Stocks A and B have the following returns:
Stock A | Stock B | |
1 | 0.08 | 0.04 |
2 | 0.04 | 0.03 |
3 | 0.13 | 0.04 |
4 | -0.03 | 0.03 |
5 | 0.07 | -0.05 |
Stocks A and B have the following returns:
Stock A |
Stock B |
||
1 |
0.080.08 |
0.040.04 |
|
2 |
0.040.04 |
0.030.03 |
|
3 |
0.130.13 |
0.040.04 |
|
4 |
negative 0.03−0.03 |
0.030.03 |
|
5 |
0.070.07 |
negative 0.05−0.05 |
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 is 0.45, what is the expected return and standard deviation of a portfolio of 79% stock A and 21% stock B?
Year | Stock A | Stock B |
1 | 8.00% | 4.00% |
2 | 4.00% | 3.00% |
3 | 13.00% | 4.00% |
4 | -3.00% | 3.00% |
5 | 7.00% | -5.00% |
a.Average= | 5.80% | 1.80% |
b.Standard dev= | 5.89% | 3.83% |
Where | |||
Average or Mean = Sum of all observations/Count of all observations | |||
Sample Standard deviation =((∑k=1 to N (observationk – average))/(N-1))^(1/2) |
c
Expected return%= | Wt Stock A*Return Stock A+Wt Stock B*Return Stock B |
Expected return%= | 0.79*0.058+0.21*0.018 |
Expected return%= | 4.96 |
Variance | =( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB)) |
Variance | =0.79^2*0.0589^2+0.21^2*0.0383^2+2*0.79*0.21*0.0589*0.0383*0.45 |
Variance | 0.00257 |
Standard deviation= | (variance)^0.5 |
Standard deviation= | 5.07% |
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