What is beta in fundamental analysis. The beta coefficient of a security. Where can I view alpha and beta coefficients?

Beta is a measure of the risk of a security relative to the risk of the entire stock market. It reflects the variability of the return of a single security relative to the return of the market as a whole. Beta is one of the main indicators (along with price-to-earnings ratio, equity ratio, debt-to-equity ratio and others) that stock analysts consider when selecting securities for investment portfolios. This article explains how to find beta and use it to calculate a security's return.

Steps

Beta calculation. Simple formula

Find the risk-free rate. This is the rate of return that an investor can expect when investing in safe assets such as U.S. Treasury bills or German government bills. This figure is usually expressed as a percentage.

Determine the corresponding returns of the security and the market or index. These numbers are also expressed as percentages. Typically, returns are calculated over a period of several months.

• One or both of these values ​​can be negative; this means that an investment in the security or market (index) as a whole will result in losses. If one of the two indicators is negative, then the beta will be negative.

1. Subtract the risk-free rate from the security's yield. If the yield on a security is 7% and the risk-free rate is 2%, then the difference is 5%.

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

   Divide the value of the first difference by the value of the second. This is beta, which is expressed as a decimal fraction. For the example above, beta = 5/6 = 0.833.

   Using beta to determine a security's return

   1. Find the risk-free rate (described in the "Calculating Beta" section above). In this section we will use the same value - 2%.

      Determine the return of a market or index. In this section we will use the same 8%.

      Multiply beta by the difference between the market return and the risk-free rate. In this section we will use a beta of 1.5. So: (8 – 2)*1.5 = 9%.

      Add the result and the risk-free rate. 9+2=11% - this is the expected return on the security.

      • The higher the beta value for a security, the higher its expected return. However, the higher the expected return, the higher the riskiness; Therefore, before making an investment decision, it is also necessary to analyze other critical indicators of the security.

   Using Excel Charts to Determine Beta

   1. Create three columns of numbers in Excel. The first column will contain dates. In the second – the price of the index (market). The third is the price of the security for which beta needs to be calculated.

      Enter data into the table. Start with one month intervals. Select a date - for example, the beginning or end of the month - and enter the corresponding price value for a stock market index (try using the S&P500) and then the price value for the security in question. Enter values ​​for 15 or 30 dates, possibly extending back a year or two.

      • The longer the time period you select, the more accurate the beta calculation will be.

   2. Create two columns to the right of the price columns. One column is for the index return, the other is for the security return. Use Excel formula to determine profitability.

      First, let's find the return of the stock index. In the second cell of the index return column, enter "=" (equal sign). Then click on second cell in the column with index prices, enter "-" (minus), click on first cell in the index price column, enter "/" (divide sign), and then click first cell in the column with index prices. Press "Return" or "Enter."

      • Nothing is calculated in the first cell, since you need at least two values ​​to calculate the yield; so you will start from the second cell.
      • To calculate profitability you subtract old price from the new one, and then divide the result by the old price. This gives you the increase or decrease in price (in %) over a certain period of time.
      • Your formula in the yield column might look something like this: = (B3 -B2)/B2

   3. Copy the formula to repeat it in all other cells in the index return column. To do this, click on the lower right corner of the cell with the formula and drag it to the end of the column (to the last value). This way, Excel will repeat the same formula, but using the appropriate data.

      Repeat the same algorithm for calculating the yield of the security in question. After completing the calculations, you will receive two columns with the return (in %) for the stock index and the security.

      Construction schedule. Select all the data in the return columns and click on the chart icon in Excel. Select a scatter plot. Label the X-axis as the index you are using (eg S&P500) and the Y-axis as the security in question.

      Add a trendline to a scatter plot. You can do this by selecting Layout Trendline or by right-clicking on the chart and selecting Add Trendline. Make sure that the equation and R 2 value appear on the graph.

