The capital assets pricing model or as 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 formed by such famous scientists as: Sharp, Lintner and Mossin. The CAPM model is designed to determine the price of a share or the value of a company in the future, in other words, the current estimate of a company's overbought or oversold status.

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

The CAPM connects components such as the future yield of a security and the risk of that security. Let's consider the CAPM model (it is also called the Sharpe model) in more detail.

(module 297)

Sharpe's formula for the relationship between the future return of a security and risk

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

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

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

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

Beta- coefficient showing the riskiness of the security.

An example of the 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 quotation by months of this stock and the RTS (RTSI) or MICEX (MICEX) index for the period from August 27, 2009 to August 27, 2010 (quotations can be exported to Excel from the finam.ru website).

Calculating beta using a 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-in
To calculate the beta coefficient through "Data Analysis", you need to install the "Data Analysis" Excel add-in. In it, select the "Regression" section and set the input intervals that correspond to the returns on Gazprom shares and the MICEX index. The report appears in the 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. Also in the report there is an indicator R-square (coefficient of determinism), the value of which is 0.63. It shows the strength of the honey dependence on independent variables (the relationship between stock returns and the index). Indicator Multiple R - is the correlation coefficient. As you can see, the correlation coefficient is 0.79, which indicates a strong relationship between the index return and the return on Gazprom shares.

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

We've calculated everything required parameters CAPM models. Now let's calculate the fair rate of return for 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 predicted price of future profitability in the following reporting period(we have a month). The Capital Assets Pricing Model (CAPM) is a powerful tool for valuing stocks and valuable papers, will allow you to create a profitable investment portfolio.

Let us analyze such an investment indicator as the beta coefficient, calculate it by real example with using Excel and consider various modern modifications.

Beta coefficient. Definition

Beta coefficient (EnglishBeta,β, beta coefficient) - determines the measure of the risk of the stock (asset) in relation to the market and shows the sensitivity of the change in the yield of the stock in relation to the change in the profitability of the market. Beta can be calculated not only for an individual stock, but also for an investment portfolio. The coefficient is used as a measure of systematic risk, and is used in the model of U. Sharp - the assessment of capital assets CAPM ( CapitalAssetsPriceModel). In the first, the beta coefficient was considered by G. Markowitz to assess the systematic risk of stocks, which was called the index of non-diversified risk. The beta coefficient allows you to compare stocks of different companies with each other according to their degree of risk.

The formula for calculating the beta coefficient

β - beta coefficient, a measure of systematic risk (market risk);

r i - profitability of the i-th acacia (investment portfolio);

r m - market yield;

σ 2 m - variance of market returns.

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(calculate your portfolio in 1 minute)
+ risk and return assessment

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Analysis of the risk level by the value of the beta coefficient (β)

The beta coefficient shows the market risk of a stock and reflects the sensitivity of a stock's change in relation to changes in market returns. The table below shows the beta risk assessment. Beta can be positive or negative, which indicates a positive or negative correlation between the stock and the market. A positive sign reflects that the returns on stocks and the market are changing in the same direction, a negative sign is a multidirectional movement.

Indicator value	Stock risk level	The direction of change in stock returns
	High	Unidirectional
	Moderate	Unidirectional
	Short	Unidirectional
-1 < β < 0	Short	Multidirectional
β = -1	Moderate	Multidirectional
	High	Multidirectional

Data for constructing the beta coefficient by information companies

The beta coefficient is used by many information and investment companies to assess systematic risk: Bloomberg, Barra, Value Line, etc. Monthly / weekly data for several years is used to construct the beta coefficient. The table shows the main parameters for assessing the indicator by various information companies.

You can see that Bloomberg is doing a short-term measure, while Barra and Value Line are using monthly stock and market returns over the past five years. Long-term valuation can be greatly distorted due to the impact on the company's shares of various crises and negative factors.

