Question

Suppose that you have $1 million and the following two opportunities from which to construct a portfolio: a. Risk-free asset earning 11% per year. b. Risky asset with expected return of 26% per year and standard deviation of 34%. If you construct a portfolio with a standard deviation of 24%, what is its expected rate of return? (Do not round your intermediate calculations. Round your answer to 1 decimal place.) Expected return on portfolio I

Answer 1

Portfolio standard deviation=(Weight of risky asset)*(Standard deviation of risky asset)+(Weight of risky free asset)*(Standard deviation of risky free asset)
Now, the standard deviation of a risk free asset will be zero.
So, portfolio standard deviation=(Weight of risky asset)*(Standard deviation of risky asset)+(Weight of risky free asset)*0
=>Portfolio standard deviation=(Weight of risky asset)*(Standard deviation of risky asset)

Given that we need to construct a portfolio with standard deviation of 24%, so the equation reduces to:

24%=(Weight of risky asset)*(34%)
=>Weight of risky asset=24%/(34%)=0.705882353
Now, weight of risky free asset=1-Weight of risky asset=1-0.705882353=0.294117647

Expected rate of return of the portfolio=(Weight of risky asset)*(Expected return of risky asset)+(Weight of risky free asset)*(Expected return of risky free asset)
=(0.705882353)*(26%)+(0.294117647)*(11%)
=0.183529412+0.032352941
=0.215882353 or 21.6% (Rounded to 1 decimal place)

Answer: Hence, the expected return on the portfolio is 21.6%

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