Question

A. The return on treasury bills is 4%. The return on a mutual fund is normally distributed with a mean of 10% and a standard deviation of 20%. An investor forms a portfolio, P, by putting 70% of his money into the mutual fund and the remainder into treasury bills. Find the expected return on the investor's portfolio. B. Find the equation of the combination line. Find the standard deviation of the investor's portfolio. Find the standard normal deviate, Zº, corresponding to a portfolio return, Rp, of 20%. Find Prob(R) <0%). Find Prob(R> 25%) G. Find Prob(-10% <Rp < 15%). C.

Answer 1

1.
=70%*10%+30%*4%
=8.20%

2.
Let w be the weight in risky portfolio
=w*10%+(1-w)*4%
=4%+6%*w

3.
=70%*20%
=14%

4.
=(20%-8.20%)/14%
=0.84

5.
=Prob(R<0%)
=Prob(Z<(0%-8.20%)/14%)
=Prob(Z<-0.59)
=0.27903377

6.
=Prob(R>25%)
=Prob(Z>(25%-8.20%)/14%)
=Prob(Z>1.20)
=1-Prob(Z<1.20)
=1-0.88493033
=0.11506967

7.
=Prob(-10%<R<15%)
=Prob(R<15%)-Prob(R<-10%)
=Prob(Z<(15%-8.20%)/14%)-Prob(Z<(-10%-8.20%)/14%)
=Prob(Z<0.49)-Prob(Z<-1.30)
=0.68793305-0.09680048
=0.59113257