Question 1 (35 %)

H.M.Arkowitz is a risk averse, rational investor and is considering building up a portfolio of assets. He can choose between two risky assets A and B, with

Asset i A B E(ri) in % p.a. 10 15

Correlation (ri) in % p.a. 12 22

The returns on these two risky assets are correlated with %(rA,rB) = 0.66. (a) H.M.Arkowitz can only invest in these two assets. Calculate the expected return, the volatility, and the portfolio

weights of the minimumvarianceportfolio, in case short sales are allowed.

(b) Assume the returns on these two risky assets are perfectly positively correlated, shortselling of risky assets is prohibited, and that there is the possibility to save or borrow at a riskfree rate of 2 % annually.

(b1) Calculate the portfolio weights, the expected return and the volatility of the tangency portfolio.

(b2) Assume H.M.Arkowitz is willing to accept an annual volatility of 3 %. Calculate the maximum return that H.M.Arkowitz can achieve in this case and determine the optimal portfolio weights.

(b3) Assume H.M.Arkowitz wants to attain an expected annual return of 14 %. Calculate the volatility and the composition of the portfolio he would have to invest in.