Question

You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 11 percent, –10 percent, 19 percent, 18 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 % b-1. Variance b-2. Standard deviation %

Answer 1

Solution
	Year	Stock Returns %
	1	11
	2	(10)
	3	19
	4	18
	5	10
		48
a.	Sum of the five years returns	=48
	Arithmetic average (Sum of returns/No. of years)	=48/5
		=9.6%
b-1.	Variance of Stock Returns
	Year	Stock Returns %	Returns-Arithmetic average		(Returns-Arithmetic average)^2
	1	0.11	0.014	(.11-.096)	0.000196	(0.014^2)
	2	-0.10	-0.196	(-.10-.096)	0.038416	(0.138416^2)
	3	0.19	0.094	(.19-.096)	0.008836	(0.008836^2)
	4	0.18	0.084	(.18-.096)	0.007056	(0.007056^2)
	5	0.10	0.004	(.10-.096)	0.000016	(0.000016^2)
		0.48			0.05452
	Variance	=(SUM(Return-Arithmetic average)^2)/n-1
		=.05452/(5-1)
		=0.01363
b-2.	Standard Deviation of the returns	=Square root of Variance
		=Square root of 0.01363
		=0.11675
		=11.67%