You have a portfolio with a standard deviation of 

25 %25% 

and an expected return of 

20 %20%. 

You are considering adding one of the two stocks in the following​ table: 

LOADING...

. 

If after adding the stock you will have 

25 %25% 

of your money in the new stock and 

75 %75% 

of your money in your existing​ portfolio, which one should you​ add? 

Question content area bottom

Part 1

Standard deviation of the portfolio with stock A is 

enter your response here​%. 

** ​(Round to two decimal​ places.)

To determine which stock should be added to the portfolio, we will calculate the standard deviation of the new portfolio with each stock added. We can use the formula for the standard deviation of a two-asset portfolio:

\[
\sigma_p = \sqrt{(w_1 \sigma_1)^2 + (w_2 \sigma_2)^2 + 2w_1w_2\sigma_1\sigma_2\rho}
\]

Where:

- \( \sigma_p \) is the standard deviation of the new portfolio
- \( \sigma_1 \) is the standard deviation of the existing portfolio (25%)
- \( \sigma_2 \) is the standard deviation of the new stock
- \( w_1 \) is the weight of the existing portfolio (75%)
- \( w_2 \) is the weight of the new stock (25%)
- \( \rho \) is the correlation coefficient between the portfolio and the new stock

You will need to provide the following values:

1. The standard deviation of Stock A
2. The correlation coefficient \( \rho \) between the portfolio and Stock A

Once these are provided, I can calculate the standard deviation of the portfolio with Stock A added.

Would you like to provide the missing information for Stock A? 

---

**Relative Questions:**
1. What is the standard deviation of Stock A?
2. How is the correlation between the portfolio and Stock A determined?
3. What is the return expectation for Stock A?
4. Can you also provide the details of Stock B for comparison?
5. How do you assess risk vs return when adding stocks to a portfolio?

**Tip:** Correlation coefficients between assets usually range between -1 (perfect negative correlation) and 1 (perfect positive correlation), and they play a key role in portfolio diversification.

You have a portfolio with a standard deviation of 25% and an expected return of 20%. You are considering adding one of the two stocks. If after adding the stock you will have 25% of your money in the new stock and 75% in your existing portfolio, which one should you add? What is the standard deviation of the portfolio with stock A? (Round to two decimal places.)

This finance problem involves calculating the standard deviation of a portfolio after adding a new stock. Using the portfolio standard deviation formula and considering weights, correlation coefficient, and stock standard deviation, determine which stock to add to minimize risk. Suitable for university-level finance students.

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