Practice Problem – CAPM Beta

Practice Question

Intro to Finance
Capital Asset Pricing Model (CAPM)
Beta
Short Answer

Assuming the correlation between an asset and market is 0.67 and the asset and market have standard deviations of 0.34 and 0.19 respectively, the asset’s beta would be closest to:

Answer +
1.200
Explanation +
Step 1: Use the Beta Formula with Correlation

The formula to compute beta from correlation and standard deviations is:

\[ \beta = \frac{\rho \cdot \sigma_a}{\sigma_m} \] where:
  • \(\rho = 0.67\)
  • \(\sigma_a = 0.34\)
  • \(\sigma_m = 0.19\)
Step 2: Plug in the Values
\[ \beta = \frac{0.67 \times 0.34}{0.19} \]
Step 3: Perform the Calculation
\[ \beta = \frac{0.2278}{0.19} \approx 1.20 \]
Final Answer

The asset’s beta is approximately 1.20.