HW4sSSII09t

HW4sSSII09t - Solution to Problem Set 4 ECN 134 Finance...

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ECN 134 Finance Economics Prof. Farshid Mojaver Risk and Return 1 . You consider investing in one of three portfolios X, Y, or Z, for one year. The following matrix gives the means and standard deviations of annual returns in % for the three portfolios; annual returns are distributed normally: X Y Z Mean 5 7 5 Std. Dev. 20 20 10 Rank the three portfolios in order of the probability of i) the one-year return being negative, Ans) Let r x , r y , r z be returns of portfolios X,Y, and Z. 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) the one-year return being less than 5 %, Ans) 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) the one-year return being less than 10 %. (Hint) you do not need a table for the normal distribution to arrive at the correct answers to i) through iii) Ans) 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) Could you imagine a rational investor preferring X to Y? Ans) 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) Could you imagine a rational investor preferring X to Z? Ans) Yes, if he is risk-lover. vi) Could you imagine a risk-averse investor preferring X to Z? Ans) No, Z offers the same expected return but lower risk.

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HW4sSSII09t - Solution to Problem Set 4 ECN 134 Finance...

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