You have a $9,000 portfolio which is invested in stocks A, B, and a risk-free asset....
You have a $9,000 portfolio which is invested in stocks A, B, and a risk-free asset. $4,000 is invested in stock A. Stock A has a beta of 1.84 and stock B has a beta of 0.68. How much needs to be invested in stock B if you want a portfolio beta of.95?
Multiple Choice
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$0
-
$1,750
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$5,000
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$3,279
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$7,279
Homework Answers
Portfolio Beta = Weighted avg beta of securites.
Beta of Risk free assets is 0.
Let "X" be the weight in Stock B
Weight in STock A = 4000 / 9000
= 0.4444
Weight in RIsk free Asset = 1 - 0.4444 -X
= 0.5556 - X
| Partciculars | Weight | Beta | Wtd Beta |
| Stock A | 0.4444 | 1.84 | 0.817696 |
| Stock B | X | 0.68 | 0.68X |
| Risk free Asset | 0.5556-X | 0 | 0 |
| Portfolio Beta | 0.68X + 0.8177 |
Thus 0.95 = 0.68X + 0.8177
0.68X = 0.95 - 0.8177
= 0.1323
X = 0.1323 / 0.68
= 0.1946
Investment in B= TotalPortfolio * Weight
= $ 9000 * 0.1946
= $ 1751
OPtion B is correct
Pls comment, if any further assistance is required
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