Problem 12-14 Calculating Returns and Variability [LO1] You find a certain stock
ID: 2716057 • Letter: P
Question
Problem 12-14 Calculating Returns and Variability [LO1]
You find a certain stock that had returns of 13 percent, 12 percent, 25 percent, and 21 percent for four of the last five years. The average return of the stock over this period was 12.16 percent.
What was the stock’s return for the missing year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place, e.g., 32.1.)
What is the standard deviation of the stock’s returns? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
You find a certain stock that had returns of 13 percent, 12 percent, 25 percent, and 21 percent for four of the last five years. The average return of the stock over this period was 12.16 percent.
Explanation / Answer
Average Annual Return (AAR)
The average annual return (AAR) is the arithmetic mean of a series of rates of return.
How it works/Example:
The formula for AAR is:
AAR = (Return in Period A + Return in Period B + Return in Period C + ...Return in Period X) / Number of Periods
12.16 =(13+(-12) + 25 + 21+x)/5
x=13.8
Standard deviation
sum of squared deviations from the mean
Mean x =12.16
Return X X-x Squared deviation
13 0.84 0.7056
-12 -24.16 583.7056
25 12.84 164.8656
21 8.84 78.1456
13.8 1.64 2.6896
Sum of squared deviations =830.112
Average of squared deviations =830.112/5=166.022
Square root of average of squared deviations =12.88