Financial Risk Manager Part 1
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The standard deviation of an asset's return is 10%, and the standard deviation of markets return is 14%. If the correlation of returns with the market index is 0.7, then what is the beta of the asset?
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TTanishq
A
1
B
0.1
C
1.8
D
0.5
Explanation:
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)
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