# 4 ways to calculate beta

Beta is the volatility or risk of a particular stock relative to the volatility of the entire market. Beta is the indicator of a particular stock's risk and is used to gauge its expected return. Beta is, along with debt and price ratios, one of the fundamental metrics that analysts look at when choosing stocks for their portfolios.

## Steps

### Method 1 of 4: Calculate beta using a simple equation

#### Step 1. Find the risk-free interest rate

This is the rate at which an investor can invest their money without risk, for example with US dollar treasury bills or French or German government bonds in euros. This number is expressed as a percentage.

#### Step 2. Determine the respective rates of return for the stock and the representative market or index

These numbers are also expressed as percentages. Usually, rates of return are calculated over several months.

### These values ​​can be negative, which means that investing in the stock or the market (or the index) would have resulted in a loss during the period. If only one of these two rates is negative, the beta will be negative

#### Step 3. Subtract the risk-free interest rate from the stock's return

If the stock's return is 7% and the risk-free interest rate is 2%, the subtraction will give a result of 5%.

#### Step 4. Subtract the risk-free interest rate from the market (or index) rate of return

If the market or index rate of return is 8% and the risk-free interest rate is 2% again, the subtraction will give a result of 6%.

#### Step 5. Divide the difference between the stock's return minus the risk-free interest rate by the difference between the market (or index) return minus the risk-free interest rate

You calculated the beta, which is usually expressed as a decimal value. In the example below, the beta would be 5 divided by 6, which is 0.833.

• The beta of the market itself or that of the representative index is by definition 1, because the market is compared against itself and the result of dividing any non-zero number by itself is equal to 1. A beta below 1 means the stock is less volatile than the overall market while a beta above 1 means the stock is more volatile than the overall market. The beta value can be less than zero, which means either the stock is losing value as the market is gaining in value (which is most likely) or the stock is gaining in value as the market is losing. in value (less likely).
• When calculating, it is common, although not essential, to use an index representative of the market in which the stock is traded. For French stocks, the CAC 40 is usually used, although a small stock can be compared to the SBF 120. For European stocks, you can use the Euro Stoxx 50.

### Method 2 of 4: Use beta to determine the performance of a stock

#### Step 1. Find the risk-free interest rate

This is the same value that is described and used above in the section "Calculating the beta of a stock". We will use the same 2% value again.

#### Step 2. Determine the performance of the representative market or index

In this example, we'll use 8% again.

#### Step 3. Multiply the value of beta by the difference between the market return and the risk-free interest rate

In this example, we'll use a beta equal to 1.5. Using 2% for the risk-free interest rate and 8% for the market return, this gives us 8 - 2 = 6%. Multiplied by a beta of 1.5 the result is 9%.

#### Step 4. Add the result to the risk-free interest rate

This produces a sum of 11%, which is the expected rate of return on the stock.

### Method 3 of 4: Use Excel charts to determine beta

#### Step 1. Create three price columns in Excel

The first column will contain the date. In the second column, report the prices of the index, it is the “market” against which you will compare your beta. In the third column, report the prices of the stock whose beta you are trying to calculate.

#### Step 2. Enter your data into the workbook

Start with one month intervals. Choose a date, for example the first day of the month and enter the corresponding value for the stock index (try with the CAC 40) then that of the stock you have chosen. Try to enter data for 15 to 30 recent dates and go back about a year or two in the past. Note the price of the index and the stock on these dates.

### The farther back you go, the more accurate your beta calculation will become. Historical beta changes as you follow the index and the stock for longer

#### Step 3. Create two performance columns to the right of the price columns

One column will contain the return on investment of the index and the second the return on investment of the stock. You will use an Excel formula to calculate the values, which you will learn in the next step.

#### Step 4. Start by calculating the return on the equity index

In the second cell of your Index Return column, enter the "=" sign. With your cursor, click on the "second" cell of your index price column, enter the "-" sign and then click on the first cell of your index price column. Finally, enter the sign "/" and click again on the first cell of your column containing the index prices then press the "Enter" key.

