Mean-variance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We describe in detail the interplay between objective and constraints in a number of single-period variants, including semivariance models. Particular emphasis is laid on avoiding the penalization of overperformance. The results are then used as building blocks in the development and theoretical analysis of multiperiod models based on scenario trees. A key property is the possibility of removing surplus money in future decisions, yielding approximate downside risk minimization.

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Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis

We study the pricing of collateralized debt obligations (CDOs) using an extensive new data set for the actively-traded CDX credit index and its tranches. We find that a three-factor portfolio credit model allowing for firm-specific, industry, and economywide default events explains virtually all of the time-series and crosssectional variation in CDX index tranche prices. These tranches are priced as if losses of 0.4, 6, and 35 percent of the portfolio occur with expected frequencies of 1.2, 41.5, and 763 years, respectively. On average, 65 percent of the CDX spread is due to firm-specific default risk, 27 percent to clustered industry or sector default risk, and 8 percent to catastrophic or systemic default risk. Recently, however, firm-specific default risk has begun to play a larger role.

An Empirical Analysis of the Pricing of Collateralized Debt Obligations

We use the information in collateralized debt obligations (CDO) prices to study market expectations about how corporate defaults cluster. A three-factor portfolio credit model explains virtually all of the time-series and cross-sectional variation in an extensive data set of CDX index tranche prices. Tranches are priced as if losses of 0.4%, 6%, and 35% of the portfolio occur with expected frequencies of 1.2, 41.5, and 763 years, respectively. On average, 65% of the CDX spread is due to firm-specific default risk, 27% to clustered industry or sector default risk, and 8% to catastrophic or systemic default risk.

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Preface Dominique Strauss-Kahn 1. Introduction Philip Daniel, Michael Keen Charles McPherson (IMF) Part 1: Conceptual Overview 2. Theoretical perspectives on resource tax design Robin Boadway (Queens University, Canada) and Michael Keen (IMF) 3. Principles of resource taxation for low-income countries Paul Collier (University of Oxford) Part 2: Sectoral Experiences and Issues 4. Petroleum fiscal regimes: Evolution and challenges Carole Nakhle (University of Surrey, UK) 5. International mineral taxation: Experience and issues Lindsay Hogan (Australian Bureau of Agricultural and Resource Economics) and Brenton Goldsworthy (IMF) 6.' Natural gas: Experience and issues Graham Kellas (Wood Mackenzie) Part 3: Special Topics 7. Evaluating fiscal regimes for resource projects: An example from oil development Philip Daniel, Brenton Goldsworthy, Wojciech Maliszewski, Diego Mesa Puyo (all IMF) and Alistair Watson 8. Resource rent taxes: A re-appraisal Bryan Land (World Bank) 9. State participation in the natural resources sectors: Evolution, issues and outlook Charles McPherson (IMF) 10. How best to auction natural resources Peter Cramton (University of Maryland) Part 4: Implementation 11. Resource tax administration: The implications of alternative policy choices 12 Resource tax administration: Functions, procedures and institutions Jack Calder 13. International tax issues for the resources sector Peter Mullins (Australian Tax Office) Part 5: Stability and Credibility 14. Contractual assurances of fiscal stability Philip Daniel (IMF) and Emil Sunley 15. Time consistency in petroleum taxation: Lessons from Norway Petter Osmundsen (University of Stavanger, Norway)

The Taxation of Petroleum and Minerals : Principles, Problems and Practice

A structural approach

A mean-variance equilibrium model is tested against data from the Italian bond market. General equilibrium models under uncertainty were first constructed by Allais [1] and Arrow [2]. The model tested is of the class formulated by Borch [3], on the basis of works by Markowitz [8] and Tobin [18], and developed further by Sharpe [17], Lintner [6] and Mossin [10]. The bonds used in the test are annuity bonds. These are bearer bonds in loans, where the loan is repaid by a constant amount per period in cover of repayment of capital and interest on the loan. A lottery is arranged before each payment date, in order to determine which bonds shall be redeemed by the forthcoming repayment of capital. The bonds not drawn for redemption then participate in the next lottery, which is held one period later. A sequence of such lotteries is arranged, until all bonds in the loan have been redeemed, and the full amount of capital in the loan has been repaid. An annuity bond thus has an uncertain maturity. Its probability of redemption on a future date is given by the repayment plan for the capital of the loan. The certainty alternative which is considered relevant to the investors is investment in Government bonds. With the market for Government bonds assumed to be in equilibrium, this property is used to take account of the time dimension of investment in the annuity bonds. The investors are then assumed to behave in accordance with the von Neumann and Morgenstern theory [11], and establish preferences over probability distributions of present wealth. Such a behavioural assumption was tested earlier in an experiment [15], and gives a reasonable description of investor behaviour. Italian data were chosen, because investors paid no taxes on income from capital gains and interest payments during the period studied.

Cornelius M. Schilbred

Papers

The market price of risk

North Sea oil taxes and the sharing of risk — a comparative case study