This paper provides an analytical framework for dynamic portfolio strategies that are mean-variance efficient and subjected to a principal-guaranteed rate. Specifying a numeraire known as growth-optimal portfolio, we apply martingale method instead of dynamic programming approach to solve the optimal problem. Under the general assumptions of the price dynamics being a semi-martingale with finite expectation and variance, the efficient strategies are identified as a combination of put options on minimum norm portfolio and zero coupon bonds with the maturity of investment horizon. In the case of a single factor interest rate model, we derive the closed-form formula for optimal weights on securities. We conduct numerical simulations to illustrate the performance of the optimal strategies in the case of an economy comprising a stock index fund, a bond index fund and a money market account. In addition, for different investors with various interests like principal guaranted rate and investment horizon, we also show how investors ought to allocate their funds. / This paper provides an analytical framework for dynamic portfolio strategies that are mean-variance efficient and subjected to a principal-guaranteed rate. Specifying a numeraire known as growth-optimal portfolio, we apply martingale method instead of dynamic programming approach to solve the optimal problem. Under the general assumptions of the price dynamics being a semi-martingale with finite expectation and variance, the efficient strategies are identified as a combination of put options on minimum norm portfolio and zero coupon bonds with the maturity of investment horizon. In the case of a single factor interest rate model, we derive the closed-form formula for optimal weights on securities. We conduct numerical simulations to illustrate the performance of the optimal strategies in the case of an economy comprising a stock index fund, a bond index fund and a money market account. In addition, for different investors with various interests like principal guaranted rate and investment horizon, we also show how investors ought to allocate their funds.

由於許多資產報酬率的分配呈現厚尾的現象，因此，本文探討將最低報酬要求限制條件加入傳統的平均數╱變異數模型中，考慮在分配已知的情形下，假設資產報酬率的分配為t分配及常態分配，來求取最適的資產配置；在分配未知的情形下，利用古典Bootstrap法、移動區塊Bootstrap法及定態Bootstrap法的抽樣方法來模擬資產報酬率的分配形式，並利用模擬的資產報酬率分配求出最適的資產配置。 同時，本文亦探討資產配置在風險管理上的運用，當分配已知時，若對分配參數的估計正確，則使用的最低要求報酬率就是此資產配置的涉險值，反之，若對參數的估計錯誤時，會對資產配置產生很大的影響及風險管理上的不正確；當分配未知時，利用模擬方法來產生分配，則使用的最低要求報酬率可看成是此資產配置的涉險值。 實證部分選取資料分成本國及全球，研究發現對於何種分配或模擬方法的資產配置績效最好？沒有一定的結論。其原因是各種分配或模擬方法皆必須視資料的性質而定，因此，本論文的貢獻僅在建議使用厚尾分配及利用模擬方法，來符合資產報酬率呈現厚尾的現象，並利用此分配，以期在考慮最低報酬要求限制條件下的資產配置更為精確。 / The distributions of many asset returns tend to be fat-tail. This paper attempts to add the shortfall constraint in Mean-Variance Analysis. When the distribution is known, we find the optimal asset allocation under student-t distribution and normal distribution. On the other hand, we use Classical Bootstrap, Moving Block Bootstrap, and Stationary Bootstrap to stimulate the distribution of asset return, and to obtain the optimal asset allocation. We also examine the risk management of asset allocation. When we use the correct estimators of parameters under the known distribution, the threshold in shortfall constraint is the value-at-risk in asset allocation. Otherwise, if using the wrong estimators, we get the incorrect asset allocation and the improper risk management. When the distribution is unknown, using simulation to generate the distribution, the value-at-risk is the threshold. The empirical study is conducted in two parts, domestic and global asset allocation. The results cannot point out which distributions and simulations are suitable. They depend on the data’s property. The contribution of this paper is to introduce some methods to fit the fat-tail behavior of asset return in asset allocation.