The beta coefficient in the capital asset pricing model isCAPM

The formula for calculating the return on shares using the capital asset model CAPM ( CapitalAssetsPriceModel, W. Sharp's model) has the following form:

where:

r is the future expected return on the company's shares;

r f is the return on the risk-free asset;

r m - market profitability;

β is the beta coefficient (a measure of market risk), reflects the sensitivity of changes in the value of the company's shares depending on changes in the market yield (index);

The CAPM model was created by W. Sharp (1964) and J. Linter (1965) and allows predicting the future value of the stock (asset) return based on linear regression. The model reflects the linear relationship between the planned return and the level of market risk, expressed by the beta coefficient.

To calculate the market yield use the yield of an index or an index futures (MICEX index, RTS - for Russia, S & P500 - USA).

An example of calculating the beta coefficient inExcel

Let's calculate the beta coefficient in Excel for the domestic company OAO Gazprom. This company has ordinary shares, the quotes of which can be viewed on the finam.ru website in the Data Export section. For the calculation, we took the monthly quotations of the shares of OJSC Gazprom (GAZP) and the RTS Index (RTSI) for the period from 01/31/2014 to 01/31/2015.

To calculate the beta coefficient, it is necessary to calculate the linear regression coefficient between the return on Gazprom shares and the RTS index. Let's consider two options for calculating the beta coefficient using Excel.

Option number 1. Calculation through the formulaExcel

Settlement through Excel formulas as follows:

INDEX (LINEST (D6: D17; E6: E17); 1)

Option number 2. Calculation through the add-in "Data Analysis"

The second option for calculating the beta coefficient uses the Data Analysis Excel add-in. To do this, go to the "Data" section in the main menu of the program, select the "Data Analysis" option (if this add-on is enabled) and select "Regression" in the analysis tools. In the “Input interval Y” field, select the profitability of OJSC Gazprom shares, and in the “Output interval X” field, select the yield of the RTS index.

Next, we will get the regression report on a separate sheet. Cell B18 shows the value of the linear regression coefficient, which is equal to the coefficient beta = 0.46. Let us also analyze other parameters of the model, for example, the R-square indicator (coefficient of determinism) shows the strength of the relationship between the profitability of a Gazprom stock and the RTS index. The determinism coefficient is 0.4, which is quite small for accurate forecasting of future returns using the CAPM model. Multiple R is a correlation coefficient (0.6) that shows the existence of a relationship between a stock and the market.

A value of 0.46 beta for a stock indicates a moderate risk and at the same time a co-directional change in returns.

★
(calculation of Sharpe, Sortino, Trainor, Kalmar, Modilyanka beta, VaR ratios)
+ predicting course movement

Disadvantages of using beta in the CAPM model

Let's consider a number of disadvantages inherent in this coefficient:

Difficulty using beta to evaluate low-liquid stocks. This situation is typical for emerging capital markets, in particular: Russia, India, Brazil, etc.
It is not possible to evaluate small companies that do not have issues of ordinary shares. Most of the domestic companies did not go through the IPO procedures.
Beta forecast volatility. Using linear regression to estimate market risk from historical data does not provide accurate risk predictions. Generally, it is difficult to predict a beta for more than 1 year.
It is not possible to take into account the non-systematic risks of the company: market capitalization, historical profitability, industry affiliation, P / E criteria, etc., which affect the value of the expected profitability.

Since the coefficient proposed by U. Sharpov did not have the proper stability and could not be used to predict future profitability in the CAPM model, various scientists proposed modifications and adjustments of this indicator ( Englishadjusted beta,modifiedbeta Let's take a look at the adjusted betas:

Modification of the beta coefficient from M. Bloom (1971)

Marshal Blum showed that over time, companies' beta ratios tend to 1. The formula for calculating the adjusted indicator is as follows:

The use of these weights allows for a more accurate prediction of future systematic risk. So this modification is used by many news agencies such as Bloomberg, Value Line and Merrill Lynch.

Beta modification from Bawa-Lindsberg (1977)

In his adjustment, Lindsberg suggested calculating a one-sided beta. The main postulate was that the change in profitability above a certain level is not considered by most investors as a risk, and only what is below the level is considered risk. The minimum level of risk in this model was the return on the risk-free asset.

where:

r i is the profitability of the share; r m - market profitability; r f is the profitability of a risk-free asset.

Scholes-Williams Beta Modification

β -1, β, β 1 - beta coefficients for the previous (-1) current and next (1) periods;

ρ m is the autocorrelation coefficient of the market yield.

