Question

Using the data in the following​ table, and the fact that the correlation of A and B is 0.39​, calculate the volatility​ (standard deviation) of a portfolio that is 70% invested in stock A and 30% invested in stock B.

Realized Returns
Year	Stock A		Stock B
2008	−8​%		27​%
2009	17​%		28​%
2010	1​%		11​%
2011	−3​%		−2​%
2012	1​%		−3​%
2013	8​%		26​%

The standard deviation of the portfolio is _%?

Answer 1

SD of Stock = SQRT [ [ Sum [ (X- Avg X)^2 ] / n ]

AVg = SUm [ Ret ] / n

Avg A = [ -8% + 17% +1% - 3% +1% +8% ] / 6

= 16% / 6

= 2.67%

Avg B = [ 27% +28% +11% - 2% -3% +26% ] / 6

= 87% / 6

= 14.5%

SD of Stock A:

Year	Ret (X)	( X - Avg X)	( X - Avg X)^2
2008	-8.00%	-0.1067	0.0114
2009	17.00%	0.1433	0.0205
2010	1.00%	-0.0167	0.0003
2011	-3.00%	-0.0567	0.0032
2012	1.00%	-0.0167	0.0003
2013	8.00%	0.0533	0.0028
Sum [ (X - AvgX)^2 ]			0.0385
Sum [ (X - AvgX)^2 ] / n			0.0064
SQRT [ Sum [ (X - AvgX)^2 ] / n ]			0.0801

SD of STock A is 8.01%

SD of Stock B:

Year	Ret (X)	( X - Avg X)	( X - Avg X)^2
2008	27.00%	0.125	0.0156
2009	28.00%	0.135	0.0182
2010	11.00%	-0.035	0.0012
2011	-2.00%	-0.165	0.0272
2012	-3.00%	-0.175	0.0306
2013	26.00%	0.115	0.0132
Sum [ (X - AvgX)^2 ]			0.1062
Sum [ (X - AvgX)^2 ] / n			0.0177
SQRT [ Sum [ (X - AvgX)^2 ] / n ]			0.1330

SD of Stock B is 13.30%

Portfolio SD:

Given Details
Particulars	Amount
Weight in A	0.7
Weight in B	0.3
SD of A	8.01%
SD of B	13.30%
r(1,2)	0.39
Portfolio SD = SQRT[((Wa*SDa)^2)+((Wb*SDb)^2)+2*(wa*SDa)*(Wb*SDb)*r(1,2)]
=SQRT[((0.7*0.0801)^2)+((0.3*0.133)^2)+2*(0.7*0.0801)*(0.3*0.133)*0.39]
=SQRT[((0.05607)^2)+((0.0399)^2)+2*(0.05607)*(0.0399)*0.39]
=SQRT[0.00648086544]
8.05%