A stock with a beta of 1.8 has an expected rate of return of 16%. If the market return this year turns out to be 6 percentage points below expectations, what is your best guess as to the rate of return on the stock?


We can solve this problem using the **Capital Asset Pricing Model (CAPM)** formula, which relates the expected return of a stock to its beta and the market's expected return:

\[
R_i = R_f + \beta_i \times (R_m - R_f)
\]

Where:
- \(R_i\) is the expected return on the stock.
- \(R_f\) is the risk-free rate.
- \(\beta_i\) is the beta of the stock (which measures the stock's sensitivity to market movements).
- \(R_m\) is the market return.

Now, in this case, we are told that the market return will be **6 percentage points below expectations**, meaning the actual market return (\(R_m\)) will be:

\[
R_m - 6\%
\]

Given the stock's **beta of 1.8**, this means that for every percentage point the market return changes, the stock return should change by \(1.8 \times \text{market change}\).

### Step-by-step solution:

1. The change in market return is \(-6\%\).
2. The stock's return will adjust by \(1.8 \times (-6\%) = -10.8\%\).
3. The expected rate of return for the stock was initially 16%. Since the market return is worse than expected, we subtract the 10.8% adjustment:
   \[
   \text{New stock return} = 16\% - 10.8\% = 5.2\%
   \]

Thus, **your best guess for the rate of return on the stock is 5.2%**.

---

Would you like any further clarification or details on this?

Here are 5 questions related to this topic:
1. How does beta affect a stock’s risk level compared to the market?
2. What would happen to the stock's return if the market exceeded expectations?
3. How does the risk-free rate influence the CAPM formula?
4. Can a stock have a negative beta, and what would that imply?
5. How would changing the market’s expected return impact the stock's performance?

**Tip:** A beta above 1 means the stock is more volatile than the market, while a beta below 1 indicates less volatility.

A stock with a beta of 1.8 has an expected rate of return of 16%. If the market return this year turns out to be 6 percentage points below expectations, what is your best guess as to the rate of return on the stock?

Learn how to calculate the stock return when a stock with a beta of 1.8 faces a market return 6 percentage points below expectations. This problem involves key finance concepts like the Capital Asset Pricing Model (CAPM) and stock market volatility. Suitable for undergraduate students in finance or economics.

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