      • Make sure you select a linear trend rather than a polynomial or moving average.
      • The display of the equation and R2 value on the graph depends on the version of Excel you are using. IN latest versions Click on Layout and find the R 2 display.
      • In older versions of Excel, this can be done by clicking on Layout - Trendline - Additional options trend lines and checking the appropriate boxes.

   4. Find the coefficient of "x" in the trend line equation. Your trend equation will be written in the form: y = βx + a. The coefficient of x is the desired beta coefficient.

   Meaning of beta

   1. Learn to interpret beta coefficient. Beta measures the risk of a security (relative to the stock market as a whole) taken on by the investor who owns it. This is why you must compare the return of one security with the return of an index that is the benchmark. The index's default risk is 1. A beta value less than 1 means the security is less risky than the index to which it is compared. A beta greater than 1 means the security is riskier than the index to which it is compared.

      • For example, the beta of the company GIN = 0.5. Compared to the S&P500 (the benchmark), the JIN security is half as risky. If the S&P falls 10%, GIN's stock price will only tend to fall 5%.
      • As another example, imagine that FRANK Company has a beta of 1.5 (compared to the S&P). If the S&P falls by 10%, then the price of FRANK securities is expected to fall by 15% (one and a half times more than the S&P).

As noted above, there is a so-called portfolio theory - the theory of financial investments, within the framework of which, with the help of statistical methods, the most profitable risk distribution of a securities portfolio and profit assessment are carried out. This theory consists of four main elements:

· asset valuation;

· investment decisions;

· portfolio optimization;

· evaluation of results.

In the process of managing an investment portfolio, a manager is constantly faced with the task of selecting new instruments and analyzing the possibility of their inclusion in the portfolio. This can be done using several methods, but the most famous is the model for assessing the return on financial assets ( Capital Asset Pricing Model, CAPM), linking systematic risk and portfolio return (see Fig. 2).

Figure 2 Logic for presenting the CAPM model

The main premises of the CAPM model include the following:

· The main goal of each investor is to maximize the possible increase in his wealth at the end of the planning period by assessing the expected returns and standard deviations of alternative investment portfolios.

· All investors can borrow and lend an unlimited amount at some risk-free interest rate, and there are no restrictions on going short. Short selling is the sale of securities that the investor does not own. The investor sells securities in the hope that in the near future the price of these assets will fall and it will be possible to buy the missing securities.” sale of any assets.

· All investors equally estimate the expected values ​​of return, dispersion and covariance of all assets; this means that investors are on a level playing field when it comes to predicting performance.

· All assets are completely divisible and completely liquid.

· There are no transaction costs.

· Taxes are not taken into account.

· All investors accept the price as an exogenously given value (i.e., it does not take into account that the actions of investors in buying and selling securities may influence the price level on the market for these securities).

· The quantity of all financial assets is predetermined and fixed.

For an investment portfolio, the beta coefficient is calculated by adding the beta coefficients of the securities included in it, multiplied by the corresponding weights (the weight of each security in the portfolio is equal to the quotient of its total value in the portfolio divided by the value of the entire portfolio). The most interesting finding from a portfolio management perspective is that a well-diversified portfolio has no inherent risk, i.e., the change in its return is equal to the change in the return of the market index multiplied by the portfolio's beta. This means that the behavior of a well-diversified portfolio is no different (up to multiplication by a constant) from the behavior of a market index.

The main problem that Markowitz posed and completely solved was formulated as follows: the investor wants to obtain a return equal to r based on a certain set of securities. How should he construct a portfolio with the least total risk and an average return of r? This is a typical optimization problem. The resulting portfolio is determined uniquely both by the indicators of the average return and risk of securities from the set, and by the covariances between them, and is called an efficient portfolio. In this case, naturally, a larger value of r will correspond to higher value overall portfolio risk.

The relationship between expected return (y) and security risk (x) is found by constructing a function. The construction is based on the following considerations:

· the profitability of a security is directly related to its inherent risk;

· risk is characterized by an indicator;

· “average” security, i.e. a security with average risk and return values ​​also has a corresponding return;

· there are risk-free securities with interest rates and.

