| Summary: | 碩士 === 國立高雄第一科技大學 === 風險管理與保險所 === 92 === One of the most important aspects in asset allocation problems is the assumed probability distribution of future returns. In most theoretical and empirical works , a normal or lognormal distribution is usually assumed. Financial managers generally suppose normal distribution, even if extreme realizations usually have an higher frequency than results in the case of normally distributed returns.
One of the main characteristics of the normal distribution is that its tail decays exponentially toward zero; thus extreme realizations are very unlikely. However, this seems to contradict empirical findings on asset return, which state that these returns generally exhibit leptokurtic behaviour, i.e., have fatter tails than normal distribution. In particular, in the optimization problem, we assume that returns are generated by a multivariate Student-t, when in reality returns come from a multivariate distribution where each marginal is a Student-t with different degrees of freedom.
As is known from the safety first principle, the shortfall constraint reflects the investor typical desire to limit downside risk by putting a (probabilistic) upper bound on the maximum loss. Results obtained reveal that the optimal asset mixes involve less of the relatively safe cash and more of the risky assets, stocks and bonds, i.e., if the required shortfall return is lower, the effect is more pronounced.
Our results also show that the shortfall probability set by the financial manager plays a crucial role for the nature of the effect of leptokurtic asset returns. If the shortfall probability is set sufficiently high, using larger freedom degree of student-t for the leptokurtic asset return leads to overly prudent and therefore inefficient asset allocations. If the shortfall probability is sufficiently small, however, the use of larger freedom degree leads to unfeasible strategies if reality is fat-tailed.
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