Question

A portfolio has $100,000 invested in bonds and $400,000 invested in stocks. The bonds have an expected return of 0.09 a with a standard deviation of 0.07. The stocks have an expected return of 0.14 with a standard deviation of 0.25. The correlation between the stocks and bonds is 0.40.

(Round to 3 decimals if necessary)

What is the portfolio weight for the bonds?

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Question 8

Refer to Scenario 3. What is the portfolio weight for the stocks?

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Question 9

Refer to Scenario 3. What is the expected return for the portfolio?

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Question 10

Refer to Scenario 3. What is the expected variance for the portfolio?

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Question 11

Refer to Scenario 3. What is the expected standard deviation for the portfolio?

Answer 1

The investment in the bonds is $100000 while that of in the stocks is $400000.

Q7) The value of the portfolio is $500000

Weightage of the Bonds
(100000 / (100000 + 400000))
= 100000 / 500000
= 0.20 or 20%

Q8) The weightage of the stocks

400000 / 50000
= 0.80 or 80%

Q9) The expected return on the portfolio is the weighted average return of each asset.

(0.2 * 0.09) + (0.8 * 0.14) = 0.13 or 13%

Q10) The expected variance of the portfolio takes into account the weight of each asset as well as correlation.
We have been given a standard deviation here so we will have to take the square of it to calculate the variance.

Variance = (Standard Deviation) ^ 2

Portfolio Variance =

(0.2^2 * 0.07^2) + (0.8^2 * 0.25^2) + (2 * 0.4 * 0.2 * 0.07 * 0.8 * 0.25)

= 0.00196 + 0.04 + 0.00224
= 0.042436 or 4.2436%

The portfolio variance is 4.2436%

Q11) The expected standard deviation of the portfolio is the square root of the expected portfolio variance.

(4.2436%) ^ 0.5 = 2.06%