Based on the above premises, it is proven that the desired relationship is a straight line. Substituting the initial data into the straight line equation, we obtain the following formula:

Considering that the variable x represents a risk characterized by an indicator , A y- expected profitability, we obtain a formula representing the CAPM model:

where is the expected return on the shares of this company;

Return on risk-free securities;

Expected return on average on the securities market;

Beta is the coefficient of a given company

The indicator has a very clear interpretation, representing the market premium for the risk of investing one’s capital not in risk-free government securities, but in risky securities (stocks, corporate bonds, etc.). Similarly, the indicator represents a premium for the risk of investing capital in the securities of a given company. The CAPM model means that the risk premium for investing in the securities of a given company is directly proportional to the market risk premium.

The CAPM model allows you to predict the profitability of a financial asset; in turn, knowing this indicator and having data on the expected income for this asset, you can calculate its theoretical value. That is why the CAPM model is also called the financial asset pricing model.

Systematic risk within the CAPM model is measured using the coefficient (beta coefficient).

Coefficient (eng. beta coefficient) - the amount of risk in relation to a particular security. Those. - coefficient is a unit of measurement that gives a quantitative relationship between the movement of the price of a given stock and the movement of the stock market as a whole.

Each type of security has its own beta coefficient. The value of the indicator is calculated based on statistical data for each company that lists its securities on the stock exchange, and is periodically published in special directories. For each company it changes over time and depends on many factors, in particular those related to the characteristics of the company’s activities from a long-term perspective. This includes, first of all, an indicator of the level of financial leverage, reflecting the structure of sources of funds: all other things being equal, the higher the share of borrowed capital, the more risky the company and the higher its Kovalev V.V. Introduction to financial management. - M.: Finance and Statistics, 2002. - p. 427.

The value also depends on the level of operating leverage, i.e. the greater the share of fixed expenses in their total amount, the higher.

The general formula for calculating the beta coefficient for an arbitrary company is:

In general, the beta coefficient for the securities market is equal to one; for individual companies it fluctuates around one, with most betas falling between 0.5 and 2.0. The interpretation of beta coefficients for a particular company's stock is as follows:

· Beta>1, - the stock is considered risky

· Beta=1, - the stock is equal to the market

· Beta<1, - акция считается защитной

· Beta=0, - the stock is considered risk-free.

An increase in the beta coefficient over time means that investing in the securities of a given company becomes more risky, and a decrease in the beta coefficient over time means that investing in the securities of a given company becomes less risky.

It is important to note that there is no unified approach to calculating coefficients, in particular with regard to the number and type of initial observations. So, for example, one company, when calculating -coefficients, can use the stock price index of one exchange and monthly data on the profitability of companies for five years, while another company can focus on the stock price index of another exchange and use a larger number of observations.

The concept of the coefficient appeared on the Russian securities market in 1995. But a limited number of companies are included in the observation list, as a rule, these are enterprises in the energy and oil and gas complex. See Appendix 1. At the same time, the values ​​of the -coefficients vary quite noticeably.

The linear relationship “return/risk” for specific securities can be represented using a graph called the security market line (Security Market Line, SML - Fig. 3.)

Figure 3 stock market line chart

An important property of the CAPM model is its linearity with respect to the degree of risk. This makes it possible, as noted above, to determine the beta coefficient of the portfolio as the weighted average of the coefficients of the financial assets included in the portfolio:

where is the value of the beta coefficient of the i-th asset in the portfolio;

Portfolio beta value;

Share of the i-th asset in the portfolio;

n- the number of different financial assets in the portfolio.

A generalization of the concept of “securities market line” is the capital market line (Capital Market Line, CML), reflecting the relationship (return/risk) for efficient portfolios, which, as a rule, combine risk-free and risky assets.

The capital market line can be used to benchmark portfolio investments. As follows from the CAPM model, each portfolio corresponds to a point in the quadrant (see Fig. 3). There are three possible locations for this point:

1. on the capital market line (in this case the portfolio is called efficient);

2. below the capital market line (inefficient portfolio);

3. above the capital market line (super-efficient portfolio).

