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 oneyear 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<(05)/20) = P(z< 0.25) is greater than
P(r
y
<0) = P(z<(07)/20) = P(z< 0.35), which in turn is greater than
P(r
z
<0) = P(z<(05)/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 oneyear 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 oneyear 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 risklover.
vi)
Could you imagine a riskaverse investor preferring X to Z?
Ans) No, Z offers the same expected return but lower risk.
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 Summer '08
 MOJAVER
 Economics

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