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	39 %
Good	0.2	25 %
Ok	0.3	10 %
Level	0.2	7 %
Slump	0.2	-10 %

Coefficient of variation

Answer 1

The expected return of gold can be calculated by taking the sum of the product of probability and return for the states

The calculations are as shown below

Expected Return of Gold, E[r] = 11.30%

Variance can be calculated using the below formula

Variance = Probability of Boom State X (Expected Return for Portfolio - Expected Return for Boom State)² + Probability of Good State X (Expected Return for Portfolio - Expected Return for Good State)² +Probability of Ok State X (Expected Return for Portfolio - Expected Return for Ok State)²+Probability of Level State X (Expected Return for Portfolio - Expected Return for Level State)²+ Probability of Slump State X (Expected Return for Portfolio - Expected Return for Slump State)²

= 0.1 X (11.30% - 39%)² + 0.2 X (11.30% - 25%)² +0.3 X (11.30% - 10%)²+0.2 X (11.30% - 7%)²+ 0.2 X (11.30% - (-10%))²

= 0.1 X 0.07673+ 0.2 X 0.01877+0.3 X 0.00017+0.2 X 0.00185+ 0.2 X 0.04537

= 0.00767 + 0.00375 + 0.00005 + 0.00037 + 0.00907

= 0.02092

Variance = 0.02092

Standard Deviation = Square Root of Variance

= √ 0.02092

= 0.14464 = 14.46409%

Coefficient of Variation = Standard Deviation / Mean = Standard Deviation / Expected Return

= 14.46409% / 11.30% = 1.28001