Rethinking risk and return: Part 1 – novel norms for non-normality?
Michael R. Powers
Purpose – 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. Design/methodology/approach – 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”. Findings – 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. Originality/value – 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.
Financial risk, Normal distribution, Portfolio investment, Probability theory, Return on investment
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