How to Calculate Portfolio Beta

By Mike Zaccardi, CMT, CFA · April 09, 2024 · 9 minute read

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How to Calculate Portfolio Beta

Portfolio beta refers to a popular metric that investors use to measure a portfolio’s risk, or its sensitivity to price swings in the broader market. While past performance does not indicate future returns, knowing a portfolio’s beta can help investors understand the price variability of their stocks, or how much their holdings may move if there’s stock volatility or big gains in a benchmark index like the S&P 500.

Investors often consider beta a measure of systematic risk, or risk that stems from the entire market and that investors can not diversify away. Macro events such as interest-rate or economic changes often fall into the category of systematic risk, while idiosyncratic, stock-specific risk includes events like a change in company management, new competitors, changed regulation, or product recalls.

How to Calculate Beta of a Portfolio

The Beta of a portfolio formula requires relatively simple math, as long as investors know the Beta for each stock that they hold and the portion of your portfolio that each stock comprises.

Here are the steps you’d follow to calculate the Beta of a hypothetical portfolio:

1.    Calculate the total value of each stock in the portfolio by multiplying the number of shares that you own of the stock by the price of its shares:

Stock ABB: 500 shares X $20 a share each = $10,000.

2.    Figure out what proportion each stock in their portfolio represents by dividing the stock’s total value by the portfolio’s total value:

Stock ABB’s total value of $10,000/Portfolio’s total value of $80,000 = 0.125.

3.    Multiply each stock’s fractional share by its Beta. This will calculate the stock’s weighted beta:

Stock ABB’s beta of 1.2 X its fractional portfolio of 0.125 = 0.15.

4.    Add up the individual weighted betas.

Here is the whole hypothetical portfolio with a total beta of 1.22, benchmarked to the S&P 500. That means when the index moves 1%, this portfolio as a whole is 22% more risky than the index.

Stock

Value

Portfolio Share

Stock Beta Weighted Beta
ABB $10,000 0.125 1.20 0.15
CDD $30,000 0.375 0.85 0.319
EFF $15,000 0.1875 1.65 0.309
GHH $25,000 0.3125 1.42 0.44375
Sum 1.22

4 Ways to Characterize Beta

Investors always measure a portfolio’s beta against a benchmark index, which they give a value of 1. Stocks that have a beta higher than one are more volatile than the overall market, and those with a beta of less than one are less volatile than the overall market.

Understanding beta is part of fundamental stock analysis. Once you know the beta of your portfolio, you can make changes in order to increase or decrease its risk based on your overall investment strategy by changing your asset allocation.

There are four ways to characterize beta:

High Beta

A high beta stock — one that tends to rise and fall along with the market often — has a value of greater than 1. So if a stock has a beta of 1.2 and is benchmarked to the S&P 500, it is 20% more volatile than the broader measure.

If the S&P 500 rises or falls 10%, then the stock would conversely rise or fall 12%. The same would be true for portfolio beta. While there’s more downside risk with high-beta stocks, they can also generate bigger returns when the market rallies – a principle of Modern Portfolio Theory.

Low Beta

A low beta stock with a beta of 0.5 would be half as volatile as the market. So if the S&P 500 moved 1%, the stock would post a 0.5% swing. Such a stock may have less volatility, but it also may have less potential to post large gains as well.

Still, investors often prefer lower volatility securities. Low beta investment strategies have shown strong risk-adjusted returns over time, too.

Negative Beta

Stocks or portfolios with a negative beta value inversely correlate with the rest of the market. So when the S&P 500 rises, shares of these companies would go down or vice versa.

Gold, for instance, often moves in the opposite direction as stocks, since investors tend to turn to the metal as a haven during stock volatility. Therefore, a portfolio of gold-mining companies could have a negative beta.

So-called defensive stocks like utility companies also sometimes have negative beta, as investors buy their shares when seeking assets less tied to the health of the economy. A downside to negative beta is that expected returns on negative beta securities tend to be weak – even less than the risk-free interest rate.

Zero Beta

A stock or portfolio can also have a beta of zero, which means it’s uncorrelated with the market. Some hedge funds seek a market-neutral strategy. Being market-neutral means attempting to perform completely indifferent to how an index like the S&P 500 behaves.
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How to Calculate an Individual Stock’s Beta

For investors, calculating the beta of all their stock holdings can be time consuming, and typically, financial data or brokerage firms offer beta values for stocks.

