Download PDF by Greg N. Gregoriou (eds.): Advances in Risk Management

By Greg N. Gregoriou (eds.)

ISBN-10: 0230625843

ISBN-13: 9780230625846

ISBN-10: 1349285439

ISBN-13: 9781349285433

ISBN-10: 2652652672

ISBN-13: 9782652652677

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1) with P representing a set of scenarios and r the riskfree rate of interest. In − our framework, EPj [−X] is replaced by Pη− j , the jth row of Pη = −min{0, Pη} as each row of Pη corresponds to a regulator’s scenario. Note that each scenario represents a probability measure. However, the expected value of the portfolio across multiple scenarios is not computed by the regulator. Instead, the worst outcome across the scenarios defines the risk of a coherent risk measure. It is important to emphasize that coherent risk measures do not account for diversification.

To achieve this objective, we define risk on portfolio holdings, a domain conducive to having diversification reduce portfolio risk. We maintain an axiomatic structure and define the risk of a portfolio as its distance from the set of acceptable portfolios. More importantly, distance involves as many components as available assets, including but not limited to riskfree capital. As a consequence, derivative as well as insurance contracts become important tools for risk management. Thus, our approach conforms to market practice while its implementation involves quadratic programming, a technique with prior applications in finance originating from portfolio theory.

The two risky assets are negatively correlated. For emphasis, no probability measure is required for the occurrence of the two states as the regulator is not concerned with their likelihood. Instead, preventing insolvency in each scenario is the regulator’s task, which is entirely independent of the portfolio’s expected value across the scenarios. Indeed, the second risky asset resembles a put option on the first security. Furthermore, the market is complete since a portfolio weight of − 13 in the first asset combined with 4 3 of risk-free capital replicates the put option.

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Advances in Risk Management by Greg N. Gregoriou (eds.)

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