Question

Stocks A and B have the following​ returns:

	Stock A	Stock B
1	0.08	0.06
2	0.05	0.01
3	0.12	0.06
4	−0.04	0.03
5	0.08	−0.02

a. What are the expected returns of the two​ stocks?

b. What are the standard deviations of the returns of the two​ stocks?

c. If their correlation is0.45​, what is the expected return and standard deviation of a portfolio of 62​%stock A and 38​%stock​ B?

Answer 1

Answer (a)

Expected reutrn of Stock A (mean of stock A) = Sum of all returns / Number of observations

= (0.08 + 0.05 + 0.12 - 0.04 + 0.08) / 5

= 0.058 or 5.80%

Expected reutrn of Stock B (mean of stock B) = Sum of all returns / Number of observations

= (0.06 + 0.01 + 0.06 + 0.03 - 0.02) / 5

= 0.028 or 2.80%

Answer (b)

Standard deviation of stock A:

Return (r)	Mean (x)	r-x	(r-x)2
0.08	0.058	0.022	0.000484
0.05	0.058	-0.008	0.00064
0.12	0.058	0.062	0.003844
-0.04	0.058	-0.098	0.009604
0.08	0.058	0.022	0.000484
Total			0.01448

Standdard deviation of stock A = [(Sum of all (r-x)²) / (Number of observations - 1)]^0.50

= [0.01448 / (5 - 1)]^0.50

⁼ 0.0602 or 6.02%

Standard deviation of stock B:

Return (r)	Mean (x)	r-x	(r-x)2
0.06	0.028	0.032	0.001024
0.01	0.028	-0.018	0.000324
0.06	0.028	0.032	0.001024
0.03	0.028	0.002	0.000004
-0.02	0.028	-0.048	0.002304
Total			0.00468

Standdard deviation of stock B = [(Sum of all (r-x)²) / (Number of observations - 1)]^0.50

= [0.00468 / (5 - 1)]^0.50

⁼ 0.0342 or 3.42%

Answer (c)

Weight of stock A (WA) = 62%

Weight of stock B (WB) = 38%

Expected return of portfolio = (Mean of stock A * WA) + (Mean of stock B * WB)

= (5.80% * 62%) + (2.80% * 38%)

= 4.66%

Standard deviation of portfolio = [(WA² * Standard deviation of A²)] + (WB² * Standard deviation of B²) + (2 * WA * WB * Standard deviation of A * Standard deviation of B * Correlation)]^0.50

= [(0.62² * 0.0602²) + (0.38² * 0.0342²) + (2 * 0.62 * 0.38 * 0.0602 * 0.0342 * 0.45)]^0.50

= 4.47%