Calculating Beta with Variance and Covariance

A financial analyst tries to calculate beta for a security. The security's standard deviation is 0.18 and the market's variance is 0.10. If the correlation between the security and the market is 0.32, the security's beta is:

Correct. The calculation of beta uses the correlation between the security and the market, the standard deviation of the security, and the standard deviation of the market, as follows: $$\displaystyle \beta_i = \frac{\rho_{i,M}\sigma_i}{\sigma_M} $$. Since the market's variance is given, the standard deviation is the square root of the variance. $$\displaystyle \beta_i = \frac{(0.32)(0.18)}{\sqrt{0.10}}=0.18$$

Incorrect. This answer choice is a calculation using the market's variance in the denominator of the beta formula.

Incorrect. This answer choice can be a calculation of beta when the market's variance is 0.10 and the security's variance is 0.18.

0.18.

0.43.

0.58.