Question

Ben would like to invest in gold and is aware that the returns on such an investment can be quite volatile. Use the following table of states, probabilities, and returns and calculate the coefficient of variation for the investment? (Round intermediate calculations and answer to 5 decimal places, e.g. 0.07680.) Probability Return Boom 0.1 36 % Good 0.2 21 % Ok 0.3 8 % Level 0.2 3 % Slump 0.2 -8 %

Coefficient of variation ?

Answer 1

Mean = Probbailties * returns

Mean = 0.1*0.36 + 0.2*0.21 + 0.3*0.08 + 0.2*0.03 + 0.2*(-0.08)

Mean = 0.036 + 0.042 + 0.024 + 0.006 - 0.016

Mean = 0.092 or 9.2%

Standard deviation = [0.1(0.36 - 0.092)^2 + 0.2(0.21 - 0.092)^2 + 0.3(0.08 - 0.092)^2 + 0.2(0.03 - 0.092)^2 + 0.2(-0.08 - 0.092)^2]^1/2

Standard deviation = [0.007182 + 0.002785 + 0.000043 + 0.000769 + 0.005917]^1/2

Standard deviation = 0.129213 or 12.9213%

coefficient of variation = standard deviation / mean

coefficient of variation = 0.129213 / 0.092

coefficient of variation = 1.40449