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

1. Complete Portfolio’s Expected Return:
2. Complete Portfolio’s Standard Deviation:
3. 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