Question

1. For this question, use the following data table:

	AT&T	Microsoft
Expected Return	0.10	0.21
Standard Deviation	0.15	0.25

a. What is the minimum-risk (standard deviation) portfolio allocation of AT&T and Microsoft if the correlation between the two stocks is 0? 0.5? 1? -1? What is the standard deviation of each of these minimum-risk portfolios?

b. What is the optimal combination of these two securities in a portfolio for each of the four given values of the correlation coefficient, assuming the existence of a money market fund that currently pays a risk-free 0.045?

Answer 1

To calculate the Standard DEviation of the Portfolio first we have to compute the weights of security for the different correlation given by using the following formula:

Step 1 : First we will calculate the Covariance between AT&T and Microsoft for each of coorelation,by using the formula:

COVAB = Coorelation * SDAT&T * SDMicrosoft

When coorelation is 0 = 0 (0*15*25)

When coorelation is 0.50 = 187.50 (0.50 * 15 * 25)

When coorelation is 1 = 375 (1 * 15 *25)

When coorelation is -1 = -375 (-1 * 15* 25)

Step 2: Now we will calculate the weights using the following formula:

WAT&T = (SDMicrosoft2 - COVAB )/(SDMicrosoft2 + SDAT&T2 - 2*COVAB)

When coorelation is 0 = [(25*25 - 0)/(25*25 + 15*15 - 2*0)]

= 0.74

When coorelation is 0.50 = [(25*25 - 187.50)/(25*25 + 15*15 - 2*187.50)]

= 0.92

When coorelation is 1 = [(25*25 - 375)/(25*25 + 15*15 - 2*375)]

= 1(Max weight can be 1)

When coorelation is -1 = [(25*25 + 375)/(25*25 + 15*15 + 2*375)]

= 0.63

Coorelation	Weight of AT&T	Weight of Microsoft
0	0.74	0.26
0.50	0.92	0.08
1	1	0
-1	0.63	0.37

The formula for calculating the risk of portfolio is:

Square root of [(SDMicrosoft2 * WMicrosoft2) + (SDAT&T2 * WAT&T2) + (2* coorelation* SDMicrosoft* WMicrosoft * SDAT&T * WAT&T)]

When coorelation is 0 = 12.86%

When coorelation is 0.50 = 17.96%

when coorelation is 1 = 15%

When coorelation is -1 = 18.70%

Coorelation	Portfolio risk
0	12.86%
0.50	17.96%
1	15%
-1	18.70%