2b. Calculate the expected return and standard deviation of a portfolio made up of 50% stock C and 50% stock D if the correlation is -0.75.
Probability | Stock C | Weighted Return | Expected Return | Deviation | SQd Dev. | Prob * Sqrd Deviaiton |
0.3 | -10% | -3.00% | 12.50% | -22.50000% | 0.0506 | 0.0151875 |
0.5 | 15% | 7.50% | 12.50% | 2.50000% | 0.0006 | 0.0003125 |
0.2 | 40% | 8.00% | 12.50% | 27.50000% | 0.0756 | 0.015125 |
Variance | 3.06% | |||||
Standard Deviation | 17.50% | |||||
Probability | Stock D | Weighted Return | Expected Return | Deviation | SQd Dev. | |
0.3 | 25% | 7.50% | 12.50% | 12.500% | 0.0156 | 0.0046875 |
0.5 | 10% | 5.00% | 12.50% | -2.500% | 0.0006 | 0.0003125 |
0.2 | 0% | 0.00% | 12.50% | -12.500% | 0.0156 | 0.003125 |
Variance | 0.813% | |||||
Standard Deviation | 9.014% |
Expected return on portfolio= (Return on Stock C * Weight of stock C) + (Return on Stock D* Weight of Stock D)
= 12.50*0.50 + 12.50*0.50
= 6.25 + 6.25
= 12.50%
Portfolio standard deviation is calculated as
Where, is portfolio standard deviation
w_{c} and w_{D} are weights of stock C and D.
and are standard deviation of stock C and D respectively.
is the correlation coefficient between returns of stock C and D.
= 6.128
Standard eviation of portfolio is therefore = 6.128%
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