Suppose that the world\'s economy consists of only two risky assets (XOM and INT

Question

Suppose that the world's economy consists of only two risky assets (XOM and INTC) and one risk-free asset (F). The risk-free rate is currently 5%. The possible risky asset returns are described below:

Suppose that you are a wealth manager for a client with the type of utility function described in class where her risk aversion is A = 2.

a) What are the expected returns and volatilities of XOM and INTC? What is their correlation?

b) If your client can purchase only a single asset (i.e., XOM only, INTC only or F only), which asset would your client prefer? (Hint: compare client's utilities)

c) Would your client prefer a portfolio (call it E) consisting of 50% XOM and 50% INTC to the asset that you identified in part (b)? (Hint: compare client's utilities)

Explanation / Answer

a>Return of XOM=0.2*10+0.2*(-10)+0.4*20+0.20*(-5) 7 Return of INTC=0.2*(-30)+0.2*(-5)+0.4*15+0.2*50 9 Variance of XOM=0.2*(10-7)^2+0.2*(-10-7)^2+0.4*(20-7)^2+0.2*(-5-7)^2 156 SD=Square Root(156) 12.49 Variance of INTC=0.2*(-30-9)+0.2*(-5-9)^2+0.4*(15-9)^2+0.2*(50-9)^2= 382 SD=Square Root(382) 19.54 Covariance=0.2*(10-7)*(-30-9)+0.2*(-10-7)*(-5-9)+0.4*(20-7)*(15-9)+0.2*(-5-7)*(50-9) -43 Corelation=Covariance/(SD of XOM * SD of INTC)=-43/(12.49*19.54) -0.176 b> XOM has a lower risk as the SD is 12.49. So the client should invest in XOM. c>Return=(7+9)/2 8 Variance =(0.5^2)*(156)+(0.5^2)*382+2*0.5*0.5*12.49*19.54*(-0.176) 113.02 SD=Square Root(113.02) 10.63 Yes, The Return is higher and SD is lower than XOM. So this is a better option.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.