Heavy-tail Sensitivity of Stable Portfolios
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This thesis documents a heavy-tailed 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 heavy-tailed. The motivation of this thesis is to study the effects of heavy-tailed 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 heavy-tailed 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 heavy-tail sensitivity analysis is performed in order to see how the optimal allocation changes as the heavy-tail coefficient is altered. In order to solve both problems, we use a mean-dispersion risk measure and a probability of loss risk measure. Our analysis is done for two-asset stable portfolios, one of the assets being risk-free, and one risky. The approach used involves changing the heavy-tail 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 risk-free 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 heavy-tail 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.
Cite this work
Marko Agatonovic (2010). Heavy-tail Sensitivity of Stable Portfolios. UWSpace. http://hdl.handle.net/10012/5427