Question

Please show your calculations, no excel.

3. Suppose that there tots: 1, 2, 3 and 4. E(n) - E(ra) - E(ra) - E(ra) -08 and 010 0 = 0 ,20. Also, P2 .85.13 = .60 and 214 .45. Suppe that your portfolio consists of 2 assets and that you have decided to hold wet 1. What other we should you hold to minimize the risk of your portfolio? Find the weight of each weet, the expected return of the portfolio and its risk, op.

Answer 1

w Let us firest consider the portfolio with asset 1 and 2. 4 = 42 = 0.08, 6, = 02 = 0.2 = 8,2 = 67 -0.04, Piz= 0.85 het weight (w) is the preoportion of investment in asset 2 re. A-w) is the proper- tion of investment in asset 1, Now objective is to minimize portfolios variance sable and determine w. nie. Min var (P) = (1-w) 6²+w2 82 + 2 6-w) w 5,62 812 = (-30.04+ w?(0.04) + 2(1-w) w 0.2) (0-2)(0.85) = 0.04ſ (1-w) +w² +1.7(1-2)w] = 0.04(1+w²2wtw?+ 1.7 (w-w2)] = 0.04 [2w²QW +1.70-1.7Wh + 1] = 0.04 [0.3 wh-B-3 W +1] = 0.12 w²-0.12 +0.04 Focl avar (P) ão = 0.24 -0.12 = 0 = 0.24 W=0.12 = w=0.5 Weights of asset 1 and 2 arce 0.5 each. =%95)চা54_O৭ -) Var (P) = 65%6-29 +0.59 (0.2) + 2 (05)(0.5)(0:2)(0:2)(6-85) = 0.01 +0.01 +0.01*1.7) - 0.01(1+1+1.7)-0.01x3.7 -0.037 Similarly, considering minimization of variance of portfolio with asset i and 3 as well as 1 and 4 yields weights (proportions) of investment of each of the asset = 0.5. i.e. W=0.5 for each of the case. > Portfolio variance with asset 1 and 3 would be Var (P) -(0.5)40:21 +0.5) (0-2) +2005)(0.5)(0-2)(0-2)(0.6) -0.01 +0.01 +0.01*12) - 0.01(1+1+1.2) -0.0193.2 -0.032 and var (P), u = 0.01 +0.01 + (0.01x 0.9) = 0.01 [1+1+0.9] = 0.029 Weight on asset 1 is always 0.5 with any of the asset 213 or 4. Expected returen ob portfolio ], = 0.5(0.08)+0.510.08) = 0.08 Expected return of portfolio] 13 = 0.08 expected reeturen of poretfoled], u = 0.08 Portfolio Risk Op = √vare (P), 2 = 0.037 = 0.192 Op = Ivar (P/13 - Jo.032 = 0.179 EP O p = varc (P) = 10.029 = 0.170 Based on the lowest risk, the portfolio cwill have asset 4 with asset 1.