Future cash flows (and thus the returns) to be received from a financial security will be influenced by economic events or ‘factors’. In this view, when buying a security, an investor is actually buying an exposure to these factors. In a factor model, this exposure is measured in terms of response coefficients or sensitivities of the security’s return for the factor movements. In giving economic content to factor models, one encounters the problems of how to identify and measure the factors (proxies) and how to measure the sensitivities.
Winfried G. Hallerbach

### A Present Value Approach to the Portfolio Selection Problem

Abstract
The traditional approach to the single-period portfolio problem is to assume that there is some given utility function such that an optimal portfolio can be found by maximizing expected utility (see, for example, [4]). However, the determination of such a utility function may cause substantial difficulties. This, in particular, holds for an investment company, which generally does not know the investors’ preferences or is able to aggregate them.
Klaus Hellwig

### Discounting When Taxes are Paid One Year Later: A Finance Application of Linear Programming Duality

Abstract
In connection with financial leases, one frequently ecounters the following valuation rule: Discount the after-tax lease payments and depreciation tax shields displaced by the lease at the company’s after-tax borrowing rate. This valuation rule, which assumes simultaneous taxes, was derived by Myers et al. (1976), Franks and Hodges (1978), and Levy and Sarnat (1979). It has since been applied by a number of authors, for instance Benninga (1989, pp. 39–66) and Brick et al. (1987). The same rule, to discount the after-tax amounts at the after-tax borrowing rate, has also been proposed for safe, nominal cash flows by Ruback (1986) and Brealey and Myers (1991, pp. 470–474). This rule follows very easily, if the problem of choosing between leasing or borrowing, or valuing a safe nominal cash flow, is posed as a linear programming (LP) problem (Jennergren 1990).
L. Peter Jennergren

### The Asset Transformation Function of Financial Intermediaries

Abstract
Financial intermediaries like commercial banks, savings banks, or savings and loan associations — we call them banks for short in the following — perform various kinds of intermediation functions in the capital market, e.g. pooling of supply and demand, providing market participants with arbitrarily sized loan or deposit volumes, supply of perfectly liquid investments, risk sharing, and asset maturity transformation. This paper focuses on the last issue, i.e. the transformation of market rate sensitive, short term liabilities (deposits) into fixed—rate, long term assets (loans). In the case of a normal (rising) yield curve, the usually resulting positive gap in the bank’s balance sheet — the volume of fixed—rate loan contracts exceeds that of fixed—rate liabilities — provides the bank with a positive net interest rate margin which is the main source of profits for most depository financial institutions. Besides this rather “classical” reasoning, more recent contributions ground the intermediaries’ asset transformation function on maturity preferences of credit customers (v. Furstenberg 1973), on trade-offs between different kinds of bank risk as, for example, interest rate risk vs. default risk (Santomero 1983, Kiirsten 1991), or on stochastic cumulation effects between market rates and future loan demand (Morgan/Smith 1987).
Wolfgang Kürsten

### Management of the Interest Rate Swaps Portfolio Under the New Capital Adequacy Guidelines

Abstract
The notional principal of interest rate swaps has exceeded \$3 trillion by the end of 1990. The massive explosion of this market over the recent years was inevitable to attract the attention of bank regulators and highlight the risks and formidable organisational and technical challenges encountered by banks engaged in the intermediation of interest rate swaps. The academic literature, however, has been dominated by issues concerning the underlying rationale of interest rate swap transactions and the complexities of pricing and hedging such transactions. With the notable exceptions of a recent paper by Cooper and Mello (1991) the issues related to the default risk of swaps still remain largely unexplored in the academic literature.
Mario Levis, Victor Suchar

### Developing a Multinational Index Fund

Abstract
Two approaches to portfolio selection from a multinational universe are described. The problem is addressed in the context of selecting a fund to track a multinational equity index such as Eurotrack 100. However, the results are general and can be applied whatever the objective of fund selection.

