Question

thanks!

Using the data in the following table, and the fact that the correlation of A and B is 0.49, 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% 20% 2009 10% 36% 2010 5% 2011 -9% 2012 5% 2013 10% 31% The standard deviation of the portfolio is %. (Round to two decimal places.)

Answer 1

First lets find out average return of both stocks

Average return =

(ΣΧ)/Ν

where X = expected return of each year

N = number of years

Year Stock A 2008 2009 2010 2011 2012 2013 Total (A-A')^2 Stock B (B-B')^2 -8 103.3679 20 56.25 10 61.35589 36 552.25 5 8.025889 90.25 -9 124.7019 -81 420.25 5 8.025889 380.25 1 061.35589 31 342.25 1336775 1842

Average return of stock A (A')= 13 / 6 = 2.167%

Average return of Stock B (B') = 75 / 6 = 12.50%

Standard Deviation is calculated using following formula

=

VE(X – X')?/N

Where X = expected return of each year

X' = average return

N = number of years

Standard deviation of Stock A = (367 / 6)^1/2 = 7.82%

Stock B = (1842 / 6)^1/2 = 17.52%

Standard Deviation of portfolio is calculated using following formula

=

(Wa * oa)2 + (W6*06)2 + 2 * Wa* W6*oa* ob *r(ab)

Where Wa , Wb = weights of socks A and B

= standard deviation of stocks A and B

σα, σή

r(ab) = correlation coefficient

= [(0.7*7.82)^2 + (0.3*17.52)^2 + 2*0.7*0.3*7.82*17.52*0.49]^1/2

Standard Deviation of Portfolio = 9.26%