Question

You find a certain stock that had returns of 16 percent, −9 percent, 23 percent, and 24 percent for four of the last five years. The average return of the stock over this period was 14.4 percent. a. What was the stock’s return for the missing year? (Do not round intermediate calculations and enter your answer as a percent rounded to 1 decimal place, e.g., 32.1.) b. What is the standard deviation of the stock’s returns? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

stock's returns = (0.16 - 0.09 + 0.23 + 0.24 + x) / 5 = 0.144

0.16 - 0.09 + 0.23 + 0.24 + x = 0.144 x 5

0.54 + x = 0.72

missing return (x) = 0.72 - 0.54 = 0.18 = 18%

variance = [(0.16 - 0.144)² + (-0.09 - 0.144)² + (0.23 - 0.144)² + (0.24 - 0.144)² + (0.18 - 0.144)²] / 5 = (0.000256 + 0.054636257 + 0.007396 + 0.009216 + 0.001296) / 5 = 0.014560051

standard deviation = √0.014560051 = 0.1207 = 12.07%