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What is the formula for calculating beta?

A:

Beta is a measure used in fundamental analysis to determine the volatility of an asset or portfolio in relation to the overall market. To calculate the beta of a security, the covariance between the return of the security and the return of market must be known, as well as the variance of the market returns.

How to Calculate Beta

The formula for calculating beta is the covariance of the return of an asset and the return of the benchmark divided by the variance of the return of the benchmark over a certain period. Similarly, beta could be calculated by first dividing the security's standard deviation of returns by the benchmark's standard deviation of returns. The resulting value is multiplied by the correlation of the security's returns and the benchmark's returns.

For example, an investor wants to calculate the beta of Apple Incorporated when compared to the SPDR S&P 500 ETF Trust. Based on hypothetical data over the past five years, assume the correlation between Apple Incorporated and the SPDR S&P 500 ETF Trust is 0.85, Apple Incorporated has a standard deviation of returns of 28% and the SPDR S&P 500 ETF Trust has a standard deviation of returns of 12%.

The beta of Apple Incorporated is 1.98, or 0.85 multiplied by 0.28 divided by 0.12. In this hypothetical case, Apple Incorporated is considered more volatile than the market exchange-traded fund (ETF). Apple Incorporated theoretically experiences 98% more volatility than the SPDR S&P 500 Exchange Traded Fund Trust.

For another example, assume the investor also wants to calculate the beta of Tesla Motors Incorporated in comparison to the SPDR S&P 500 ETF Trust. In this hypothetical case, based on data over the past five years, assume Tesla Motors Incorporated and the S&P 500 ETF have a covariance of 0.032 and the variance of the S&P 500 ETF is 0.015. Tesla Motors Incorporated has a beta of 2.13, or 0.032 divided by 0.015. Therefore, Tesla Motors Incorporated is theoretically 113% more volatile than the SPDR S&P 500 ETF Trust.

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