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I see that you've uploaded an image containing a question about calculating the expected return, standard deviation, and coefficient of variation based on business cycles. Let's break it down step by step:

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### a) **Expected Return (7 Marks)**

The expected return is the weighted average of the returns for each business cycle, where the weights are the probabilities of each cycle occurring.

The formula for **expected return** is:

\[
\text{Expected Return} = \sum (\text{Probability of Cycle} \times \text{Return in that Cycle})
\]

From the table, we have:

- **Growth**: 7% probability, 70% return
- **Peak**: 12% probability, 46% return
- **Recession**: 53% probability, 20% return
- **Trough**: 25% probability, 5% return
- **Recovery**: 3% probability, 1% return

So, the expected return is calculated as:

\[
\text{Expected Return} = (0.07 \times 70) + (0.12 \times 46) + (0.53 \times 20) + (0.25 \times 5) + (0.03 \times 1)
\]

Let me calculate this.

### b) **Standard Deviation of Expected Return (14 Marks)**

To calculate the standard deviation, we need the variance first. The formula for **variance** is:

\[
\text{Variance} = \sum (\text{Probability of Cycle} \times (\text{Return in that Cycle} - \text{Expected Return})^2)
\]

Once the variance is calculated, the **standard deviation** is the square root of the variance:

\[
\text{Standard Deviation} = \sqrt{\text{Variance}}
\]

### c) **Coefficient of Variation (4 Marks)**

The **coefficient of variation (CV)** is the ratio of the standard deviation to the expected return:

\[
\text{CV} = \frac{\text{Standard Deviation}}{\text{Expected Return}}
\]

Now, I will calculate all these values based on the provided data. Let me work through the calculations.### Calculations:

a) **Expected Return**:  
\[
\text{Expected Return} = 22.30\%
\]

b) **Variance**:  
\[
\text{Variance} = 317.91
\]  
**Standard Deviation**:  
\[
\text{Standard Deviation} = 17.83\%
\]

c) **Coefficient of Variation (CV)**:  
\[
\text{CV} = 0.80
\]

---

These values provide insights into the expected return, risk (as measured by standard deviation), and the relative risk (CV) for ABX Ltd.

Let me know if you need further clarification or details.

Here are 5 related questions for practice:
1. How would the expected return change if the probability of recession increased to 60%?
2. How does a higher coefficient of variation affect an investment's attractiveness?
3. If the standard deviation increased to 20%, what would happen to the coefficient of variation?
4. Why is it important to calculate variance when analyzing returns?
5. What happens to expected return if all the returns increase by 5%?

**Tip:** The coefficient of variation is particularly useful when comparing investments with different expected returns to assess relative risk.

ABX LTD is a Russian firm interested in investing in the BRICS nations market. The firm is considering investing in Research and Development in the South African Market. Based on the predicted business cycles and probabilities, calculate the expected return, standard deviation of expected return, and the coefficient of variation for the investment.

Learn how to calculate the expected return, standard deviation, and coefficient of variation for ABX LTD, a Russian firm investing in South Africa, based on predicted business cycles and probabilities. This problem uses key probability and statistical concepts relevant for undergraduate finance or economics students.

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