How to Calculate Beta

Beta is a ratio that measures the volatility or riskiness of a particular security relative to the volatility of the entire stock market. ^{[1] X Research Source} The beta is a measure of the riskiness of a particular security, and it is used to evaluate the expected return of that security. This ratio is one of the basic principles often considered by analysts when choosing stocks for their portfolio, besides the price-to-earnings ratio, shareholder equity, debt-to-equity ratio, and debt-to-earnings ratio. equity and other factors.

Table of Contents

Calculate beta using simple equation

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Find the risk-free coefficient. This is the rate of return an investor expects to achieve on his or her investment, which is free of monetary risk, such as US Treasury Bills on investments. denominated in US Dollars and German Treasury Bills for commercial investments in Euros. This number is usually expressed as a percentage.

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Determine the respective rate of return for the appropriate stock and market or index. This metric is also expressed as a percentage. Usually the rate of return is calculated over several months.

If one or all of these values are negative, investing in the stock or market (indices) generally means a loss for the period. If only one of these two ratios is negative, the beta will be negative.

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Subtract the stock’s return from the risk-free rate. If the stock’s return is 7% and the risk-free rate is 2%, the difference between the return and the risk-free rate will be 5%.

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Subtract the risk-free rate from the market return (index). If the market or index return is 8% and the risk-free rate is 2%, the difference between the market return and the risk-free rate will be 6%.

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Divide the first spread by the second spread. The result is the beta coefficient, and this is usually expressed as a decimal. In the example above, the beta would be 5 divided by 6, which is 0.833.

The beta of the market itself (or the appropriate index) is essentially 1.0 – when the market is compared to itself, and any number (except zero) divided by itself equals 1. ^{[2 ] X Research Source} If the beta is less than 1, the stock is less volatile than the overall market, and a beta greater than 1 means the stock is more volatile than the overall market. The beta value can be less than zero, when the stock loses money while the whole market is up (more likely) or the stock rallies while the market as a whole loses money (less likely). ).
When calculating beta, although not required, it is common to use an index that represents the market in which the stock is trading. For US stocks, the S&P 500 index is commonly used, although an analysis of industrial stocks may be more accurate when comparing the stock to the Dow Jones Industrial Average. There are several other indicators that can be used. For internationally traded stocks, the MSCI EAFE (representing Europe, Australasia, and the Far East) is a suitable proxy.

Use Beta to determine a stock’s rate of return

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Find the risk ratio. This ratio has the same value as described above, in the “Calculating Beta for Stocks” section. For this part, we will use the same value as the above example of 2%.

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Determine the rate of return for the market or a representative index of the market. In this example, we also use the 8% ratio above.

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Multiply the beta by the difference between the market return and the risk-free rate. In this example, we will use a beta value of 1.5, a risk-free rate of 2%, and a market return of 8%, so that the difference between the market return and the risk-free rate is the risk is 8-2, get 6%. Multiply this difference by the beta coefficient of 1.5%, resulting in 9%.

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Add this result to the risk-free rate. The result is 11%, which is the expected return of the stock.

The higher the beta value of a stock, the higher the stock’s rate of return. However, high returns come with increased risk, so it’s important to consider the stock’s other fundamentals before considering whether to add it to your portfolio. Are not.

Use the Excel graph to determine the Beta . value

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Create three price columns in Excel. The first column will be the date column. The second column will enter the index price; this is the “overall market” you are comparing to your beta value. In the third column, enter the price of the stock you are trying to beta.

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Enter data into the spreadsheet. Try to start counting for a period of about a month. For example, select the first or last day of the month – and enter the corresponding value for the stock market index (try using the S&P 500 index) and then the stock price for that day. Try selecting the last 15 or 30 days, or you can expand to a year or two ago. Notice the index and stock prices for each day.

The longer the timeframe you choose, the more accurate the beta calculation will be. You’ll see the beta change when you track both the stock and the index over a longer period of time.

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Create two columns for profitability to the right of the price column. One column will enter the index’s return; The second column will enter the stock’s return. You will use the Excel formula shown in the next step to determine the rate of return.

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Start calculating the stock market index return. In the second cell of the index return column, enter “=” (equal sign). Click the cursor in the second cell in the index column, then enter “-” (minus sign), and then click the first cell in the index column. Next, enter “/” (“divide”), and click the first cell in the index column again. Finally press the “Return” or “Enter” key.

