You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 14 percent, –7 percent, 17 percent, 15 percent, and 10 percent.

Problem 12-9 Calculating Returns and Variability [LO1]

You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 14 percent, –7 percent, 17 percent, 15 percent, and 10 percent.

a.	What was the arithmetic average return on Crash-n-Burn’s stock over this five-year period? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place, e.g., 32.1.)

Average return

%

b-1	What was the variance of Crash-n-Burn’s returns over this period? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)

Variance

b-2	What was the standard deviation of Crash-n-Burn’s returns over this period? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation

%

 

Explanation:

a.

To find the average return, we sum all the returns and divide by the number of returns, so:

Average return = (.14 – .07 + .17 + .15 + .10) / 5

Average return = .098, or 9.8%

b.

Using the equation to calculate variance, we find:

Variance = 1/4[(.14 – .098)2 + (–.07 – .098)2 + (.17 – .098)2 + (.15 – .098)2 + (.10 – .098)2]

Variance = .00947

  

So, the standard deviation is:

Standard deviation = (.00947)1/2

Standard deviation = .0973, or 9.73%