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Heavytail Sensitivity of Stable PortfoliosAgatonovic, Marko 24 August 2010 (has links)
This thesis documents a heavytailed analysis of stable portfolios. Stock market crashes occur more often than is predicted by a normal distribution,which provides empirical evidence that asset returns are heavytailed. The motivation of this thesis is to study the effects of heavytailed distributions of asset returns. It is imperative to know the risk that is incurred for unlikely tail events in order to develop a safer and more accurate portfolio. The heavytailed distribution that is used to model asset returns is the stable distribution. The problem of optimally allocating assets between normal and stable distribution portfolios is studied. Furthermore, a heavytail sensitivity analysis is performed in order to see how the optimal allocation changes as the heavytail coefficient is altered. In order to solve both problems, we use a meandispersion risk measure and a probability of loss risk measure. Our analysis is done for twoasset stable portfolios, one of the assets being riskfree, and one risky. The approach used involves changing the heavytail parameter of the stable distribution and finding the differences in the optimal asset allocation. The key result is that relatively more wealth is allocated to the riskfree asset when using stable distributions than when using normal distributions. The exception occurs when using a loss probability risk measure with a very high risk tolerance. We conclude that portfolios assuming normal distributions incorrectly calculate the risk in two types of situations. These portfolios do not account for the heavytail risk when the risk tolerance is low and they do not account for the higher peak around the mean when the risk tolerance is high.

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Heavytail Sensitivity of Stable PortfoliosAgatonovic, Marko 24 August 2010 (has links)
This thesis documents a heavytailed analysis of stable portfolios. Stock market crashes occur more often than is predicted by a normal distribution,which provides empirical evidence that asset returns are heavytailed. The motivation of this thesis is to study the effects of heavytailed distributions of asset returns. It is imperative to know the risk that is incurred for unlikely tail events in order to develop a safer and more accurate portfolio. The heavytailed distribution that is used to model asset returns is the stable distribution. The problem of optimally allocating assets between normal and stable distribution portfolios is studied. Furthermore, a heavytail sensitivity analysis is performed in order to see how the optimal allocation changes as the heavytail coefficient is altered. In order to solve both problems, we use a meandispersion risk measure and a probability of loss risk measure. Our analysis is done for twoasset stable portfolios, one of the assets being riskfree, and one risky. The approach used involves changing the heavytail parameter of the stable distribution and finding the differences in the optimal asset allocation. The key result is that relatively more wealth is allocated to the riskfree asset when using stable distributions than when using normal distributions. The exception occurs when using a loss probability risk measure with a very high risk tolerance. We conclude that portfolios assuming normal distributions incorrectly calculate the risk in two types of situations. These portfolios do not account for the heavytail risk when the risk tolerance is low and they do not account for the higher peak around the mean when the risk tolerance is high.

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