金融经济学问题

1。There are a portfolio consisting of two assets XA, and XB, with expected return and standard deviation（9%，13%） and （11%，16%）, correlation ρ=-1. Calculate risk-free rate and the risk-free portfolio with proportion xa and xb
2。
The risk-free rate is 5%, and the market portfolio of risky securities has the expected rate of return 13% and standard deviation 20%. Assume you can lend or borrowing money in risk-free rate.
（1）Write out the efficient set of portfolio with risk-free asset (in the form of function).
（2）What will the efficient set change if the interest rate of borrowing is 6% and lending is still risk-free rate? Describe graphically.

3。
Assume you are in an isolated island where storage is the only investment opportunity. There is no capital market. Given the utility function U (C0, C1) =ln C0+βln C1, and the endowment (y0, y1). Describe two period utility-maximized decision of consumption (C0, C1)。





请问这些题怎么做？

王江那本书的题吗、
？

当p=1,sigmaA<sigmaB时，可以使得sigma最小为0，及存在无风险资产组合（risk-free portfolio），无风险权重分别为wA=-sigmaB/(sigmaA-sigmaB)=-16%/(13%-16%)=5.33，即买进5.33份资产B，
wB=sigmaA/(sigmaA-sigmaB)=13%/(13%-16%)=-4.33，即卖空4.33份资产A
risk-free rate=u=(sigmaA*uB-sigmaBuA)/(sigmaA-sigmaB)=(13%*11%-16%*9%)/(13%-16%)=0.0033=0.33%
相信我，我们这学期学的数理金融，而且这是一般讲CAPM书上都会教的

当p=1,sigmaA<sigmaB时，可以使得sigma最小为0，及存在无风险资产组合（risk-free portfolio），无风险权重分别为wA=-sigmaB/(sigmaA-sigmaB)=-16%/(13%-16%)=5.33，即买进5.33份资产B，
wB=sigmaA/(sigmaA-sigmaB)=13%/(13%-16%)=-4.33，即卖空4.33份资产A
risk-free rate=u=(sigmaA*uB-sigmaBuA)/(sigmaA-sigmaB)=(13%*11%-16%*9%)/(13%-16%)=0.0033=0.33%
相信我，我们这学期学的数理金融，而且这是一般讲CAPM书上都会教的