Quiz for Two-Asset Portfolio Given two assets with the following characteristics: E(RA) = 0.16 CA = 0.12 E(RB) = 0.06 OR = 0.06 PA. B =-0.50 a. What are the weights of A and B that would yield a minimum variance for the portfolio? What are the expected return, E(RMVP), and standard deviation. OMVP, of this minimum variance portfolio, MVP? (6 marks) Hints: @ =- (0) -201+07) or and @; =1-@ b. Suppose your client, Mr. X, is risk-averse with coefficient of risk aversion, A, equal to 8. The weights of A and B that would yield an optimal risky portfolio, R, with the highest utility are 0.7817 and 0.2183 respectively. What are the expected return, E(RR), standard deviation, OR, and utility level, UR. of this optimal risky portfolio, R? (6 marks) Hints: @, = [E(R. )- E(R, )I+ ALG; -GA,al Ao +0; -20 Aal =0.7817 @, =1-@, =0.2183 FIN4006-192081 I of 5c. According to the data given in question 2, the indifferent curve with maximum utility level is drawn in the below mean-variance plane. Draw the risky-asset investment opportunity set, the efficient frontier and various assets and portfolios according to the names in this question. Please FULLY label the diagram including the values of utility level, weights of A in various portfolios. (10 marks) Optimal portfolio without a risk free asset 20% Indifference curve of Mr. X 18% with A = B that touches the efficient frontier and U =_ 14% 12% 10%% 0% 0% 2% 3% 10% 12% d. Suppose there is a risk free asset available at 6%. The weights of A and B that would yield a market portfolio, M with the highest Sharpe ratio are 0.5 and 0.5 respectively. What are the expected return, E(RM), standard deviation, oM, Sharpe ratio, SRar, and utility level, UM, of this market portfolio, M? (8 marks) [E(R. )-R, 10; -[E(R.)-R,1 .. "TE(R.) R, 10; +[E(R.) R, 10; -[E(R. ) R, + E(R.)-R, IC.. -0.5 Hints: " =1-m. =0.5 FIN4006-192051 2 of 5e. Describe what will happen to the old efficient frontier when a risk free asset is available. Describe where the new efficient frontier will lie and draw it onto the diagram in c) above. What is the name of this new efficient frontier and what is the composition of portfolios that lie on this new efficient frontier? (8 marks) f. When there is a risk free asset available for Mr. X, what are the weights of market portfolio, M and risk free asset, RF, that would yield an optimal complete portfolio, C, with the highest utility? What are the expected return, E(Rc), standard deviation, or, and utility level, Uc, of this optimal complete portfolio, C? What are the composition of this optimal complete portfolio, C, in terms of assets RF, A and B? (12 marks) FIN4006-192081 3 of 5Hints: M = E(R )-Ry SR. and Or =1-@y AOM AOM Composition of C in terms of RF, A and B:......... g. If Mr. X is not allowed to borrow, which of the portfolios M. R and C would be optimal for him? Please explain. (5 marks) h. Please summarize the results in a) to f) above and fill in the below empty boxes. (Optional 0 mark] Expected Standard Utility Sharpe Weigh Weigh of B Weighi Weight Return Deviation Level Ratio of A of RF of M MVP NA Less than M Market Portiolio, M NA SON Optimal Risky Portlollol without Risk Free asset, R Less than M 21.83T Optimal Complete Portfolio with Risk Free Bama as M - End of Section 2 - FIN4006-192081 4 of 5
