You own a portfolio of 2 stocks, E(R
a
)=10%,
σ
a
=20%; E(R
b
)=15%,
σ
b
=25% and
ρ
ab
=1
Which of the following is most correct?
Portfolio return is 12.5%
Portfolio variance is 22.5%
It will be to your advantage to have as much of stock B in
your portfolio as possible since that will increase portfolio
return.
While
ρ
=1 reduces risk, it would be better to have
ρ
=0.
It is possible to create a portfolio of A and B with zero risk.
Answer a is correct only when the portfolio weights are .5 for stock A
and .5 for stock B.
In this case, portfolio return will be .5 x .1 + .5 x .15 = .125 or
12.5%.
At any other weights, the portfolio return will not be 12.5%.
Since the
problem doesn’t specify weights, answer a in incorrect.
Answer b is correct only if the portfolio weights are .5/.5 and the
correlation coefficient is +1, perfect positive correlation.
In this case, the portfolio
variance is x
1
2
σ
1
2
+ x
2
2
σ
2
2
+ 2x
1
x
2
ρ
12
σ
1
σ
2 = .5
2
*.2
2
+.5
2
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 Spring '08
 WHITE
 Finance, Correlation Coefficient, Probability theory, portfolio variance

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