A stock with a beta of 0.5 has an expected rate of return of 10%. If the market return this year turns out to be 9 percentage points below expectations, what is your best guess as to the rate of return on the stock?

Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.

To calculate the expected return on the stock given that the market return turns out to be 9 percentage points below expectations, we can use the **CAPM (Capital Asset Pricing Model)** formula adjusted for actual market return changes.

### CAPM Formula:
\[
R_s = R_f + \beta (R_m - R_f)
\]
Where:
- \( R_s \) is the stock's expected return.
- \( R_f \) is the risk-free rate.
- \( \beta \) is the stock's beta.
- \( R_m \) is the expected return on the market.
  
However, this question is about how the stock's return reacts when the market return is lower than expected by 9 percentage points.

Since the stock's beta represents its sensitivity to the market, the change in the stock's return can be approximated by:
\[
\Delta R_s = \beta \times \Delta R_m
\]

### Steps:
1. **Market Return Change:**
   - The market return is 9 percentage points lower than expected, so \( \Delta R_m = -9\% \).
  
2. **Stock Return Change:**
   Using the beta of 0.5, the change in the stock's return is:
   \[
   \Delta R_s = 0.5 \times (-9\%) = -4.5\%
   \]
   
3. **Adjusted Stock Return:**
   The expected stock return was originally 10%. With the market return falling, we adjust this by subtracting the stock return change:
   \[
   R_s = 10\% - 4.5\% = 5.5\%
   \]

Thus, the best guess for the stock's rate of return is **5.5%**.

---

Would you like any details on how the beta impacts stock returns or any other clarifications?

Here are 5 related questions:
1. How does a higher beta affect the sensitivity of a stock to market changes?
2. What does a beta of 1 imply for a stock’s expected return relative to the market?
3. What role does the risk-free rate play in the CAPM formula?
4. How would the expected return change if the market return was above expectations by 5%?
5. How can a negative beta stock perform during market downturns?

**Tip:** A stock with a beta less than 1 is considered less volatile than the market and may perform better during market downturns.

A stock with a beta of 0.5 has an expected rate of return of 10%. If the market return this year turns out to be 9 percentage points below expectations, what is your best guess as to the rate of return on the stock? Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.

Calculate the expected return on a stock with a beta of 0.5, given a 9% lower-than-expected market return. This problem demonstrates how to adjust the stock's return using the Capital Asset Pricing Model (CAPM) and beta sensitivity. Ideal for college-level finance or economics students.

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