Question

50% invested in stock A and 50% invested in stock B. the following table, and the fact that the correlation of A and B is 0.47, calculate the volatility (standard deviation) of a portfolio that Using the data Realized Returns Stock B Stock A Year - 5 % 19% 2008 35% 8% 2009 7% 8% 2010 -9% -2% 2011 -14 % 2% 2012 27% 12% 2013 . (Round to two decimal places.) The standard deviation of the portfolio is

Answer 1

Stock A

Year	Return(%)	Deviation form expected return (D)	D^2
2008	(5.00)	(8.83)	77.97
2009	8.00	4.17	17.39
2010	8.00	4.17	17.39
2011	(2.00)	(5.83)	33.99
2012	2.00	(1.83)	3.35
2013	12.00	8.17	66.75

Expected Return = Sum of returns/No. of returns

= (-5+8+8-2+2+12)/6

= 23/6

= 3.83%

Variance = ${\sum }$D^2/n-1

= (77.97+17.39+17.39+33.99+3.35+66.75)/5

= 216.83/5

= 43.366

Standard Deviation = $\sqrt{}$Variance

= $\sqrt{}$43.366

= 6.59%

Stock B

Year	Return(%)	Deviation form expected return (D)	D^2
2008	19.00	8.17	66.75
2009	35.00	24.17	584.19
2010	7.00	(3.83)	14.67
2011	(9.00)	(19.83)	393.23
2012	(14.00)	(24.83)	616.53
2013	27.00	16.17	261.47

Expected Return = Sum of returns/No. of returns

= (19+35+7-9-14+27)/6

= 65/6

= 10.83%

Variance = ${\sum }$D^2/n-1

= (66.75+584.19+14.67+393.23+616.53+261.47)/5

= 1936.83/5

= 387.366

Standard Deviation = $\sqrt{}$Variance

= $\sqrt{}$387.366

= 19.68%

Portfolio Standard Deviation = [(WA*SDA)^2 + (WB*SDB)^2 + (2*WA*WB*SDA*SDB*CorAB)]

where

WA - Weight of stock A =.5

WB - Weight of stock B =.5

SDA - Standard Deviation of stock A = 6.59

SDB - Standard Deviation of stock B =19.68

CorAB - Correlation coefficient = .47

Portfolio Standard Deviation = [(.5*6.59)^2 + (.5*19.68)^2 + (2*.5*.5*6.59*19.68*.47)]

= [10.857025+96.8256+30.477432]

= 138.160057

= 11.75%

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