In: Finance
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 (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%