Stock X has a standard deviation of return of 30%. Stock Y has a standard deviation of return of 20%. The correlation coefficient between the two stocks is 0.69. If you invest 60% of your funds in Stock X and 40% in Stock Y.

The standard deviation of your portfolio is, therefore ______**%**.

(Please enter your answer as a *percentage* to two decimal places. i.e. 12.35 rather than 0.1235)

To calculate the **standard deviation of a two-asset portfolio**, we use the following formula:

\[
\sigma_p = \sqrt{w_X^2 \sigma_X^2 + w_Y^2 \sigma_Y^2 + 2 w_X w_Y \rho \sigma_X \sigma_Y}
\]

Where:
- \( \sigma_p \) = Portfolio standard deviation (what we are solving for)
- \( w_X = 0.60 \) (Weight of Stock X)
- \( w_Y = 0.40 \) (Weight of Stock Y)
- \( \sigma_X = 30\% = 0.30 \) (Standard deviation of Stock X)
- \( \sigma_Y = 20\% = 0.20 \) (Standard deviation of Stock Y)
- \( \rho = 0.69 \) (Correlation coefficient between the two stocks)

---

### Step-by-Step Calculation:

1. **Calculate the terms:**
   - \( w_X^2 \sigma_X^2 = (0.60)^2 \times (0.30)^2 = 0.36 \times 0.09 = 0.0324 \)
   - \( w_Y^2 \sigma_Y^2 = (0.40)^2 \times (0.20)^2 = 0.16 \times 0.04 = 0.0064 \)
   - \( 2 w_X w_Y \rho \sigma_X \sigma_Y = 2 \times 0.60 \times 0.40 \times 0.69 \times 0.30 \times 0.20 \)

     \[ 
     = 2 \times 0.60 \times 0.40 \times 0.69 \times 0.06 
     \]
     \[ 
     = 0.3312 \times 0.06 = 0.019872 
     \]

2. **Sum all terms inside the square root:**
   \[
   0.0324 + 0.0064 + 0.019872 = 0.058672
   \]

3. **Take the square root:**
   \[
   \sqrt{0.058672} = 0.2423
   \]

4. **Convert to a percentage:**
   \[
   0.2423 \times 100 = 24.23\%
   \]

---

### Final Answer:
The standard deviation of the portfolio is **24.23%**.

---

Would you like further details or have any other questions?  

---

Here are some related questions to explore:  
1. How does correlation affect portfolio risk?  
2. What happens to portfolio risk if the weights change to 50-50?  
3. How is portfolio variance different from portfolio standard deviation?  
4. How would the portfolio standard deviation change if the correlation were -1?  
5. What are the benefits of diversification based on this example?  

**Tip:** Lower correlation between assets reduces overall portfolio risk, even if individual assets are volatile.

Stock X has a standard deviation of return of 30%. Stock Y has a standard deviation of return of 20%. The correlation coefficient between the two stocks is 0.69. If you invest 60% of your funds in Stock X and 40% in Stock Y. The standard deviation of your portfolio is, therefore ______% (Please enter your answer as a percentage to two decimal places. i.e. 12.35 rather than 0.1235).

Learn how to calculate the standard deviation of a portfolio consisting of Stock X and Stock Y with a 60-40 investment split. The problem includes key concepts such as the portfolio standard deviation formula, risk analysis, and correlation coefficient. The answer is calculated to be 24.23%.

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