Explanation

The formula for calculating beta is:

$\beta_i = \rho_{i,m} \left( \frac{\sigma_i}{\sigma_m} \right)$

Where:

• $\beta_i$ = beta of the asset
• $\rho_{i,m}$ = correlation coefficient between asset and market returns = 0.8
• $\sigma_i$ = standard deviation of asset returns = 30% = 0.3
• $\sigma_m$ = standard deviation of market returns = 20% = 0.2

Substituting the values:

$\beta_i = 0.8 \left( \frac{0.3}{0.2} \right) = 0.8 \times 1.5 = 1.2$

Therefore, the asset's beta is 1.2.

Why other options are incorrect:

• A (0.24): This would be the result if you multiplied the correlation coefficient by the ratio of market to asset standard deviation (0.8 × 0.2/0.3 = 0.8 × 0.667 = 0.533) or made other calculation errors
• B (2.4): This would be the result if you incorrectly calculated 0.8 × 3.0 instead of 0.8 × 1.5
• C (1.4): This appears to be an arbitrary value not supported by the calculation