Question

need help with number 6

5. Suppose Ki and K, have the following distribution: Scenario Probability return Ki return K, wi -10% 10% 0.4 0% 20% W3 0.3 20% -10% 0.3 وليد (a) (b) (c) Find the risk of the portfolio with wu = 30% and W2 = 70%. Find the risk of the portfolio with w1 = 50% and w2 50% Which of the portfolios above (in part (a) and (b)), has higher expected returns? 6. Using the data in problem 5, compute the weights in the portfolio with mini- mum risk. What are the expected return and risk of this minimum risk portfolio?

Answer 1

SOLUTION:

Solution :- Given that, Scenario probability return to retwin Ke -10% 10% 0% 20% 20 % -10% wi 0.3 ولا 0.4 W3 0.3 x= returns from ki from ke = returns Scenario P/ xy. Px|py|DX| DY | PDX²|PDY² 50.7 1.2 0.3 40 10-3 3 -13 a 3.6 576 2 0:40 20 08-31 10.3/20 - 10 6 1-3 3. 17-18 86:7 972 E(x) ECY) V(x)= y) = eu ll 3 8 141 156, EQ) = Expected value of x and Similarly ECY)= Expected value of y. NCX) = Variance Variance of X

For this first calculate Dx values x Values E(x) ine, -10-3 = -13..-- 0-3 = -3....20-3 =17 Now, PDX² prob * DX * DX.......0.30*(-3)*(-13) 50.7 ...., 0.40 * (-3) (-3) = 316. WX weight of funds invested in ki WY weight of funds invested in Ky - and wx+ Wy = 1 (As pea, two only assets Variance of a portfolios a = wird + we z there are 2 Wy² + 156 141 + wy² WX? * 141+ (1 - Wy) * 156 e kix? * 141 + (WX2-220X+1) * 156 2 Wx? * 140+ WX?* 156 -312 WX + 156 al 397 WX?- 312 WX + 156 - Derive with respect to wx = 594 WX-312

Now put Derivate = 0 ( For minimum Varance nce) 594 WX - 312 =0 WX = 3121594. = 0.53 WY=1-WX = 1 - 0.53 = 0.47 Now final requirements of the question E(0) = Expected return on portfolio Elx) *0:53+ ELY) * 0.43 = 7 *0.53 + 2 * 0.47 5.35 2 Risk Squawor root over - Squar zoot Ovew 297 WXP-312WX + 156 with W X = 0.53 Square root ovew 74.0673 = 8.61%.
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