Answer: Asset 2.

## Explanation To determine which asset has the highest standard deviation, we need to use the relationship between beta, market standard deviation, and asset standard deviation: **Key Formula:** \[ \beta_i = \frac{\sigma_i \times \rho_{i,m}}{\sigma_m} \] Where: - \(\beta_i\) = beta of asset i - \(\sigma_i\) = standard deviation of asset i - \(\rho_{i,m}\) = correlation between asset i and the market - \(\sigma_m\) = standard deviation of the market (given as 20% or 0.20) Rearranging the formula: \[ \sigma_i = \frac{\beta_i \times \sigma_m}{\rho_{i,m}} \] **Step 1: Calculate correlation coefficients** We can calculate the correlation coefficient for each asset using the given data: \[ \rho_{i,m} = \frac{\beta_i \times \sigma_m^2}{\sigma_i \times \sigma_m} = \frac{\beta_i \times \sigma_m}{\sigma_i} \] But we don't have \(\sigma_i\) directly. However, we can use the fact that: \[ \beta_i = \frac{Cov(R_i, R_m)}{\sigma_m^2} \] And we know that: \[ \sigma_i = \sqrt{\beta_i^2 \times \sigma_m^2 + \sigma_{\epsilon_i}^2} \] But we don't have the residual variance. However, we can use the Sharpe ratio approach or recognize that for a given beta and return, the asset with higher beta will generally have higher systematic risk, but we need to consider total risk. **Step 2: Alternative approach** Given that we have returns and betas, and we're told the market standard deviation is 20%, we can use: \[ \sigma_i = \beta_i \times \sigma_m \times \frac{1}{\rho_{i,m}} \] Since correlation \(\rho_{i,m}\) is between -1 and 1, and for most assets it's positive, the asset with the highest beta will have the highest standard deviation IF correlations are similar. **Step 3: Calculate systematic risk component** Systematic risk component = \(\beta_i \times \sigma_m\) - Asset 1: \(1.000 \times 0.20 = 0.20\) or 20% - Asset 2: \(1.225 \times 0.20 = 0.245\) or 24.5% - Asset 3: \(1.125 \times 0.20 = 0.225\) or 22.5% **Step 4: Consider total risk** Total risk = Systematic risk + Unsystematic risk Since we don't have information about unsystematic risk, and typically assets with higher beta also tend to have higher total risk, Asset 2 has the highest systematic risk component. **Step 5: Final determination** Asset 2 has the highest beta (1.225), which means it has the highest sensitivity to market movements. Given that the market standard deviation is constant at 20%, and assuming correlations are reasonably similar across assets, Asset 2 will have the highest standard deviation. **Answer: B (Asset 2)** **Verification:** Even if we consider that correlations might differ, Asset 2's beta is significantly higher than the others (22.5% higher than Asset 1 and 8.9% higher than Asset 3), making it very likely to have the highest standard deviation regardless of reasonable correlation differences.