Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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8-13

**Calculating the Expected Return on a Portfolio**

You own a portfolio that has $2,900 invested in Stock A and $3,900 invested in Stock B. If the expected returns on these stocks are 7 percent and 10 percent, respectively, what is the expected return on the portfolio? 

**Important Note**: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16%.

Below the problem statement, there is a space provided for the answer with a label for "Portfolio expected return" followed by a text box and a percentage sign (%).

To solve this, use the formula for the expected return on a portfolio:

\[ \text{Expected Return} = \left( \frac{\text{Investment in Stock A}}{\text{Total Investment}} \right) \times \text{Return of Stock A} + \left( \frac{\text{Investment in Stock B}}{\text{Total Investment}} \right) \times \text{Return of Stock B} \]

1. Calculate the total investment in the portfolio:
   \[ \text{Total Investment} = \$2,900 + \$3,900 = \$6,800 \]

2. Determine the weight of each stock in the portfolio:
   \[ \text{Weight of Stock A} = \frac{\$2,900}{\$6,800} \]
   \[ \text{Weight of Stock B} = \frac{\$3,900}{\$6,800} \]

3. Use the weights and the expected returns of each stock to find the expected return of the portfolio:
   \[ \text{Expected Return} = \left( \frac{2900}{6800} \right) \times 0.07 + \left( \frac{3900}{6800} \right) \times 0.10 \]

4. Perform the calculations:
   \[ \text{Weight of Stock A} = 0.4265 \]
   \[ \text{Weight of Stock B} = 0.5735 \]
 
5. Calculate the contribution of each stock to the expected return:
   \[ \text{Contribution of Stock A} = 0.4265 \times 0.07 = 0.029855 \]
   \[ \text{Contribution of Stock B} = 0.573
Transcribed Image Text:**Calculating the Expected Return on a Portfolio** You own a portfolio that has $2,900 invested in Stock A and $3,900 invested in Stock B. If the expected returns on these stocks are 7 percent and 10 percent, respectively, what is the expected return on the portfolio? **Important Note**: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16%. Below the problem statement, there is a space provided for the answer with a label for "Portfolio expected return" followed by a text box and a percentage sign (%). To solve this, use the formula for the expected return on a portfolio: \[ \text{Expected Return} = \left( \frac{\text{Investment in Stock A}}{\text{Total Investment}} \right) \times \text{Return of Stock A} + \left( \frac{\text{Investment in Stock B}}{\text{Total Investment}} \right) \times \text{Return of Stock B} \] 1. Calculate the total investment in the portfolio: \[ \text{Total Investment} = \$2,900 + \$3,900 = \$6,800 \] 2. Determine the weight of each stock in the portfolio: \[ \text{Weight of Stock A} = \frac{\$2,900}{\$6,800} \] \[ \text{Weight of Stock B} = \frac{\$3,900}{\$6,800} \] 3. Use the weights and the expected returns of each stock to find the expected return of the portfolio: \[ \text{Expected Return} = \left( \frac{2900}{6800} \right) \times 0.07 + \left( \frac{3900}{6800} \right) \times 0.10 \] 4. Perform the calculations: \[ \text{Weight of Stock A} = 0.4265 \] \[ \text{Weight of Stock B} = 0.5735 \] 5. Calculate the contribution of each stock to the expected return: \[ \text{Contribution of Stock A} = 0.4265 \times 0.07 = 0.029855 \] \[ \text{Contribution of Stock B} = 0.573
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