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HW2_solution - Econ 4751 Solution to HW 2 Learning about...

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Econ 4751 Solution to HW 2 Learning about Return and Risk from the Historical Record 1 . (15’) A ) r = (1+R) / (1+I) - 1; 1.10% / 1.05% - 1 = 4.8%. B) 6.29%. C) i_norminal > i_inflation 2. (10’) A) (1.0125) 4 -1 = 5.09% B) (1+x/n)^n--- exp(x) 3. (15’) A) HPR = .30 (18%) + .50 (12%) + .20 (-5%) = 10.4% B) s = [.30 (18 - 10.4) 2 + .50 (12 - 10.4) 2 + .20 (-5 - 10.4) 2 ] 1/2 = 8.13% C) s = [.30 (18 - 10.4) 2 + .50 (12 - 10.4) 2 + .20 (-5 - 10.4) 2 ] = .6604% Risk Aversion and Capital Allocation to Risky Assets 4. (10’) A) U(c) = 0.21 - 4/2(0.16) 2 = 15.88%, highest utility of choices B) If you are risk neutral, your only concern is with return, not risk.
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5. (10’) A) For $100, (115 - 100)/100 = 15%; .15 = w 1 (.12) + (1 - w 1 )(.05); .15 = .12w 1 + .05 - .05w 1 ; 0.10 = 0.07w 1 ; w 1 = 1.43($100) = $143; (1 - w 1 )$100 = -$43. B) E(r p ) = .1 .1 = 5w + 12.4(1 - w); x = 0.32 (weight of T-bills); As composition of X and Y are .6 and .4 of P, respectively, then for 0.68 weight in P, the respective weights must be 0.41 and 0.27; where .6(.68) = 41%; .4(.68) = 27%
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