Question

you manage a portfolio of stocks with an expected return of 12% and a standard de...

you manage a portfolio of stocks with an expected return of 12% and a standard de of 16%. Additionally, you have available a risk free asset with a return of 4.5%.

a) your client wants to invest a proportion of her total investment in your risky portfolio to provide an expected rate of return on her overall portfolio equal to 8%should she in the risky portfolio P, and what proportion in the risk free asset?

b) what will be the standard deviation of the rate of return on her portfolio?

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Answer #1

a

Expected return of Portfolio = Weight of Stock portfolio*Expected return of Stock portfolio+Weight of Risk free asset*Expected return of Risk free asset
8 = 12*Weight of Stock portfolio+4.5*(1-weight of Stock portfolio)
Weight of Stock portfolio = 0.467

Weight in risk free asset = 1-Weight of Stock portfolio = 1-0.467=0.533

b

Std dev of Portfolio = Weight of Stock portfolio*Std dev of Stock portfolio+Weight of Risk free asset*Std dev of Risk free asset
Std dev of Portfolio = 16*0.467+0*0.533
Std dev of Portfolio = 7.472
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