Question

The rates of return on Cherry Jalopies, Inc., stock over the last five years were 10 percent, 11 percent,-5 percent, 4 percent, and 8 percent. Over the same period, the returns on Straw Construction Company's stock were 16 percent, 18 percent,-4 percent, 1 percent and 16 percent. Calculate the variances and the standard deviations for Cherry and Straw. (Do not round intermediate calculations. Enter your variance as a decimal rounded to 5 decimal places. Enter your standard deviation as a percent rounded to 2 decimal places.) Cherry Straw Variance Standard deviation

Answer 1

Cherry:

Average return=Total return/Total time period

=(10+11-5+4+8)/5=5.6%

Return	(Return-Average Return)^2
10	(10-5.6)^2=19.36
11	(11-5.6)^2=29.16
-5	(-5-5.6)^2=112.36
4	(4-5.6)^2=2.56
8	(8-5.6)^2=5.76
	Total=169.2%

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

=[169.2/(5-1)]^(1/2)

=[169.2/4]^(1/2)

=6.50%(Approx)

Variance=Standard deviation^2

=0.00423

Straw:

Average return=Total return/Total time period

=(16+18-4+1+16)/5=9.4%

Return	(Return-Average Return)^2
16	(16-9.4)^2=43.56
18	(18-9.4)^2=73.96
-4	(-4-9.4)^2=179.56
1	(1-9.4)^2=70.56
16	(16-9.4)^2=43.56
	Total=411.2%

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

=[411.2/(5-1)]^(1/2)

=[411.2/4]^(1/2)

=10.14%(Approx)

Variance=Standard deviation^2

=0.01028

	Cherry	Straw
Variance	0.00423	0.01028
Standard deviation	6.50%	10.14%(Approx).