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Difference Between Beta and Correlation Coefficient

Correlation measures the degree to which two variables relate to each other. In the other words it is the linear relationship between them. As you probably know the correlationcan be calculated as:

Corr(Asset!arket" # Cov(Asset!arket" $ %d(Asset" & %d(!arket"

Beta is a measure of the systematic non'diversifiable risk of an investment. I was taughtthat a popular misconception about beta is that it measures the volatility of a securityrelative to the volatility of the market. If we would assume that it is true then a security with a beta of would have the same volatility of returns as the volatility of marketreturns. It is not true since beta also incorporates the correlation of returns between thesecurity and the market. Beta can be calculated as:

Beta # Corr(Asset!arket" & )%d(Asset" $ %d(!arket"*

Beta shows how strongly one stock (or portfolio" responds to systemic volatility of theentire market. A beta of means that the stock responds to market volatility in tandem with the market on average. A larger beta means that the stock is more susceptible tomarket risk while a beta less than means that the stock is less responsive to market risk.Beta values are not bounded like the correlation coefficient.

Correlation coefficient on the other hand must be between ' and where ' means thatthe stock and the market move opposite of each other + means that the stock and themarket movements don,t have a relationship and means that the stock moves with themarket.

Because of their different value meanings and bounds the formulas are different. -rom ikipedia the correlation coefficient is

 where X is the stock return and Y  is the market return.

Beta is defined as

 which is e/uivalent to

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