Question

The expected return on the risky portfolio is 15%. The risk-free rate is 5%. The standard deviation of return on the risky portfolio is 22%. Tina constructed a complete portfolio from this risky portfolio and the risk-free asset. If her portfolio has an expected return of 12%, what is the standard deviation of her complete portfolio?

Answer #1

Suppose the weight of the risky portfolio is x, then the weight
of the risk free asset will be 1-x.

The expected return ofthe complete portfolio should be=x*15%
+(1-x)*5%

Given that the return on the portfolio with both the risky
portfolio and risk free asset is 12%

=>12%=x*15% +(1-x)*5%

=>12%=x*15% +5% -x*5%

=>12%=x*10% +5%

=>12% - 5% = x*10%

=>7% = x*10%

=>7%/10% = x

=>x=0.70

The standard deviation of a risk free asset is 0.

So, standard deviation of her complete portfolio=(Weight of the
risky portfolio)*(Standard deviation of return on the risky
portfolio)

=(0.70)*(22%)=0.1540 or 15.40%

**Answer: Hence, the standard deviation of the complete
portfolio is 15.40%**

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