• Since the yield is a calculation over two or more dates, you won't enter anything in the first cell. You'll need at least two data samples to calculate the returns, which is why we're starting at the second cell of our returns column.
• You have subtracted the most recent value from the oldest value and divided the result of that subtraction by the oldest value. This gives you the percentage gain or loss for that period.
• Your equation in the yield column should look like: = (B3-B2) / B2

#### Step 5. Use the copy function to repeat this process for all the data points in your index price column

You can do this by clicking on the little square at the bottom right of the first cell in the yield column and stretching it to the last data point. You then instruct Excel to replicate the same formula for all of the data points.

#### Step 6. Repeat the same process to calculate the returns for the stock you have chosen

When completed, you should have two columns, formatted as percentages, which will contain the returns of the stock and the index.

#### Step 7. Create a chart from the data

Select all of the data from both yield columns and click the Excel Chart button. Select a scatter plot from the list of available options. Give the horizontal axis the name of the index you are using (for example CAC 40) and the vertical axis the name of the action you are using.

You can do this by selecting the trendline from the menu bar in newer versions of Excel or manually finding it in Graph → Add Trendline. Make sure you display the equation on the graph, along with the R value2.

• Make sure you choose a linear trendline and not a moving average or polynomial line.
• Display the equation on the graph, along with the value of R2, depending on the version of Excel you have. Newer versions of Excel will allow you to view the equation and R-value2 by finding the correct layout of the graph in the Graph Tools tab of the menu bar.
• In older versions of Excel, navigate to Graph → Add Trendline → Options. Then check the boxes "Display the equation on the graph" and "Display the coefficient of determination (R2) on the chart”.

#### Step 9. Find the coefficient for the value of "x" in the trendline equation

The equation of the trend line will be written in the form y = βx + a. The coefficient of the value of x is the beta you are looking for.

• R-value2 is the relationship between the variance of the stock's return and the variance of the market's return. A large number, like 0.869, indicates that the variance of the two is strongly related. A low number, like 0.253, indicates a less related variance between the two.

### Method 4 of 4: Interpret the beta

#### Step 1. Know how to interpret beta

Beta is the risk, relative to the overall market, that an investor takes by owning a given stock. This is why you need to compare the performance of a stock against the performance of an index, the index is the benchmark. The risk of an index is fixed with a value equal to 1. A beta of less than 1 means that the stock is less risky than the index against which it is compared. A beta greater than 1 means that the stock is riskier than the index to which it is compared.

• Let's take an example. Let's say that the beta of the Gino Pest Killer is calculated with a value of 0.5. This stock is, compared to the CAC 40 which is the benchmark index, half the risk. If the CAC 40 loses 10%, the Gino share will tend to lose only 5%.
• Let's take another example, the Funeral Home Frank has a beta of 1.5 against the CAC 40. If the CAC 40 drops 10%, you can expect the Frank Funeral Home share price to drop more. than the CAC 40, or around 15%.

#### Step 2. Realize that risk is also correlated with return

High risk, high reward; low risk, low reward. A stock with a low beta will not lose as much as the CAC 40 when it falls, but will not gain as much as the CAC 40 when it gains in value. In contrast, a stock with a beta greater than 1 will lose more than the CAC 40 when it falls, but will also gain more when the market is bullish.

### For example, let's go back to our example of the Pest Killer Gino which has a beta of 0.5. When the market goes up 30%, Gino only goes up 15%. But when the market concedes 30%, Gino only gives up 15%

#### Step 3. Know that a stock with a beta of 1 will move in sync with the market

If you do your beta calculations and find that the stock has a beta of 1, that means it is no more and no less risky than the index you are using as a benchmark. If the market gains 2%, your stock will gain 2%; if the market loses 8%, your stock will lose 8%.

#### Step 4. Place stocks with high and low betas in your portfolio to diversify it adequately

The right mix will allow you to resist bear markets. Of course, stocks with a low beta usually underperform the market when it is bullish, a good mix of betas also means that you will not benefit from the maximum potential of the markets when the market is in great shape.

#### Step 5. Realize that, like most financial prediction tools, beta cannot fully predict the future

Beta actually measures the volatility of a stock in the past. We usually project volatility into the future, but not always effectively. The beta of a stock can change dramatically from year to year. Using a stock's historical beta may therefore not always be an accurate way to predict its current and future volatility.