Question

Consider a risky asset with an expected return of 12% and
standard deviation of 16%. Assume that the risk free rate is 3%,
and that you allocate 70% in the risky asset and the remaining in
risk-free T-Bill. Calculate the following: **show all
formulas and calculations**

**Complete Portfolio’s Expected Return:****Complete Portfolio’s Standard Deviation:****Risky asset’s Sharpe ratio:**

**Complete Portfolio’s Sharpe ratio:**

Answer #1

a). Portfolio's Expected Return = [Weight(Risky) * Return(Risky)] + [Weight(risk-free) * Return(risk-free)]

= [0.70 * 16%] + [0.30 * 3%] = 11.20% + 0.90% = 12.10%

b). Portfolio's Standard Deviation = [{Weight(Risky) * (Expected
Return - Return(Risky))^{2}} + {Weight(risk-free) *
(Expected Return -
Return(risk-free))^{2}}]^{1/2}

= [{0.7 * (12.10% - 16%)^{2}} + {0.3 * (12.10 -
3.00%)^{2}}]^{1/2}

= [10.647%^{2} + 24.843%^{2}]^{1/2} =
[35.49%^{2}]^{1/2} = 5.96%

c). Sharpe Ratio = [Expected Return - Risk-free Rate] / Standard Deviation

= [12.10% - 3%] / 5.96% = 9.10% / 5.96% = 1.53

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