Question

Year	Stock	House
2006	12%	30%
2007	5%	10%
2008	-10%	-5%
2009	5%	5%
2010	7%	10%
2011	15%	15%

Standard deviations are for stock and house respectively are :

• A. 7.66% 11.58%
• B. 0.66% 0.58%
• C. 8.66% 11.58%
• D. 8.66% 1.58%

Answer 1

Answer is 8.66% and 11.58%

Stock:

Expected Return = [0.12 + 0.05 + (-0.10) + 0.05 + 0.07 + 0.15] / 6
Expected Return = 0.34 / 6
Expected Return = 0.05667 or 5.667%

Variance = [(0.12 - 0.05667)^2 + (0.05 - 0.05667)^2 + (-0.10 - 0.05667)^2 + (0.05 - 0.05667)^2 + (0.07 - 0.05667)^2 + (0.15 - 0.05667)^2] / 5
Variance = 0.0375333 / 5
Variance = 0.0075067

Standard Deviation = (0.0075067)^(1/2)
Standard Deviation = 0.0866 or 8.66%

House:

Expected Return = [0.30 + 0.10 + (-0.05) + 0.05 + 0.10 + 0.15] / 6
Expected Return = 0.65 / 6
Expected Return = 0.10833 or 10.833%

Variance = [(0.30 - 0.10833)^2 + (0.10 - 0.10833)^2 + (-0.05 - 0.10833)^2 + (0.05 - 0.10833)^2 + (0.10 - 0.10833)^2 + (0.15 - 0.10833)^2] / 5
Variance = 0.0670833 / 5
Variance = 0.0134167

Standard Deviation = (0.0134167)^(1/2)
Standard Deviation = 0.1158 or 11.58%