Question

You've assembled the following portfolio: Stock Expected return Portfolio weight 1 6.8% 30% 11.8% 16.1% Part 1. What is the weight for stock 3 if you want to achieve an expected portfolio return of 14%?

Answer 1

To find the weight for stock 3 in order to achieve an expected portfolio return of 14%, you can use the formula for expected portfolio return. By rearranging the formula and plugging in the values for the expected returns and weights of stocks 1 and 2, you can solve for the weight of stock 3. The weight of stock 3 is 10.0382% divided by the expected return of stock 3.

Step-by-step explanation:

To find the weight for stock 3, we need to use the formula for expected portfolio return. The formula is:

Expected Portfolio Return = (Expected Return of Stock 1 * Weight of Stock 1) + (Expected Return of Stock 2 * Weight of Stock 2) + (Expected Return of Stock 3 * Weight of Stock 3)

Since we have the expected return and weight for Stock 1 and Stock 2, we can plug in the values and solve for the weight of Stock 3. Here's the step-by-step calculation:

1. Expected Portfolio Return = 14%
2. Expected Return of Stock 1 = 6.8%
3. Weight of Stock 1 = 30%
4. Expected Return of Stock 2 = 11.8%
5. Weight of Stock 2 = 16.1%
6. Expected Return of Stock 3 = ?
7. Weight of Stock 3 = ?

Using the formula, we can solve for the weight of Stock 3.

Expected Portfolio Return = (6.8% * 30%) + (11.8% * 16.1%) + (Expected Return of Stock 3 * Weight of Stock 3) = 14%

Now, we can rearrange the equation and solve for the weight of Stock 3:

Expected Return of Stock 3 * Weight of Stock 3 = Expected Portfolio Return - (6.8% * 30%) - (11.8% * 16.1%)

Weight of Stock 3 = (Expected Portfolio Return - (6.8% * 30%) - (11.8% * 16.1%)) / Expected Return of Stock 3

Calculating the values:

Weight of Stock 3 = (14% - (6.8% * 0.3) - (11.8% * 0.161)) / Expected Return of Stock 3

Weight of Stock 3 = (14% - 2.04% - 1.9018%) / Expected Return of Stock 3

Weight of Stock 3 = 10.0382% / Expected Return of Stock 3

Weight of Stock 3 = 10.0382% / Expected Return of Stock 3

Answer 2

To achieve the desired expected portfolio return of 14%, the portfolio weight for stock 3 must be 53.9%, assuming the known weights of the other two stocks and the contribution of their expected returns.

Step-by-step explanation:

The objective is to find the portfolio weight for stock 3 to achieve an expected portfolio return of 14%. We are given:

• Stock 1 Expected Return: 6.8% and Portfolio Weight: 30%
• Stock 2 Expected Return: 11.8% and Portfolio Weight: 16.1%
• Desired Portfolio Expected Return: 14%

First, let's calculate the contribution to the expected return from stocks 1 and 2:

• Stock 1: 6.8% * 30% = 2.04%
• Stock 2: 11.8% * 16.1% = 1.8998%

The sum of these contributions is 2.04% + 1.8998% = 3.9398%.
To achieve the overall expected portfolio return of 14%, the contribution from stock 3 needs to be 14% - 3.9398% = 10.0602%.
Let's assume the expected return for stock 3 is r3 and the portfolio weight for stock 3 is w3:

Equation: r3 * w3 = 10.0602%
Knowing that the total weights must add up to 100%, we can also say:

w1 + w2 + w3 = 100%
where w1 = 30% and w2 = 16.1%, therefore:

w3 = 100% - 30% - 16.1% = 53.9%

So, the portfolio weight for stock 3 is 53.9% to achieve the desired expected portfolio return of 14%.