Question

Problem 7. [9 pts]. Stock A and B have the following returns: (Show your calculations Stock A 0.10 0.17 0.05 0.05 -0.08 0.09 0.10 0.14 Stock B 0.03 0.10 0.05 0.15 0.12 0.05 0.07 0.05 a- What are the expected returns of the two stocks? b- What are the standard deviations of the two stocks? c- If their correlation is -0.49, what is the expected return and standard deviation of a portfolio of 35% stock A and 65% stock B?

Answer 1

Scenario	return	Deviation=Return-Expected return	Deviation^2
1	10.000%	3.500%	0.123%
2	17.000%	10.500%	1.103%
3	5.000%	-1.500%	0.023%
4	-5.000%	-11.500%	1.323%
5	-8.000%	-14.500%	2.103%
6	9.000%	2.500%	0.063%
7	10.000%	3.500%	0.123%
8	14.000%	7.500%	0.563%
Total	52.000%		5.420%
So expected return is 6.5%	52%/8
Stock variance-5.42%/8	0.6775%
Stock Standard deviation	'0.6775%^(0.5)
Stock Standard deviation	8.23%

Scenario	return	Deviation=Return-Expected return	Deviation^2
1	-3.000%	-8.750%	0.766%
2	10.000%	4.250%	0.181%
3	5.000%	-0.750%	0.006%
4	15.000%	9.250%	0.856%
5	12.000%	6.250%	0.391%
6	-5.000%	-10.750%	1.156%
7	7.000%	1.250%	0.016%
8	5.000%	-0.750%	0.006%
Total	46.000%		3.375%
So expected return is 5.75%	46%/8
Stock variance-3.375%/8	0.4219%
Stock Standard deviation	'0.4218%^(0.5)
Stock Standard deviation	6.50%
	Expected return	Weight	Standard Deviation
Stock A	6.50%	35%	8.2310%
Stock B	5.75%	65%	6.4952%
Calculation of standard deviation
The first step is to calculate the covariance:
COVAB = SDA × SDB × rAB, where rAB is the correlation coefficient between securities A and B.
Now, calculate the standard deviation for the portfolio:
[(SDA2 × WA2) + (SDB2 × WB2) + 2 (WA)(WB)(COVAB)]½
Let's calcualte the co-variance	=8.2310% * 6.4952% * -0.49
	-0.00262
Now lets calculate the SD
SD portfolio=	((8.2310%^2 * 35%^2)+(6.4952%^2*65%^2)+(2*35%*65%*-0.00262))^(0.5)
SD portfolio=	3.769%