Calculating Alpha And Beta Value Of A Security

The Alpha and Beta value for a security are key metrics in finance derived from the Capital Asset Pricing Model (CAPM).

Beta () is calculated first, as it is a required input for calculating Alpha.

Alpha () is then calculated using the CAPM formula, which incorporates the Beta value.

1. Calculating Beta ()

Beta () is a measure of a security’s volatility (or systematic risk) in relation to the overall market (benchmark).

Beta Formula:

The most common way to calculate Beta is using historical returns through a regression analysis, which mathematically is the covariance of the security’s returns with the market’s returns, divided by the variance of the market’s returns:

Where:

= The return on the individual security (e.g., stock).

= The return on the overall market (the benchmark index, like the S&P 500 or FTSE 100).

= Measures how the security’s returns move in relation to the market’s returns.

= Measures how dispersed the market’s returns are from their mean.

Interpretation of Beta:

Beta Value	Interpretation
	The security moves exactly with the market. Its volatility is the same as the benchmark.
	The security is more volatile than the market. It tends to amplify market movements (e.g., a of means the stock is more volatile than the market).
	The security is less volatile than the market. It moves in the same direction but less dramatically (e.g., a of means it’s less volatile).
	The security’s price movements are completely uncorrelated with the market.
	The security moves in the opposite direction to the market (i.e., when the market goes up, the security tends to go down).

Real Business Example:

A major, established utility company like E.ON (Germany/UK) often has a low Beta (e.g., to ) because its business is stable and less sensitive to overall economic cycles.

A high-growth technology company like NVIDIA (USA) often has a high Beta (e.g., or higher) because its stock is more volatile and sensitive to market sentiment and growth expectations.

2. Calculating Alpha ()

Alpha (), specifically Jensen’s Alpha, is the excess return a security or portfolio generates compared to the return that was expected given its Beta (risk). It measures the value added by a security’s active management or performance unique to the company.

Alpha Formula:

Alpha is calculated by rearranging the CAPM formula to solve for the difference between the actual return and the expected return:

Where:

= Alpha (the excess return).

= The actual return of the security or portfolio.

= The risk-free rate of return (typically the yield on a short-term government bond).

= The Beta of the security (calculated in step 1).

= The market return (the return of the benchmark index).

= The expected return according to CAPM.

Interpretation of Alpha:

Alpha Value	Interpretation
(Positive)	Outperformance. The security or manager earned a return higher than expected given the level of risk (). This is generally sought after by investors.
(Zero)	In-line performance. The security’s return was exactly what was expected given its risk.
(Negative)	Underperformance. The security or manager earned a return lower than expected given the level of risk ().

Real Business Example:

If a global actively managed equity fund focusing on emerging markets like the Templeton Emerging Markets Fund achieves a positive Alpha (e.g., ), it suggests the fund manager’s investment selection and strategy successfully delivered returns higher than what the market risk () alone would predict for a similar fund. This is considered “skill.”