Beta vs. Correlation

CFA Level II
#1

the formula of beta is Cov i,m / Varm

meaning the covariance between the asset and the market over the variance of the market.

The formula of correlation coefficient is

Cov 1, m / SD1x SDM

meaning the correlation coefficient is calculated as the covariance between the asset and the market over the product of both standard deviations.

Why is there a difference in the way it is calculated?

#2

Because beta isn’t correlation.

beta = cor(sec. returns, mkt. returns) × (σ sec. returns / σ mkt. returns)

Beta is the correlation of returns times the relative volatility of returns.