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%