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The market portfolio has an expected return of 12 % and a standard deviation of 10%. the
risk free rate is 5%. 1)What is the expected return on a well diversified portfolio with a
standard deviation of 7%? 2)What is the standard deviation of a well diversified portfolio
with an expected return of 20%?
Since a well-diversified portfolio has no unsystematic risk, this portfolio should like
on the Capital Market Line (CML). The slope of the CML equals:
SlopeCML= [E(RM) – rf] / M
where E(RM) = the expected return on the market portfolio
rf
= the risk-free rate
M
= the standard deviation of the market portfolio
SlopeCML= [E(RM) – rf] / M
= (0.12 – 0.05) / 0.10
= 0.70
a.
The expected return on the portfolio equals:
E(RP)
= rf + SlopeCML(P)
where
rf
P
E(RP) = the expected return on the portfolio
= the risk-free rate
= the standard deviation of the portfolio
E(RP)
= rf + SlopeCML(P)
= 0.05 + (0.70)(0.07)
= 0.99
= 9.9%
A portfolio with a standard deviation of 7% has an expected return of 9.9%.
b.
E(RP)
= rf + SlopeCML(P)
0.20 = 0.05 + (0.70)(P)
P
= (0.20 – 0.05) / 0.70
= 0.2143
= 21.43%
A portfolio with an expected return of 20% has a standard deviation of 21.43%.
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