投资组合理论的一道习题

bule601

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收藏 2012-12-21

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某一投资者的效用函数为U=E（r）-0.5Aσ2，E（r）为预期收益，σ为资产的风险标准差，A为常数。无风险资产收益率为7%，风险资产组合收益rp=15%，σp=22%，A=4。试问为使投资者效用最大化，风险资产和无风险资产分配的比例为多少？

注：效用函数中σ 后面的2为上标，rp=15%，σp=22% 里的p为下标

最佳答案

Chemist_MZ 查看完整内容

suppose you put x percent of your wealth on the risky asset, thus： E(r)=x*0.15+(1-x)*0.07 σ2=var(x*Rrisky+(1-x)*Rf)=var(x*Rrisy)=x^2*σp the question is converted into: max U=x*0.15+(1-x)*0.07-0.5*4*x^2*0.22 take f.o.c with respect to x, you can get the optimal weight.

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Chemist_MZ

2012-12-21 20:15:16

suppose you put x percent of your wealth on the risky asset, thus：

E(r)=x*0.15+(1-x)*0.07

σ2=var(x*Rrisky+(1-x)*Rf)=var(x*Rrisy)=x^2*σp

the question is converted into:

max U=x*0.15+(1-x)*0.07-0.5*4*x^2*0.22

take f.o.c with respect to x, you can get the optimal weight.