One of the most important indicators for a stock is the beta coefficient - it shows the change in the share price relative to the market situation. When the coefficient β increases, we can talk about an increase in the price of the asset, and a decrease in β indicates a fall in price. With a low beta coefficient, there is almost zero dependence of the price of a given asset on the general market trend.

Beta can be calculated for a single stock or for a selected set of stocks. Using β, you can evaluate the risks and returns of both an individual asset and a selected portfolio of investments relative to a similar portfolio. In other words, a stock's beta indicates the degree of risk associated with a selected portfolio or individual security.

Description

The first person to propose using the beta coefficient of a portfolio to calculate systemic risk was the American economist Harry Markowitz, back in the early 50s of the last century. He first characterized such ratios as “indices of non-diversifiable risk.” The basis is the direct dependence of the profitability of a particular exchange instrument on the average profitability of the market where the asset is traded. For example, IBM shares - when calculating their beta coefficient, we will need the profitability of the stock itself and the profitability of the exchange platform itself where they are traded. Similarly, to calculate the profitability of a corporation or even an entire industry: we take the profitability indicator of a specific company or industry and the average profitability ratio of the entire industry.

If we get β = 1, then the conclusion will be simple: the risk of a particular instrument that is not subject to diversification coincides with the general market risk. If β = 0, which means we have come across an absolutely risk-free asset – relative to the risk that is not subject to diversification. The higher the beta value, the higher the risks for the selected investment. An important advantage of the β-coefficient is the ability to calculate the portion of risk to be diversified for a specific investment object in both macro- and microeconomics.

But an investor, as a rule, tries to find the overall value of risk, so relying only on the β coefficient when forming an investment portfolio will be a dubious decision. This picture can be observed when investing in production, when there are not enough funds for full-fledged investments or there is no option to distribute investments. Often there is a need to calculate the risks for specific investment objects consisting of different niches, at the same time, the β-coefficient evaluates the risks of an asset relative to a specific market. That is, you will not be able to compare the risk of purchasing shares with the risk of investing in the construction of a manufacturing factory.

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Beta coefficient calculation

For an asset consisting of a selected set or relative to other securities, or an asset in the form of a stock market index of a relative reference portfolio, the coefficient βa is calculated in linear regression for the time period Ra,t relative to the portfolio return for the time period Rp,t:

Ra,t = a + βаrp,е+ Еt

To calculate the beta of a security:

βa = Cov (ra,rp) : Var(rp)

Now let's look at the components of the formulas:

• ra is the profitability of the asset in question or the size of the assessment for which the asset is calculated;
• rp – the return of a security or market is compared with this value;
• Cov – covariance of the estimated value and the standard;
• Var – the magnitude of the possible deviation of the indicator.

Essentially, beta is a single case of the relationship between several variables. And the variables here are the securities of the selected company relative to other securities of the stock market.

What will the beta coefficient show?

Upon obtaining the value β = 1, we can conclude that the risk of underdiversification for a given stock is equal to the general market risk indicator. If beta is zero, then you are working with a risk-free asset. In general, the higher your beta value, the more risky the asset is. In this way, it is possible to analyze the distribution of investment risks at both the micro and macroeconomic levels.

To calculate the coefficient β, two quantities are needed:

• The company's profitability level. It represents the difference between the opening and closing of a company's shares on the stock market for a selected period of time.
• Average market level of profitability. This is the average rate of return of all securities included in a particular investment portfolio. The portfolio may be composed of shares of the company in question.

The capital asset pricing model, or its English abbreviation CAPM (Capital Assets Price Model), was created in the 70s of the last century to evaluate the financial assets of an enterprise: cash and securities. This model was developed and shaped by such famous scientists as: Sharpe, Lintner and Mossin. The CAPM model is designed to determine the price of a stock or the value of a company in the future, in other words, the current assessment of whether a company is overbought or oversold.

