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%.

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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.