Question

EXPECTED RETURN A stock’s returns have the following distribution: Demand for the Company’s Products Weak Below average Average Above average Strong Probability of this Demand Occurring 0.1 0.1 0.3 0.3 0.2 1.0 Rate of Return if this Demand Occurs (30%) (14) 11 20 45 Assume the risk-free rate is 2%. Calculate the stock’s expected return, standard deviation, coefficient of variation, and Sharpe ratio.

1Expected return = 0.1*(-30%) + 0.1*(-14%) + 0.3*(11%) + 0.3*(20%) + 0.2*(45%) = 13.90%

Standard deviation = Sqrt( 0.1*(-30%-13.9%)2 ​+ 0.1*(-14%-13.9%)2 ​+ 0.3*(11%-13.9%)2 ​+ 0.3*(20%-13.9%)2 ​+ 0.2*(45%-13.9%)2 ​) = Sqrt (4.78%) = 21.86%

Coefficient of variation = Standard deviation ​/ Expected return​ = 21.86%​ / 13.90 %​ = 1.57

Sharpe ratio ?

Answer 1

Expected Return = 0.10 * (-0.30) + 0.10 * (-0.14) + 0.30 * 0.11 + 0.30 * 0.20 + 0.20 * 0.45
Expected Return = 0.1390 or 13.90%

Variance = 0.10 * (-0.30 - 0.1390)^2 + 0.10 * (-0.14 - 0.1390)^2 + 0.30 * (0.11 - 0.1390)^2 + 0.30 * (0.20 - 0.1390)^2 + 0.20 * (0.45 - 0.1390)^2
Variance = 0.047769

Standard Deviation = (0.047769)^(1/2)
Standard Deviation = 0.2186 or 21.86%

Coefficient of Variation = Standard Deviation / Expected Return
Coefficient of Variation = 0.2186 / 0.1390
Coefficient of Variation = 1.57

Sharpe Ratio = (Expected Return - Risk-free Rate) / Standard Deviation
Sharpe Ratio = (0.1390 - 0.02) / 0.2186
Sharpe Ratio = 0.1190 / 0.2186
Sharpe Ratio = 0.54