Question

1. The following table shows rates of return for two stocks.

	A	B	C
1	Year	Stock A	Stock B
2	1	14%	13%
3	2	-15%	-14%
4	3	-6%	-9%
5	4	5%	28%
6	5	14%	8%
7	6	15%	7%

a. What is the arithmetic average return for stock B?

b. What is the variance for stock B?

c. What is the covariance of returns?

2. The following table shows realized rates of return for two stocks.

	A	B	C
1	Year	Stock A	Stock B
2	1	-10%	15%
3	2	-20%	-14%
4	3	-6%	-2%
5	4	5%	28%
6	5	14%	8%
7	6	19%	3%

a. What is the arithmetic average return for stock B?

b. What is the variance for stock B?

c. What is the covariance of returns?

d. What is the correlation coefficient?

3. The return on Samsung stock has a standard deviation of 35% and the return on Toyota stock has a standard deviation of 14%. Their covariance is 0.0196.

a. If you invest 70% in Samsung and 30% in Toyota, what is the variance of the portfolio?

b. What is the standard deviation of the portfolio?

Answer 1

1. a)Average Return of B=(13%-14%-9%+28%+8%+7%)/6 =5.50%


b) Variance of B =(13%-5.5%)^2+(-14%-5.50%)^2+(-9%-5.50%)^2+(28%-5.50%)^2+((8%-5.50%)^2+(7%-5.50%)^2)/(6-1) = 11.55%

Average Return of A =(14%-15%-6%+5%+14%+15%)/6 =4.50%

c) Covariance of Return =((14%-4.50%)*((13%-5.5%)+(-15%-4.50%)*((-14%-5.50%)+(-6%-4.50%)*((-9%-5.50%)+(5%-4.50%)*((28%-5.50%)+(14%-4.50%)*((8%-5.50%)+(15%-4.50%)*((7%-5.50%))/(6-1) = 0.1309

Max 1 question its subparts can be solved.

Please Discuss in case of Doubt

Best of Luck. God Bless
Please Rate Well