Question

Using the data in the following​ table, and the fact that the correlation of A and B is

0.21​,

calculate the volatility​ (standard deviation) of a portfolio that is

60%

invested in stock A and

40%

invested in stock B.

	Realized Returns
Year	Stock A		Stock B
2008	−2​%		27​%
2009	9​%		38​%
2010	10​%		1​%
2011	−1​%		−6​%
2012	5​%		−15​%
2013	10​%		26​%

The standard deviation of the portfolio is

nothing​%.

​(Round to two decimal​ places.)

Answer 1

Expected Return of Stock A =(-2%+9%+10%-1%+5%+10%)/6 =5.1667%
Standard Deviation of Stock A =(((-2%-5.1667%)^2+(9%-5.1667%)^2+(10%-5.1667%)^2+(-1%-5.1667%)^2+(5%-5.1667%)^2+(10%-5.1667%)^2)/(6-1))^0.5=5.4924%

Expected Return of Stock B =(27%+38%+1%-6%-15%+26%)/6 =11.8333%
Standard Deviation of Stock B =(((27%-11.8333%)^2+(38%-11.8333%)^2+(1%-11.8333%)^2+(-6%-11.8333%)^2+(-15%-11.8333%)^2+(26%-11.8333%)^2)/(6-1))^0.5 =21.3112%

Standard Deviation of Portfolio =((Weight of A*Standard Deviation of A)^2+(Weight of B*Standard Deviation of B)^2+2*Weight of A*Weight of B*Standard Deviation of A* Standard Deviatio of B*Correlation)^0.5
=((60%*5.4924%)^2+(40%*21.3112%)^2+2*60%*40%*5.4924%*21.3112%*0.21)^0.5=9.76%