# Alpha & Beta Calculations: How These 2 Investing Tools Help You Determine Performance & Market Volatility

By Chika

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Last Updated: March 26, 2022

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Understanding the numbers behind an investment can be what sets apart a successful portfolio from a depreciating one.

There are several quantitative tools that investors use to select stocks and build portfolios. Perhaps the most famous of these are alpha and beta.

Each is calculated using the historical performance of the underlying equity but with different focal points.

While alpha is used to identify performance relative to an index, beta measures the relative volatility of an investment.

Let's have a look at these metrics and show how you can use each one to choose a suitable stock for your portfolio based on your trading or investing strategy.

## The Difference Between Alpha and Beta

Alpha and beta are both Option Greeks - a terminology frequently used by traders to refer to characteristics of specific securities or derivatives in the market. In essence, both terms are used to define the characteristics of security. Here are the differences between alpha and beta.

### Alpha

The alpha figure for a stock is represented as a single number, like 3 or -5. However, the number indicates the percentage above or below a benchmark index that the stock or fund price achieved. In this case, the stock or fund did 3% better and 5% worse, respectively, than the index.

• An alpha of 1.0 means the investment outperformed its benchmark index by 1%
• An alpha of -1.0 means the investment underperformed its benchmark index by 1%
• If the alpha is zero, its return matches the benchmark

For individual investors, alpha helps reveal how a stock or fund might perform in relation to its peers or the market as a whole.

Professional portfolio managers calculate alpha as the rate of return that exceeds the model's prediction or comes short of it. They use a capital asset pricing model (CAPM) to project the potential returns of an investment portfolio.

That is generally a higher bar. If the CAPM analysis indicates that the portfolio should have earned 5%, based on risk, economic conditions, and other factors, but instead the portfolio earned just 3%, the alpha of the portfolio would be a discouraging -2%.

Formula for Alpha:

Alpha = R – Rf – beta (Rm-Rf)

Whereby:

• R represents the portfolio return
• Rf represents the risk-free rate of return
• Beta represents the systematic risk of a portfolio
• Rm represents the market return, per benchmark

Portfolio managers seek to generate a higher alpha by diversifying their portfolios to balance risk.

Why it Pays to Diversify Your Portfolio

Because alpha represents the performance of a portfolio relative to a benchmark, it represents the value that a portfolio manager adds or subtracts from a fund's return.

The baseline number for alpha is zero, which indicates that the portfolio or fund is tracking perfectly with the benchmark index. In this case, the investment manager has neither added nor lost any value.

### Beta

Often referred to as the beta coefficient, beta is an indication of the volatility of a stock, a fund, or a stock portfolio in comparison with the market as a whole.

A benchmark index (most commonly the S&P 500) is used as the proxy measurement for the market. Knowing how volatile a stock's price is can help an investor decide whether it is worth the risk.

The baseline number for beta is one, which indicates that the security's price moves exactly as the market moves.

• A beta of less than 1 means that the security is less volatile than the market
• A beta greater than 1 indicates that its price is more volatile than the market
• If a stock's beta is 1.5, it is considered to be 50% more volatile than the overall market

Like alpha, beta is a historical number.

### Beta Examples

Here are the betas at the time of writing for three well-known stocks as of November 2021:

• Tesla (TSLA): 2.05
• Micron Technology Inc. (MU): 1.17
• Apple (APPL): 1.19
• Gamestop (GME) -1.50
• SPDR S&P 500 ETY (SPY): 1.00

We can see that Tesla is 105% more volatile than the broader market (S&P 500), while Apple and Micron are 19% and 17% more volatile than the border market respectively.

On the other hand, GameStop has a negative beta of -1.50 because its stock performance is inversely related to the market as a whole.

When the market rises, a negative-beta investment generally falls.

When the market falls, the negative-beta investment will tend to rise. This is generally true of gold stocks and meme stocks.

Acceptable betas differ by company and industry. The beta of many utility equities is less than 1, while the beta of many high-tech Nasdaq-listed firms is larger than 1.

To investors, this means that while tech companies may give bigger returns, they also carry more risk, whereas utility stocks are consistent earners.

While a positive alpha is always preferable to a negative alpha, the case for beta is less apparent. Lower beta appeals to risk-averse investors, such as pensioners wanting a stable income.

Risk-averse investors seeking better returns are frequently prepared to invest in equities with a higher beta.

### How to Use Beta's Formula

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 =  Variance/Covariance

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

Covariance is used to measure the correlation in price moves of any two stocks.

• A positive covariance means the stocks tend to move in lockstep
• Anegative covariance means they move in opposite directions.

On the other hand, variance refers to how far a stock moves relative to its mean. It is frequently used to measure the volatility of a stock's price over time.

## How to Use Alpha & Beta to Choose Stocks

Alphas and betas can be used to select stocks to invest in. Some investors use them when carrying out due diligence on a stock, while traders may use them to get a sense of volatility and price action on a stock.

How you use them ultimately depends on your investment or trading strategy

Let’s say your goal is to invest in a stock that has consistently outperformed the stock market.

• You would refer to the alpha of a stock to determine how well it performs
• Compare with that of the S&P 500
• Then pick the best stock

If you are someone who doesn’t like volatile investments, you can use the beta to help find investments that align with your risk tolerance.

Alternatively, if you are a trader and prefer shorter time frames (5 mins, 15 minutes), you can use the beta to select a stock that suits your trading strategy.

## The Bottom Line

Investors use alpha and beta to compare the performance and volatility of underlying securities. Investors can use alpha to compare a fund's performance to that of an index or another fund. Beta allows investors to compare a security's volatility to that of an index, allowing them to better align their investments with their risk tolerance.

Keep in mind that alpha and beta are based on past data and do not predict how a stock or fund will perform in the future. To choose assets that meet a certain investing aim, alpha and beta are frequently employed in combination with other ratios or metrics. As such, they are not to be used in isolation as this may lead to wrong analysis and investment choices.

Photo by MART PRODUCTION

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