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The Basics of Calculating Portfolio Beta

November 30, 2020 · 5 minute read

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The Basics of Calculating Portfolio Beta

Investors can gauge the risk in their stock holdings by calculating their portfolio’s beta, or its sensitivity to price swings in the broader market.

While past performance is not indicative of future returns, knowing their 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.

Beta is often considered a measure of systematic risk, or risk that stems from the entire market and cannot be diversified 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.

Calculating portfolio beta involves determining the weighted betas of all the individual stocks in a portfolio and adding up the values.

How Is Portfolio Beta Measured?

A stock or portfolio’s beta is always measured against a benchmark index. The market’s beta always has a value of 1. Beta can be characterized in these four ways:

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. And 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 be less volatile but it also may have less potential to post large gains as well.

Negative Beta

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

Gold, for instance, often moves in the opposite direction as stocks as investors tend to turn to the metal as a haven when stock markets get volatile. 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.

Zero Beta

A stock or portfolio can also have a beta of zero, which means it’s uncorrelated with the market.

How to Calculate Portfolio Beta

Calculating the beta of a portfolio can be done with relatively simple math, as long as investors know the beta for each stock that they hold.

Let’s take a look at a hypothetical portfolio:

  1.   Investors can calculate the total value of each stock in their portfolio by multiplying the number of shares that they own of the stock by the price of its shares:

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

  2.   Then they can 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.   Investors can multiply each stock’s fractional share with 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.   Then they can add up the individual weighted betas, which will equal the portfolio’s overall beta.

Here is the whole hypothetical portfolio with a total beta of 1.22. Say this portfolio is 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 it’s benchmarked against.



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

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 here’s a breakdown of how beta is usually calculated.

Beta is figured out by dividing 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.

Alpha vs. Beta vs. Smart Beta

Beta is one of the Greeks, or 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 movement 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, like the SoFi 50 ETF, are funds that incorporate rules- or factor-based strategies.

Important Things to Know About Beta

  1.   A stock’s beta may change over time. Because beta is reliant 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 their 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.

  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 if its shares aren’t frequently traded. Thin liquidity for a stock may bias its beta value since the historical price data will be less robust.

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

The Takeaway

For investors, knowing their stock holdings’ betas can be important information when building their portfolios. They can calculate their portfolio beta using simple math as long as they’re able to obtain the individual betas for their 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.

By monitoring the stock-specific fundamentals of all their holdings and diversifying their portfolio, investors can better protect themselves.

Open a SoFi Invest account and start diversifying today.

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The information provided is not meant to provide investment or financial advice. Investment decisions should be based on an individual’s specific financial needs, goals and risk profile. SoFi can’t guarantee future financial performance. Advisory services offered through SoFi Wealth, LLC. SoFi Securities, LLC, member FINRA / SIPC . The umbrella term “SoFi Invest” refers to the three investment and trading platforms operated by Social Finance, Inc. and its affiliates (described below). Individual customer accounts may be subject to the terms applicable to one or more of the platforms below.

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