Because returns are calculated over time , you don’t need to enter anything in the first box; leave this box blank. You need at least two data points to calculate the return, which is why you will start in the second cell of the index’s return column.
The calculation above is essentially subtracting the older value from the closest value and then dividing the result by the older value. This calculation shows you the percentage of loss or growth for that period.
The equation for your yield column would probably look like this: =(B3-B2)/B2

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Use the copy function to repeat this process for all data points in the price column of the index. You can do this by clicking on the small square at the bottom right of the index’s yield box and dragging down to the bottom data point. This has the effect of asking Excel to replicate the same formula (above) for each data point.

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Repeat the same process as above, but this time calculate the yield for each stock instead of the index. Once done, you’ll have two columns, formatted as a percentage, that list returns for both stocks and stock indexes.

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Graph the data. Highlight (Highlight) all the data in the two profitability columns and click the Chart icon in Excel. Select the scatter chart type from the list of options. Name the X-axis after the name of the index you’re using (for example, the S&P 500), and the Y-axis will be named after the stock.

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Insert a trendline into the scatter chart. You can add this line by choosing a linear trendline layout in new versions of Excel, or by searching manually by clicking Chart → Add Trendline. Note: you must make sure on the graph show the equation, as well as the R ² value.

Choose a linear trend line, not a polynomial or a moving average.
Whether your chart shows the equation and R value of ² will depend on the version of Excel you are using. Newer versions will allow you to plot the equation and R ² value by clicking on Excel’s Chart Quick Layouts and finding the equation template and R ² value.
For older versions of Excel, navigate to Chart → Add Trendline → Options. Then check both the “Display equation on chart” and “Display R ² value on chart,” “Display R ² value on chart,” boxes.

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Find the coefficient for the “x” value in the trendline equation. ^{[3] X Research Source} Your trendline equation will be written as y = βx + a . The coefficient of the x value is your beta coefficient.

The R value of ² represents the correlation between the variance of stock returns and the variance of overall market returns. For example, this value is high, 0.869, indicating that stock returns are strongly correlated with overall market returns. For example, this value is low, around 0.253, indicating that the two types of returns are not very correlated with each other. ^{[4] X Research Sources}

Find out the meaning of Beta

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Learn how to interpret beta. Beta coefficient is the level of risk a particular stock that an investor assumes is owning to the overall stock market. That’s why you need to compare the return of a stock with the return of an index. This index is the benchmark against which securities are evaluated. The risk of an index is fixed at 1. If the beta is less than 1, the stock is less risky than the index against which it is being compared. If a beta value is higher than 1, the stock is riskier than the index it is being compared to.

Example: Assuming the beta of Gino’s Germ Exterminator stock is calculated at 0.5 relative to the S&P 500 index – the benchmark against which Gino is being compared, the stock is only half as risky. If the S&P index drops 10%, Gino’s stock price will tend to fall only 5%.
As another example, let’s say Frank’s Funeral Service stock has a beta of 1.5 against the S&P index. Thus, if the S&P falls 10%, then Frank’s stock price falls more than the S&P, about 15%.

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Recognize that risk is often related to the rate of return. The higher the risk, the larger the profit; The lower the risk, the less profit will be. A stock with a low beta will of course lose less than the S&P when it falls, but won’t gain more than the S&P when it rises. On the other hand, a stock with a beta above 1 will lose more than the S&P index when it falls, but will also gain more than the S&P index when it rises.

For example, let’s say Vermeer’s Venom Extraction stock has a beta value of 0.5. When the stock market rallied 30%, Vermeer’s stock rose only 15%. But when the stock market fell 30%, Vermeer lost only 15%.

Advice

Note: it is possible that classical covariance is not used because time series financial data are often “tilted towards the end”. In practice, the standard deviation and standard mean of the underlying distribution may not exist! So, instead of using the standard deviation and standard mean, we can use the interquartile scatter and the median instead.
Beta coefficient analyzes the volatility of a stock over a certain period of time, regardless of whether the market is up or down. As with other fundamentals, analysis of past movements cannot guarantee future stock movements.

Warning

Beta alone cannot be used to determine which of the two stocks is riskier if the stock is more volatile, but there is a correlation between lower returns to the market and less volatility. stocks with lower volatility but higher correlation between returns relative to the market.

Steps