The CAPM model is often used as an addition to the portfolio theory of G. Markowitz. In the practice of constructing investment portfolios, the CAPM model is usually used to select assets from the entire set, then using the G. Markowitz model, an optimal portfolio is formed.

The CAPM model connects such components as the future profitability of a security and the risk of this security. Let's look at the CAPM model (also called the Sharpe model) in more detail.

(module 297)

Sharpe's formula for the relationship between future security returns and risk

Where:
R - expected rate of return;
R f - risk-free rate of return, usually the rate on government bonds;
R d - market profitability;
β is the beta coefficient, which is a measure of market risk (non-diversifiable risk) and reflects the sensitivity of the security's return to changes in the return of the market as a whole.

So, expected rate of return– this is the return on the security that the investor expects. In other words, this is the profit of this security.

Risk-free rate of return– this is the yield obtained on risk-free securities. As a rule, they take the rate on government bonds. To see rates on government bonds, you can go to the website of the Central Bank of the Russian Federation. http://cbr.ru/hd_base/OpenMarket.asp. In Russia, at the moment, it is 5.04%.

Under market profitability understand the return of the index of a given market, in our case the RTS Index (RTSI). For American stocks, take the S&P500 index.

Beta– a coefficient indicating the riskiness of a security.

Example of application of the capital asset pricing model
And so, let's try to calculate the future profitability of Gazprom's GAZP stock. Let's take the monthly quote for this stock and the RTS index (RTSI) or MICEX index (MICEX) for the period from August 27, 2009 to August 27, 2010 (quotes can be exported to Excel from the website finam.ru).

Calculating beta using formula
In cell F2, enter the following formula:
=INDEX(LINEST(C3:C13,D3:D13),1)
The beta coefficient will be 1.043.

Beta calculation using the Data Analysis add-on
To calculate the beta coefficient using Data Analysis, you must install the Data Analysis Excel add-in. In it, select the “Regression” section and set input intervals that correspond to the returns on Gazprom shares and the MICEX index. The report will appear in a new worksheet.

The regression report looks like this: Cell B18 contains the calculation of the linear regression coefficient, just the required beta coefficient. The beta coefficient is 0.67. The report also contains an R-squared indicator (coefficient of determinism), the value of which is 0.63. It shows the strength of the relationship between independent variables (the relationship between stock returns and the index). The Multiple R indicator is a correlation coefficient. As you can see, the correlation coefficient is 0.79, which indicates a strong connection between the return of the index and the return of Gazprom shares.

It remains to calculate the monthly market return, the return on the MICEX index, which is calculated as the arithmetic mean return of the index. The average monthly return on the MICEX index is -0.81%, and the average monthly return on Gazprom shares is 1.21%.

We calculated all the necessary parameters of the CAPM model. Now let's calculate the fair rate of return on Gazprom shares for the next month. R f =5.04%, β=0.67, R d =-0.81%.

R GAZP =5.04%+0.67*(-0.81%-5.04%)=1.12%

The rate of return on Gazprom shares is 1.12% for the next month. We can say that this is the forecast price of future profitability in the next reporting period (we have a month). The Capital Asset Pricing Model (CAPM) is a powerful tool for evaluating stocks and securities that will allow you to create a profitable investment portfolio.

Beta coefficient(beta factor)- an indicator calculated for a security or a portfolio of securities. It is a measure of market risk, reflecting the variability of the return of a security (portfolio) in relation to the return of the portfolio (market) on average (the average market portfolio).

If the security (the portfolio in the second case) is less risky than the portfolio (the market as a whole in the second case), then the beta coefficient is less than 1. Otherwise, the beta coefficient is greater than 1.

Beta coefficient (β) shows the sensitivity of the price of an individual security to the value of the index. For example, a beta of 2 means that if the index rises by 1 percent, the price of the security will rise by 2 percent. A negative beta indicates an inverse relationship between changes in the price of a security and the value of the index. A beta coefficient of zero indicates that there is no relationship between changes in the security's price and the index.

1. Here you can see the coefficients: beta (β), alpha (α) and volatility for different periods.