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How to Calculate Beta
Financial Accounting (07 BOAC)
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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.
Beta: Covariance (ri,rm )/Variance of Market
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.
_Beta: Correlation (ri,rm) S(i)/ S(m)_*
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, 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, or 0 multiplied by 0 divided by 0. 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 and the variance of the S&P 500 ETF is 0. Tesla Motors Incorporated has a beta of 2, or 0 divided by 0. Therefore, Tesla Motors Incorporated is theoretically 113% more volatile than the SPDR S&P 500 ETF Trust.
Exercise
a) A share has a beta of 0 and an expected return of 9%. Expected return on the market is 11%. What is the risk free rate?
b) You have found that the share of Nictus Holdings pays a return of 8%. The return of an average asset at the NSX is 13%. The covariance of Nictus Holdings’ share with that of the market is 18 while the variance of the market returns is 9.
Required:
1) If the three month Namibian Government Treasury Bill pays 6% currently, is the return on the share of Nictus Holdings correct or fair? 2) Explain the justification for using the beta value when calculating returns using the CAPM.
How to Calculate Beta
Course: Financial Accounting (07 BOAC)
University: Namibia University of Science and Technology
