Question

Over the past six years, a stock produced returns of 21 percent, -18 percent, 2 percent, 11 percent, -1 percent, and 24 percent. Based on these six years, what range of returns would you expect to see 99 percent of the time?

A. -53.24 percent to 40.24 percent

B. -40.24 percent to 53.24 percent

C. -36.67 percent to 48.38 percent

D. -48.38 percent to 36.67 percent

E. -54.00 percent to 72.00 percent

Answer 1

Past Six years returns are 21%, -18%, 2%, 11%, -1% and 24%

Average Return = (0.21 + (-0.18) + 0.02 + 0.11 + (-0.01) + 0.24) / 6
Average Return = 0.065
Average Return = 6.50%

Variance = [(0.21-0.065)^2 + (-0.18-0.065)^2 + (0.02-0.065)^2 + (0.11-0.065)^2 + (-0.01-0.065)^2 + (0.24-0.065)^2] / 5
Variance = 0.12135 / 5
Variance = 0.02427

Standard Deviation = (0.02427)^(1/2)
Standard Deviation = 0.1558
Standard Deviation = 15.58%

99% Confidence Interval:

CI = [Average Return - 3 * Standard Deviation] to [Average Return + 3 * Standard Deviation]
CI = [6.50% - 3 * 15.58%] to [6.50% + 3 * 15.58%]
CI = -40.24% to 53.24%