The Formula for Calculating Beta

Beta is a measure used in fundamental analysis to determine the volatility of an asset or portfolio in relation to the overall market. The overall market has a beta of 1.0, and individual stocks are ranked according to how much they deviate from the market.

What Is Beta?

A stock that swings more than the market over time has a beta greater than 1.0. If a stock moves less than the market, the stock's beta is less than 1.0. High-beta stocks tend to be riskier but provide the potential for higher returns. Low-beta stocks pose less risk but typically yield lower returns.

As a result, beta is often used as a risk-reward measure, meaning it helps investors determine how much risk they are willing to take to achieve the return for taking on that risk. A stock's price variability is important to consider when assessing risk. If you think of risk as the possibility of a stock losing its value, beta is useful as a proxy for risk.

How to Calculate Beta

To calculate the beta of a security, the covariance between the return of the security and the return of the market must be known, as well as the variance of the market returns.

 Beta = Covariance Variance where: Covariance = Measure of a stock’s return relative to that of the market Variance = Measure of how the market moves relative to its mean \begin{aligned} &\text{Beta} = \frac{ \text{Covariance} }{ \text{Variance} } \\ &\textbf{where:} \\ &\text{Covariance} = \text{Measure of a stock's return relative} \\ &\text{to that of the market} \\ &\text{Variance} = \text{Measure of how the market moves relative} \\ &\text{to its mean} \\ \end{aligned} Beta=VarianceCovariancewhere:Covariance=Measure of a stock’s return relativeto that of the marketVariance=Measure of how the market moves relativeto its mean

Covariance measures how two stocks move together. A positive covariance means the stocks tend to move together when their prices go up or down. A negative covariance means the stocks move opposite of each other.

Variance, on the other hand, refers to how far a stock moves relative to its mean. For example, variance is used in measuring the volatility of an individual stock's price over time. Covariance is used to measure the correlation in price moves of two different stocks. 

The formula for calculating beta is the covariance of the return of an asset with the return of the benchmark, divided by the variance of the return of the benchmark over a certain period.

Beta Examples

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.

Calculating the Beta for Apple:

An investor is looking to calculate the beta of Apple (AAPL) as compared to the SPDR S&P 500 ETF Trust (SPY). Based on recent five-year data, the correlation between AAPL and SPY is 0.83. AAPL has a standard deviation of returns of 23.42% and SPY has a standard deviation of returns of 32.21%.

 Beta of AAPL = 0 . 8 3 × ( 0 . 2 3 4 2 0 . 3 2 2 1 ) = 0 . 6 0 3 5 \begin{aligned} &\text{Beta of AAPL} = 0.83 \times \left ( \frac{ 0.2342 }{ 0.3221 } \right ) = 0.6035 \\ \end{aligned} Beta of AAPL=0.83×(0.32210.2342)=0.6035

In this case, AAPL would be considered less volatile than SPY, as its beta of 0.6035 indicates the stock theoretically experiences 40% less volatility.

Calculating the Beta for Tesla:

Let's assume the investor also wants to calculate the beta of Tesla (TSLA) in comparison to SPY. Based on recent five-year data, TSLA and SPY have a covariance of 0.032, and the variance of SPY is 0.015.

 Beta of TLSA = 0 . 0 3 2 0 . 0 1 5 = 2 . 1 3 \begin{aligned} &\text{Beta of TLSA} = \frac{ 0.032 }{ 0.015 } = 2.13 \\ \end{aligned} Beta of TLSA=0.0150.032=2.13

Therefore, TSLA is theoretically 113% more volatile than SPY.


How Do You Calculate Beta In Excel?

The Bottom Line

Betas vary across companies and sectors. Many utility stocks, for example, have a beta of less than 1. Conversely, many high-tech stocks on the Nasdaq have a beta greater than 1, offering the possibility of a higher rate of return, but also posing more risk.

It's important that investors distinguish between short-term risks (where beta and price volatility are useful) and long-term risks (where big picture fundamental risk factors are more prevalent).

Investors looking for low-risk investments might gravitate to low beta stocks, meaning their prices won't fall as much as the overall market during downturns. However, those same stocks won't rise as much as the overall market during upswings. By calculating and comparing betas, investors can determine their optimal risk-reward ratio for their portfolio.

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