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This editorial, the second of a two‐part series, proposes a new measure of risk for analyzing highly non‐normal (i.e. asymmetric and long‐tailed) random variables in the context of both investment and insurance portfolios. The proposed measure replaces the p‐norm‐based definition of “risk” – found wanting in Part 1 – with a cosine‐based alternative.

Just as p‐norm‐based risk measures were derived as generalizations of the standard deviation in Part 1, the paper now extend this approach to a cosine‐based risk measure. This involves computing the Fourier transform of the underlying random variable for a given frequency value. Methods for selecting an appropriate frequency are then discussed.

The cosine‐based risk measure provides an effective alternative to p‐norm‐based measures because the Fourier transform is always well defined, even for long‐tailed random variables. The frequency parameter necessary for the Fourier transform may be computed according to several interesting criteria, including the maximization of marginal Shannon information, as well as consideration of “Planck boundaries” in human cognition.

The editorial explores the use of cosine‐based measures in constructing a general definition of “risk” that is equally applicable to asymmetric and long‐tailed random variables as to normal random variables.

The purpose of this paper is to explore the roles of diversification, hedging, and a third risk‐reduction process – “pacification” – in risk finance.

After briefly reviewing the concepts of diversification and hedging, a simple mathematical model is offered for reducing the standard deviation of a portfolio of traditional “insurance” and/or other financial risks.

The findings show that: neither diversification nor hedging, by itself, can guarantee a reduction of a portfolio's standard deviation; diversification and hedging, taken together, are still insufficient to guarantee a reduction of a portfolio's standard deviation; but either diversification or hedging, taken together with pacification, is sufficient to guarantee a reduction of a portfolio's standard deviation.

The paper provides a simple mathematical model for diversification and hedging, and also quantifies a further risk‐reduction process (pacification).

The purpose of this editorial is to explore the usefulness of distinguishing between “risk” and “Knightian uncertainty.”

The paper presents a representative, insurance‐based model of Knightian uncertainty arising out of potential major structural changes (without historical precedent) in liability claim settlements. It then considers whether or not formal statistical forecasting and decision making are possible in this context.

For real‐world settings, it is found that a Bayesian statistical framework is sufficiently comprehensive to permit forecasting and decision making in the presence of Knightian uncertainty. The paper then shows that the Bayesian approach fails only if the sample space underlying the potential structural change is truly nonmeasurable.

It is argued that, under a Bayesian worldview, the distinction between risk and uncertainty is necessary only in highly abstract epistemological modeling.

A brief survey of the development of the study of risk and probability is given together with some basic observations on their application to insurance. This is followed with observations on the lack of appreciation of probability studies and an elementary feeling for probability by the public at large and a suggestion that the time is ripe for a new science museum involving basic economics and the exposition of the role of probability in finance.

The purpose of this paper (the first of two) is to consider measures of risk commonly used in the analysis of both investment and insurance portfolios, and argue that there is a need for more appropriate measures to capture the uncertainty inherent in non‐normal (i.e. asymmetric and/or long tailed) probability distributions.

In Part 1, the risk measures used most frequently in finance and insurance – i.e. the standard deviation (variance), value at risk, tail value at risk, default value, etc. – are reviewed and then the paper explores whether such measures are sufficient for all contexts, including those in which the subject random variable is characterized by asymmetry and/or long tails. As an alternative to conventional measures, the paper assesses the potential of a general p‐norm‐based definition of “risk”.

Virtually, all commonly used risk measures, even those designed specifically to capture the behavior of asymmetric randomness, require that the underlying random variable possess a finite variance, or at least a finite mean. To overcome such difficulties, the paper considers a general definition of “risk” based upon a quantity closely related to the p‐norm – the p‐mean of absolute‐centered deviations (of which the standard deviation is a special case) – and show that this approach yields a single, but degenerate, result for all distributions.

The paper explores the use of p‐norm‐based measures in constructing a general definition of “risk” that is equally applicable to asymmetric and long‐tailed random variables as to normal random variables.

The paper presents a treatment for the measurement and disclosure of market and credit risks in the context of capital adequacy regulation. The proposed approach is in conformity with the Basle Committee's latest proposal on risk measurement, and is based on the Value-at-Risk (VaR) methodology. This approach is applied to investments in close-end country funds of emerging markets. For 13 .such funds listed in the New York Stock Exchange during the period October 1994 to December 1997, the average VaR estimate is found to be well above the capital adequacy ratio of 8% required by most regulatory authorities and to be sensitive to the emergence of increased financial turbulence.

Multinational firms will engage in operational hedging only when both exchange rate uncertainty and demand uncertainty are present. Operational hedging is less important for managing short-term exposures, since demand uncertainty is lower in the short term. Operational hedging is also less important for commodity-based firms, which face price but not quantity uncertainty. For firms with plants in both a domestic and foreign location, the foreign currency cash flow generally will not be independent of the exchange rate. Consequently the optimal financial hedging policy cannot be implemented with forward contracts alone but can be implemented using foreign currency call and put options, and forward contracts.

This article discusses strategies in which taxpayers use derivatives to attain better tax treatment for hedge fund investments. In response to an early planning strategy, Congress enacted the constructive ownership rule of Section 1260. This measure's success has proved surprising, given the similarity of section 1260 to the constructive sale rule of section 1259; the latter rule, which targets a different use of derivatives in tax planning, has proved easy to avoid. Theoretically, either rule can be avoided through relatively modest changes in economic return. While this strategy is common for section 1259, it is much more difficult for section 1260 because securities dealers cannot supply the necessary derivative. Instead, taxpayers have sought tax-advantaged hedge fund returns through strategies involving insurance and offshore corporations.