Question

James, a portfolio manager, would like to form the following portfolio between Microsoft and Coca-Cola:

            Expected return (%)      Standard Deviation (%) Weight

Microsoft                 28                          42                    0.4                  

Coca-Cola              12.5                         21                    0.6

The correlation between the two stocks is 0.5.

Now, suppose James can include the Treasury bills (T-bills) into his two-stock portfolio. The interest rate of the T-bills is 3.8%.

What is the Sharpe ratio of James’ portfolio?

For this question, please round up to the third decimal places.

Answer 1

	Expected Return	Standard Deviation	Weight
Microsoft	28%	42%	0.4
Coca-Cola	12.50%	21%	0.6

Correlation between two stocks = ρ = 0.5

Weight of Microsoft in the portfolio = w₁ = 0.4, Expected return on Microsoft = R₁ = 28%, Standard Deviation of Microsoft = σ₁ = 42%

Weight of Coca-Cola in the portfolio = w₂ = 0.6, Expected return on Coca-Cola = R₂ = 12.5%, Standard deviation of Coca-Cola = σ₂ = 21%

Expected return of the portfolio is calculated using the formula: E[R_P] = w₁*R₁ + w₂*R₂ = 0.4*28% + 0.6*12.5% = 18.7%

Variance of the portfolio is calculated using the formula:

σ_P² = w₁²*σ₁² + w₂²*σ₂² + 2*ρ*w₁*w₂*σ₁*σ₂ = 0.4²*(42%)² + 0.6²*(21%)² + 2*0.5*0.4*0.6*(42%)*(21%) = 0.028224 + 0.015876 + 0.021168 = 0.065268

Standard deviation of the portfolio is square root of variance

Standard Devaition of the portfolio = σ_P = 0.065268^1/2 = 0.255476026272525 = 25.5476026272525%

Risk-free rate = R_F = 3.8%

Sharpe's ratio is calculated using the formula:

Sharpe's ratio = (E[R_P] - R_F)/σ_P = (18.7% - 3.8%)/25.5476026272525% = 0.583224978773768

Answer -> Sharpe's ratio of portfolio = 0.583