Modification of the beta coefficient from Harlow-Rao (1989)

The formula reflects a one-sided beta, with the assumption that investors only view risk as a downward deviation from average market returns. In contrast to the Bawa-Lindsberg model, the level of the average market return was taken as the minimum level of risk.

where: μ i is the average profitability of a share; μ m is the average profitability of the market;

Summary

The beta coefficient is one of the classic market risk measures for assessing the performance of stocks, investment portfolios and mutual funds. Despite the complexity of using this tool to assess domestic low-liquid stocks and the instability of its change over time, the beta coefficient is a key indicator for assessing investment risks. The considered modifications of the coefficient make it possible to correct and give a better assessment of the systematic risk. Ivan Zhdanov was with you, thank you for your attention.

The dynamic methods of evaluating investment projects are based on the principle of discounting cash flows. The discount operation is based on the discount rate. The discount rate is a measure of not only profitability, but also risk. The rationale for the discount rate is largely determined by the calculation of the beta. The beta coefficient for calculating the discount rate in relation to investments in real assets is an indicator calculated for the planned type of operating activity of the enterprise, which will arise as a result of the implementation of investment project... It is a measure of market risk, reflecting the variability of the profitability of an enterprise's operating activities in relation to the average market profitability of a given type of activity in a country or region.

evaluation of investment projects

dynamic assessment methods

discount rate

real asset investment beta

1. Roche J. Company Value: From Desired to Actual / Julian Roche; per. from English E.I. Nedbalskaya; scientific. ed. P.V. Lebedev. - Minsk: "Grevtsov Publisher", 2008 - 352 p.

2. What is the beta coefficient of a stock // URL: http://www.homearchive.ru/business/in0042.html.

3. Podkopaev O.A. On the issue of the shortcomings of dynamic methods for evaluating investment projects // Success of modern natural science. - 2014. - No. 7. - P. 144-147.

4. Sokolov D. Beta coefficient for a non-tradable company. How to use similar companies? // URL: http://p2ib.ru/beta_koefficient.

As you know, investments are always characterized not only by a certain return, but also by the level of risk corresponding to this return. In this regard, the discount rate is a measure of not only profitability, but also risk. The approach that is based on the asset return assessment model (CAPM) has become widespread in determining the discount rate. According to this model, the profitability of a financial asset will depend on the risk-free rate, "beta" and market profitability, i.e. the required rate of return (discount rate, opportunity costs) for any type of investment depends on the risk associated with these investments and is determined by the expression:

Rtot = R0 + R1 = R0 + Rm - R0) * β (1)

● R0 is the return on risk-free assets;

● R1 - risk premium;

● Rm - average market rate of return;

● β - beta coefficient characterizing the level of systematic risk for an investment project (a measure of investment risk).

Recall that based on the classical "portfolio" theory, financial assets inherent risks that can be quantified. First, it is the specific risk of the company's stock. In another way, it is called non-systematic. This risk can be mitigated by diversifying the assets in the portfolio. Second, by buying a stock, an investor assumes the risk of the entire system. Systematic risk is a risk that cannot be radically reduced by increasing the number of assets in the portfolio, i.e. the diversification method does not "work". This non-diversified risk is assessed using the beta coefficient. The beta coefficient describes the relationship between the behavior of a particular asset and the market as a whole. The beta coefficient is needed to determine the discount rate in various fundamental analysis models, including when calculating the fair price of a share using the discounted cash flow method.

The beta coefficient evaluates a measure of the sensitivity of one variable (for example, the return of a particular stock) to another variable (the average market return or portfolio return). The beta factor (beta factor) in the CAPM used to calculate the discount rate for an investment in securities is a measure 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 (average market portfolio).

The beta coefficient shows the change in the price of a security in comparison with the dynamics of the entire stock market:

● for the composite index 500 by Standard & Poor's, the beta coefficient is 1;

● for more volatile stocks, the beta coefficient is greater than 1;

● for less volatile stocks, the beta is less than 1.

