Consider the following returns: Year End Lowes Realized Return Home Depot Realiz
ID: 2742637 • Letter: C
Question
Consider the following returns:
Year End
Lowes Realized Return
Home Depot Realized Return
IBM
Realized Return
2000
20.1%
-14.6%
0.2%
2001
72.7%
4.3%
-3.2%
2002
-25.7%
-58.1%
-27.0%
2003
56.9%
71.1%
27.9%
2004
6.7%
17.3%
-5.1%
2005
17.9%
0.9%
-11.3%
Required: Calculate the variance on a portfolio that is made up of equal investments in Home Depot and IBM stock.
Year End
Lowes Realized Return
Home Depot Realized Return
IBM
Realized Return
2000
20.1%
-14.6%
0.2%
2001
72.7%
4.3%
-3.2%
2002
-25.7%
-58.1%
-27.0%
2003
56.9%
71.1%
27.9%
2004
6.7%
17.3%
-5.1%
2005
17.9%
0.9%
-11.3%
Explanation / Answer
The portfolio return would be the weighted average returns of Home Depot and IBM = (0.5*Home depot return)+(0.5*IBM return)
Portfolio returns:
We will now calculate the variance in returns of Home Depot, IBM and their covariance.
Variance = [sum of (returns - average returns)^2](n-1) n is the number of years = 6
Covariance calculation:
Covariance = [sum of (return of home depot - averge return of home depot)*(return of IBM-average return of IBM)]/n-1
Thus covariance = 7%
Now portfolio variance = (w2Home depot*Home depot's variance)+ (w2IBM*IBM's variance)+2*(w of Home depot*w of IBM)*Covariance
where w = weight = 0.5 for both Home depot and IBM
= (0.5)^2*17.78%+(0.5)^2*3.23%+2*(0.5*0.5*5.84%)
= 4.44%+0.81%+2.92%
= 8.17%
This is the variance of the portfolio.
Year Home Depot return IBM return Portfolio return 2000 -14.60% 0.20% -7.20% 2001 4.30% -3.20% 0.55% 2002 -58.10% -27.00% -42.55% 2003 71.10% 27.90% 49.50% 2004 17.30% -5.10% 6.10% 2005 0.90% -11.30% -5.20% Average 3.48% -3.08% 0.20%