But if you wanted to calculate beta for an individual stock, you’d divide a measure of a stock’s returns relative to the broader market over a given time frame by a measure of the market’s return by its mean, also over a specific time frame. Here is the formula:

Beta = covariance/variance

Covariance is a measure of a security’s returns relative to the market’s returns.

Variance is a measure of the market’s return relative to its mean or average.

Recommended: What Is Covariance and How Do You Calculate It?

Alpha vs Beta vs Smart Beta

Beta is one of the Option Greeks, terminology frequently used by traders to refer to characteristics of specific securities or derivatives in the market. Another commonly used Greek term is Alpha. While beta refers to an asset’s volatility relative to the broader market, Alpha is a measure of outperformance relative to the rest of the market.

Beta also comes up a lot in the exchange-traded fund or ETF industry. Smart Beta ETFs are funds that incorporate rules- or factor-based strategies.

What Impacts Beta?

A variety of factors impact an asset’s beta. In general, stocks seen as riskier than average typically feature higher betas. Stock-specific factors such as debt levels, aggressive management, bold projects, volatile cash flows, and even ESG factors can influence a stock’s idiosyncratic risk. Higher business risk, while stock-specific, can lead to a more volatile stock price than the overall market, hence a higher beta.

Higher betas often appear in particular sectors. There are even investment fund strategies that play on beta – you can buy funds that exclusively own high beta or low beta stocks. A stock’s sector, industry, geographic location, and market cap size all impact a stock’s volatility and beta.

Cyclical and growth sectors like energy, industrials, information technology, and consumer discretionary often feature high betas. Utilities, consumer staples, real estate, and much of the healthcare sector typically have low beta.

Small caps and stocks domiciled in emerging-market economies also often have a higher beta (compared to the U.S. large-cap S&P 500).


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Important Things to Know About Beta

1.    A stock’s beta may change over time. Because beta relies on historical price data, it is subject to change.

2.    Beta is not a complete measure of risk. It can be a useful way for investors to estimate short-term risk but it’s less helpful when it comes to considering a long-term investment because the macroeconomic environment and company’s fundamentals may change. In some cases, beta is not the best measure of a stock or a portfolio’s risk.

3.    Beta is an input when investors are using the Capital Asset Pricing Model (CAPM) — a way to measure the expected return of assets taking into account systematic risk. It’s a method that also looks at the cost of capital for investors.

4.    The estimated beta of a stock will be less helpful for companies that do not trade as frequently. Thin liquidity for a stock may bias its beta value since there is less robust historical price data.

5.    Beta does not offer a complete picture of a stock’s risk profile as it’s linked to systematic risk. Investors must also consider stock-specific risk when managing their portfolios.

The Takeaway

As discussed, beta is a popular metric that investors use to measure a portfolio’s risk, or its sensitivity to price swings in the broader market. Knowing stock holdings’ betas can be important information when you’re building your portfolios.

You can calculate their portfolio beta using simple math as long as you’re able to obtain the individual betas for your stock holdings. While beta is a helpful tool to try to gauge potential volatility in a portfolio, its reliance on historical data makes it limited in measuring the complete risk profile of an asset or portfolio.

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FAQ

What is a good beta for a portfolio?

In a general sense, a good beta for a portfolio would be 1. That’s only a general guideline or rule of thumb, however, as it means that a portfolio’s value is roughly as volatile as the market overall.

What does a beta of 1.3 mean?

A beta of 1.3 means that a portfolio’s value is 30% more volatile than the overall market, which means its value will swing more wildly than the market.

Why is market portfolio beta 1?

Beta measures a portfolio or asset’s sensitivity relative to the overall market. If a portfolio’s beta is 1, it is equally as volatile as the market, not more or less so.

How do I reduce my portfolio beta?

Perhaps the simplest way to reduce your overall portfolio’s beta is to replace higher-beta assets within the portfolio with assets that have lower associated beta.

Is it possible to have zero beta portfolio?

It is possible, and would amount to a zero-beta portfolio, which means the portfolio itself has no systemic risk whatsoever. In other words, this portfolio would have no relationship to the overall movements of the market, and likely have low returns.

What is the difference between stock beta and portfolio beta?

A stock beta is a measure of an individual stock’s volatility, while portfolio beta is a measure of an overall investment portfolio’s volatility.


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