James is considering investing in security A that has offered average annual return of 12% and standard deviation of 18% and security B which has offered average annual returns of 10% and standard deviation of 14% in the recent past.

(a) If the correlation between A and B is 0.35, what is the least risky combination of these two assets?

(b) James does not mind taking excess risk provided he can earn an average return of 10% from the portfolio. The returns on 90-day T-bills are around 2.50% per annum. Assuming that James can borrow and lend at the risk-free rate of return, advise how much James should invest in the portfolio (comprising of security A and security B) and the risk-free asset so that the combination of risky portfolio and risk free asset provides 10% return. How much would be invested in security A, security B, and the risk free asset and what would be the risk of the new portfolio?