不确定条件下的资产配置问题无论对于学术研究还是投资行为都具有重大的理论和实际意义。本文选取广义范围上的现金、股票、债券作为投资者进行资产配置的产品,在CRRA(Constant Relative Risk Aversion)和HARA(Hyperbolic Absolute Risk Aversion)两种偏好假设下,分别求出了投资者效用最大化时的最优财富以及最优资产组合中各资产的权重,并比较分析了两种偏好假设下通货膨胀、风险偏好、投资期限三种因素对资产配置的影响。研究结论表明:通货膨胀会影响股票和债券的风险溢价,进而影响最优资产组合中各资产的权重;股票的权重不会受投资期限的影响,在通货膨胀率和风险偏好不变时,其值始终为一常数,但债券和现金的权重则由投资期限、通货膨胀和风险偏好共同决定;此外,在CRRA和HARA偏好假设下,以上三种因素对资产配置的影响存在较大差异,特别是在HARA框架下存在买空行为。
Abstract:Asset allocation problem in the condition of uncertainty is both important for academic research and individual investment.The traditional approach to asset allocation relies on Markowitz's paradigm which provides an elegant mathematical framework of an optimal asset allocation.Then Merton lays the foundation for dynamic asset allocation who considers an expected utility approach to study the optimal portfolio in a continuous time framework which is a breakthrough for modern finance theory.Cash, stock and bond in the generalized definition have been selected in this paper which are the most important three assets for investors and we obtain the optimal wealth and optimal portfolio weights of investors in the CRRA and HARA framework.The portfolio choice of a power utility that investors can maximize expected utility of wealth at a given investment horizon is considered.Closed form solutions are obtained in a dynamic portfolio optimization model.Also, the effects of inflation, risk preference, investment horizon on the asset allocation are analyzed.The results indicate that inflation which has an effect on the risk premium of stock and bond will finally influence the weights of them in the optimal portfolio.The weight of stock is not determined by the investment horizon, and the value is a constant when the inflation rate and risk preference are not changed.While the weight of bond and cash is determined by investment horizon, inflation rate and risk preference.In addition, the factors have great different influences on the asset allocation in the framework of CRRA and HARA.Especially, short sale will happen in the framework of HARA.
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