Explanation

The beta of an asset is calculated using the formula:

$\beta = \rho \times \frac{\sigma_{asset}}{\sigma_{market}}$

Where:

• $\rho$ = correlation coefficient between asset and market returns = 0.7
• $\sigma_{asset}$ = standard deviation of asset returns = 10%
• $\sigma_{market}$ = standard deviation of market returns = 14%

Substituting the values:

$\beta = 0.7 \times \frac{10\%}{14\%} = 0.7 \times 0.7143 = 0.5$

Therefore, the beta of the asset is 0.5.

Key Points:

• Beta measures the sensitivity of an asset's returns to market returns
• A beta of 0.5 means the asset is half as volatile as the market
• This calculation is fundamental in the Capital Asset Pricing Model (CAPM)