A stock had returns of 5 percent 16 percent 18 percent and 1

A stock had returns of 5 percent, 16 percent, -18 percent, and 11 percent for the past four years. Based on this information what is the 99 percent probability range for any one given year? (Use the arithmetic mean)

Solution

Arithmetric Mean = (0.05 + 0.16 - 0.18 + 0.11)/4 = 0.14/4 = 0.035, or 3.5%

? = [{(0.05-0.035)² + (0.16-0.035)² + (-0.18-0.035)² + (0.11-0.035)²}x{1/(4-1)}]^0.5

= [0.0677/3]^0.5 = 0.0226^0.5 = 0.1502, or 15.02%

Lower bound of 99 percent range = 0.035 - (3 x .1502) = -0.4157, or -41.57%

Upper bound of 99 percent range = 0.035 + (3 x .1502) = 0.4857, or 48.57%