The economic meaning of the beta coefficient: the higher the beta coefficient of an asset, the higher the risk of investing in this asset. If the beta coefficient is greater than one, this means that during times of market growth, the analyzed security is ahead of it. In conditions of decline, on the contrary, it “pulls” down faster. The higher the beta of an asset, the higher its volatility. So, for example, if the beta coefficient of the shares of the company "LTD" is equal to 1.5, then this means that these shares are 1.5 times more volatile than the "market": if the "market" grows by 10%, then the share of the company in question will grow by 15 %. Conversely, if the "market" falls by 10%, then the stock of the given company will fall by 15%.

Cautious investors prefer stocks with low level beta coefficient. So, for example, if the beta coefficient of a RCM stock is 0.5, then this means that these stocks are 50% less volatile than the market: if the market rises by 10%, then the stock of the company in question will rise by only 5%. Conversely, if the "market" falls by 10%, then the price shares will fall only 5%.

Beta value can change over time. Therefore, its calculation is based on at least 60 indicators of monthly income (weekly income is considered acceptable "only if the shares are liquid and are traded every day"). However, this raises many problems. First, the company closed type may find it difficult to find comparable public companies, especially with the same equity / debt ratio. And with a different ratio of equity and borrowed capital, the recalculation of the beta coefficient may turn out to be erroneous. Secondly, different sources give completely different values of the beta coefficient, both for the past and for future period... For example, BARRA's 1999 beta for IBM was 1.18 / 1.39; according to Bloomberg - 1.16; according to S&P - 1.24; and according to the "ValueLine" - 1.15.

Many sources offer information on beta rates; the problem is that they contradict each other. The same issues arise with timeframes: should beta rates be daily, weekly, or monthly? For what period and with what statistical error? Should you make adjustments according to Bayes' theorem? Should you take into account special circumstances? Should changes be made to reflect the lack of liquidity on certain stocks? What about the changes that occur over time? How to take into account foreign affiliates? Moreover, using the beta to evaluate the performance of an investment or company in a takeover is not always correct. The trader may be acquiring a company with a different degree of risk. There may be benefits from the merger by reducing the level of fixed costs in the buying company and in the target company. There may be transactions in debt instruments, such as leases or risk sharing agreements, or projects that include option clauses. The theoretical rationale behind the choice of the study period for the beta coefficient is rather contradictory. On the one hand, if the data are taken for too short a time period, the results obtained will be distorted by short-term market factors. For example, “the beta coefficient of Mosenergo shares in May would be negative. After all, when the market fell, the company's securities, on the contrary, grew. It was just that then someone was actively buying them. " Thus, the beta can vary greatly depending on the selected period. The market is unpredictable for short periods of time, and, on the other hand, the horizon for calculating the beta coefficient should not be too large, since for the Russian financial market high volatility is typical.

Investments in real assets are associated with the creation of a new or development of an existing operating activity of an enterprise. As a reminder, the operating activity of a company is understood as its main activity. It is operating activities that are the main source of income (obtaining operating profit, EBIT) and Money at a normally functioning enterprise.

Investments in real assets, as well as financial investments, have risks that can be quantified. These risks include: unsystematic (specific to specific enterprise) and systematic risks (risks inherent in the entire market). First, the specific risk real investment- This is the risk of operating activities arising from investments inherent in a particular enterprise. This risk also called non-systematic and in many ways it is associated with the internal environment of the enterprise. An investor whose interests, for example, are related to the production and sale of furniture, can diversify their capital by investing in different companies in the furniture business to reduce non-systematic risk. Secondly, by choosing operating activities (for example, the production and sale of furniture), the investor assumes the risk of the entire market (furniture market). Thus, systematic risk (nondiversifiable) is a risk inherent in the entire market. Systematic risks include the risk of change interest rate, currency risk, inflation risk, political risk. Systematic risks are associated with the economic situation in the country, rising resource prices, rising inflation, changes in monetary and credit policy and others. In this regard, the risk that cannot be radically reduced by increasing the number of assets (investments in different companies in the furniture business) in the real investment portfolio is called systematic. It is this non-diversified real investment risk that is estimated using the beta coefficient. V this case The beta coefficient describes the relationship between the behavior of a particular enterprise and the market as a whole. The beta coefficient adjusts the market premium equal to the difference between the average market and risk-free returns, depending on the degree of the investee's exposure to nondiversifiable risks.

