Investment Risk
1. **State the problem:** We need to compare the relative risk of two stocks, X and Y, using the coefficient of variation (CV), and then recommend which stock is better for a risk-averse investor.
2. **Calculate the coefficient of variation (CV):** The CV is defined as the ratio of the standard deviation to the mean (average price), expressed as
$$\text{CV} = \frac{\text{Standard Deviation}}{\text{Mean}}$$
3. **Calculate CV for Stock X:**
$$\text{CV}_X = \frac{4.20}{45} = 0.0933$$
4. **Calculate CV for Stock Y:**
$$\text{CV}_Y = \frac{8.50}{120} = 0.0708$$
5. **Interpretation:** The coefficient of variation measures relative risk; a lower CV means less risk relative to the expected return.
6. **Comparison:** Since $$0.0708 < 0.0933$$, Stock Y has a lower relative risk than Stock X.
7. **Recommendation for a risk-averse investor:** A risk-averse investor prefers investments with lower relative risk. Therefore, Stock Y is recommended because it has a lower coefficient of variation, indicating less risk per unit of expected return.
**Final answer:**
- CV of Stock X = 0.0933
- CV of Stock Y = 0.0708
- Recommend Stock Y for a risk-averse investor due to its lower relative risk.