You have $10 million invested in long-term corporate bonds. This bond portfolios expected annual rate of return is rB = 9%, and the annual standard deviation is B = 10%. You are recommended to consider investing in a mutual fund. The mutual fund has an expected return of rM = 14%, and its standard deviation is M = 16%.

1) Suppose you put all your money in a combination of the index fund and Treasury bills. Can you thereby improve your expected rate of return without changing the risk (as measured by the standard deviation) of your portfolio? The Treasury bill yield is rf = 6% and it has zero risk.

2) Could you do even better by investing equal amounts in the corporate bond portfolio and the mutual fund? The correlation coefficient between the bond portfolio and the fund is 0.1.

3) You are now choosing between two stocks. One has the expected return of r1 = 20% and the standard deviation of 1 = 25%, while the second stock has the expected return of r1 = 12% and the standard deviation of 1 = 12%. If the Treasury bill is the risk-free rate, which stock would you choose?

Please show all steps and formula used. Thank you :)