hw4_ak-1 - Solution to Problem Set 4 ECN 134 Finance...

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Solution to Problem Set 4 ECN 134 Finance Economics Prof. Farshid Mojaver Risk and Return 1. Let r x , r y , r z be returns of portfolios X,Y, and Z. (i) P(r x <0) = P(z<(0-5)/20) = P(z< -0.25) is greater than P(r y <0) = P(z<(0-7)/20) = P(z< -0.35), which in turn is greater than P(r z <0) = P(z<(0-5)/10) = P(z< -0.5). You can determine the rank order of the probabilities by the rank order of the z scores without looking at the table for the normal distributions since P(z<-0.25) > P(z<-0.35) > P(z > -0.5). (ii) Similarly, P(r x <5) = P(z<0); P(r y <5) = P(z<-0.1); P(r z <5) = P(z<0) and P(z<0) >P(z<-0.1). (iii) P(r x <10) = P(z<0.25); P(r y <10) = P(z<0.15); P(r z <10) = P(z<0.5). Clearly, P(z<0.5)> P(z<0.25) > P(z<0.15). (iv) No, since X has lower mean than Y with the same risk. (You can draw a graph in the (risk=μ, mean=σ) plane.) (v) Yes, if he is risk-lover. (vi) No, Z offers the same expected return but lower risk. 2. E(r) = [0.2 × (−25%)] + [0.3 × 10%] + [0.5 × 24%] =10% 3. E(r X ) = [0.2 × (−20%)] + [0.5 × 18%] + [0.3 × 50%] =20% E(r Y) = [0.2 × (−15%)] + [0.5 × 20%] + [0.3 × 10%] =10% 4. σ X 2 = [0.2 × (– 20 – 20) 2 ] + [0.5 × (18 – 20) 2 ] + [0.3 × (50 – 20) 2 ] = 592 σ X = 24.33% σ Y 2 = [0.2 × (– 15 – 10) 2 ] + [0.5 × (20 – 10) 2 ] + [0.3 × (10 – 10) 2 ] = 175 σ X = 13.23% 5. E(r) = (0.9 × 20%) + (0.1 × 10%) =19%
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hw4_ak-1 - Solution to Problem Set 4 ECN 134 Finance...

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