### Directional Judgemental Financial Forecasting: Trends and Random Walks

Abstract
In the volatile and rapidly changing financial environment human judgement is an essential ingredient in decision-making. Effective exchange rate and stock price forecasting not only require quantitative models but also the personal beliefs and views of a forecaster formed according to some subjective procedure. It is important, then, to understand how people involved in the financial world make judgements on currency or stock price movements. This paper reports an exploratory investigation of this issue undertaken with a sample of delegates at the 9th. Meeting of the Euro-Working Group on Financial Modelling at Curacao, Netherlands Antilles, in April 1991.
Andrew C. Pollock, Mary E. Wilkie

### Forecasting the Behaviour of Bankruptcies

Abstract
This paper explores the determinate of corporate failures in Finland. The analysis makes use of aggregate monthly time series for some financial and non-financial variables covering the period 1922-1990. It is partly based on some recent Finnish micro evidence on bankruptcies and partly on recent literature on the role of financial intermediation in the propagation of aggregate economic shocks. The empirical analyses indicate that bankruptcies constitute an important ingredient in terms of the determination of other variables. In particular, it turns out that overall liquidity and firm failures are closely related. We also find the basic relationships strikingly stable over long periods. Finally, we find some, although not very strong, evidence of non-linearities in the financial and non-financial time series.
Christian Starck, Matti Virén

### Theoretical Analysis of the Difference Between the Traditional and the Annuity Stream Principles Applied to Inventory Evaluation

Abstract
This paper compares consequences from a theoretical standpoint as to capital costs derived from two inventory evaluation principles. On the one hand, according to the traditional principle, physical inventory is valued at cost-incurred-to-date and the capital costs are then estimated as an interest charge on this average value. On the other hand, according to the annuity stream principle, the capital costs of inventory are obtained as the interest-dependent part of the annuity stream derived from the cash flow associated with the physical inventory build-up. Whereas the traditional approach attempts at approximating traditional accounting procedures, the annuity stream principle is in agreement with financial theory and it is therefore considered the superior of the two, since it implies that a coherent methodology is applied to the evaluation of capital used in any type of investment, whether it be inventory or other working capital, plant, equipment, or any other type of material or immaterial asset. The present inquiry highlights some theoretical issues concerning the differences between the two evaluation principles. It is shown how the first-order difference in capital costs depends on the fluctuation of profit around its long-run average.
Anders Thorstenson, Robert W. Grubbström

### A Micro-Simulation Model for Pension Funds

Abstract
In recent years there is a growing interest in the management of pension funds:
• The population in the developed countries is ageing. In countries where the pension rights are financed by means of a capitalization system, this implies for example that many pension funds, that had a contribution cash inflow that was larger than the current pension benefits, are now in the position that a part of the investment returns has to be used to pay the benefits. As a result a closer look at the contribution and pension benefit cash flows is necessary.
• The pension contributions are an important element of the total costs of the plan sponsor and of the difference between gross and net wage for the employees. They both prefer low and stable contributions. In this field there is a growing role for dynamic contribution systems, that try to smooth the contributions over time.
• Usually pension contributions are tax-deductable and this part of the income of employees is only taxed at the moment of the pension benefit: many years later and at a probably lower tax rate. Especially in countries with a large public debt, governments would like to accelerate this tax-levy.
Paul C. van Aalst, C. Guus E. Boender

### Asset Allocation and the Investor’s Relative Risk Aversion

Abstract
This paper addresses the issue of how an investor allocates his wealth among assets and examines the nature of the dependency of the portfolio selection on the willingness to take on extra risks. We focus on two two-asset allocation models where only the relative risk aversion is needed to establish the investor’s risk-return trade-off. A methodological comparison is made between Sharpe’s (1987) analysis concerning the two-asset allocation problem and the mean-variance approach, based on the second order Taylor series approximation.
Nico L. Van der Sar

### Financing Behaviour of Small Retailing Firms

Abstract
Many financing decisions have effects that stretch well into the future. Long term loans can cover periods of 5 to 10 years and contracts like mortgages may be concluded for periods of 30 years. As a consequence, the amounts presented in a financial statement at any point in time can be regarded as resultants of many decisions in the past. Analysing financial structure expressed in terms of these amounts may, to a certain extent, obscure the behaviour which induces changes in financial structure, i.e. obscure the effects of single decisions or decisions in a short period of time. This is particularly true if the changes are small compared with the observed amounts. Hence, many researchers have focussed on single decisions, like the choice between debt and equity in the issue of new securities [e.g. Baxter and Cragg (1970), Taub (1975), Marsh (1982)].
D. van der Wijst

### Computing Price Paths of Mortgage-Backed Securities Using Massively Parallel Computing

Abstract
We consider the problem of pricing fixed-rate mortgage-backed securities (abbreviated: MBS). In particular, we develop a model that tracks the price of MBS across time, but also under different scenarios of the term structure. Central to the developments of this paper is the use of massively parallel computing technology. The computational complexities of MBS, and the related pricing model, rendered them intractable on current workstations or large mainframes. The paper also develops practical procedures for the computation of the pricing model on massively parallel systems, like the Connection Machine CM—2.
Stavros A. Zenios, Raymond A. McKendall
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