Question

1. Security X has the following historical returns.

Year	Return
1	10%
2	5%
3	-8%
4	7%

1. What is the average return of security X (arithmetic return)? (5 points)

2. What is the standard deviation of security X? (5 points)

3. What range of returns would you expect to see 95% of the time for this security? (5 points)

4. What is the geometric return of security X? (5 points)

Answer 1

Answer 1.

Average Return = [0.10 + 0.05 + (-0.08) + 0.07] / 4
Average Return = 0.14 / 4
Average Return = 0.035 or 3.50%

Answer 2.

Variance = [(0.10 - 0.035)^2 + (0.05 - 0.035)^2 + (-0.08 - 0.035)^2 + (0.07 - 0.035)^2] / 3
Variance = 0.0189 / 3
Variance = 0.0063

Standard Deviation = (0.0063)^(1/2)
Standard Deviation = 0.0794 or 7.94%

Answer 3.

95% Range of Return = Average Return - 2 * Standard Deviation, Average Return + 2 * Standard Deviation
95% Range of Return = 3.50% - 2 * 7.94%, 3.50% + 2 * 7.94%
95% Range of Return = -12.38%, 19.38%

Answer 4.

Geometric Return = [(1 + 0.10) * (1 + 0.05) * (1 - 0.08) * (1 + 0.07)]^(1/4) - 1
Geometric Return = 1.136982^(1/4) - 1
Geometric Return = 1.0326 - 1
Geometric Return = 0.0326 or 3.26%