Question

Using the data in the following table, and the fact that the correlation of A and B is 0.35, calculate the volatility (standard deviation) of a portfolio that is 50% invested in stock A and 50% invested in stock B Realized Returns Year 2008 2009 2010 2011 2012 2013 Stock A -2% 10% 5% -4% 2% 7% Stock B 28% 26% 5% 18% The standard deviation of the portfolio is Џ96 (Round to two decimal places)

Answer 1

The standard deviation is calculated using excel:

Year	A	B
2008	-2%	28%
2009	10%	26%
2010	5%	5%
2011	-4%	-1%
2012	2%	-7%
2013	7%	18%
Stdev	4.90%	13.33%

Formula for 2 asset portfolio standard deviation:

Portfolio variance = w²_A*σ²(R_A) + w²_B*σ²(R_B) + 2*(w_A)*(w_B)*σ(R_A)*σ²(R_B)*Correlation(R_A, R_B)

Variance is standard deviation squared.

(0.50*4.90)^2+(0.50*13.33)^2+(2*0.50*0.50*4.90*13.33*0.35)
=Standard deviation=7.86%