Question

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: 16 percent, –5 percent, 19 percent, 13 percent, and 10 percent.

a.	What was the arithmetic average return on the company’s stock over this five-year period? (Do not round intermediate calculations and enter your answer as a percent rounded to 1 decimal place, e.g., 32.1.)
b-1.	What was the variance of the company’s returns over this period? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., .16161.)
b-2.	What was the standard deviation of the company’s returns over this period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	a. Average return 10.6 % b-1. Variance b-2. Standard deviation 9.34 %

I have tried several different methods to find the variance and cannot come up with the correct answer. Most of the solved attempts for this question give the variance as a percentage, however this is not what this question is asking.

Answer 1

Average return=Total return/Total time period

=(16-5+19+13+10)/5=10.6%

Return	(Return-Average return)^2
16	(16-10.6)^2=29.16
-5	(-5-10.6)^2=243.36
19	(19-10.6)^2=70.56
13	(13-10.6)^2=5.76
10	(10-10.6)^2=0.36
	Total=349.2%

Standard deviation=[Total (Return-Average return)^2/(Time period-1)]^(1/2)

=[349.2/(5-1)]^(1/2)

=[349.2/4]^(1/2)

=9.34%(Approx).

Variance=Standard deviation^2

=0.00873