Thus, the beta coefficient for calculating the discount rate in relation to investments in real assets is an indicator calculated for the planned type of operating activity of the enterprise, which will arise as a result of the investment project. It is a measure of market risk, reflecting the variability of the profitability of an enterprise's operating activities in relation to the average market profitability of a given type of activity in a country or region.

If the beta of an operating activity is one, then that business has the same systematic risk as the market as a whole.

If the beta coefficient is greater than one, then the operating activities of the company in question are more risky than the same economic activities on average in the market. For example, due to the use by the enterprise of a larger share borrowed money in the structure of liabilities than the market average. However, the fundamental concept of the relationship between return and risk is that the higher the risk, the higher the required return. Indeed, an aggressive policy of asset financing, which presupposes a large share of borrowed funds in the structure of funding sources, indicates a high level of financial risk, but allows you to get more profitability equity capital due to the effect of financial leverage. At the same time, with a worsening economic situation in the country, interest expenses on raising capital (WACC) will increase due to an increase in interest on loans and borrowings (CC), which in to a greater extent will reduce the company's profitability (in particular, the return on assets calculated by net profit) than the market average.

If the coefficient is less than one, then the operating activity of the analyzed enterprise is less risky than the same economic activity on average in the market. For example, because the firm uses more equity capital and risk management tools than the market average. Application of a conservative asset financing policy, i.e. the predominance of a large share of equity capital in the sources of financing assets, reduces the opportunities for obtaining higher returns and limits the pace of development of the enterprise in comparison with the more risky aggressive model of financing the company's assets, but increases it financial stability... The use of risk management tools (insurance, hedging, factoring, etc.) is associated with additional financial costs and also reduces the company's ability to obtain high returns for the sake of the economic stability of the company. At the same time, with the deterioration of the economic situation in the country, the profitability of this enterprise will decrease to a lesser extent than the market average.

The beta coefficient can be calculated by statistical methods based on monitoring the change in the average market return and the return on a particular asset over a sufficiently long period. The expert method for determining the value of the β-coefficient is based on the analysis of the degree of influence different types systematic risk to the investment object for subsequent weighted assessment. As indicators of profitability, you can take the return on assets, calculated on the basis of net profit. Finding a realistic total risk value in relative terms is a laborious and very difficult task for practical implementation using the knowledge of probability theory and mathematical statistics. The calculation of the β-coefficient also requires the availability of statistics themselves on profitability and on risks affecting a specific type of operating activity of the company. Therefore, the model can be applied by entrepreneurs already engaged in business and only for those types of operating activities that they intend to develop or expand. Finding the β-coefficient is not possible for aspiring entrepreneurs starting their own business. That is, this method will not be able to apply to firms that do not have sufficient statistics to calculate their β-coefficient, as well as are unable to find an analogous enterprise, whose β-coefficient they could use in their own calculations. To determine the discount rate, such companies should use other calculation methods or improve the methodology according to their needs.

The beta coefficient is calculated as the ratio of the covariance of two variables to the variance of the second variable. So, the beta coefficient for the planned profitability of the operating activity of the enterprise relative to the average market profitability of this type of activity is the ratio of the covariance of the values under consideration to the variance of the market, respectively:

● ra is the estimated value for which the beta coefficient is calculated: the planned profitability of operating activities that will arise as a result of the implementation of the investment project;

● rp is the reference value with which the comparison is made: the average market profitability of the type of activity planned to be carried out in the country or region;

● Cov - covariance of the estimated and reference values;

● Var - variance of the reference value.

In practice, the method of calculating the beta coefficient is also used, based on comparison with the indicators of peers. Such companies are firms from the same industry, whose business is most similar to the business of the analyzed company. When calculating the beta coefficient, it is necessary to make a number of adjustments, in particular, for the difference in the capital structure of a company planning to implement an investment project in real assets (or in the structure of project financing sources) and analogous companies (the ratio of debt and equity (pooled) capital). If the beta of assets is the variability of the cash flows generated by these assets, then the beta share capital depends on the level of debt in the ownership structure.

Accordingly, the beta of assets can be mathematically represented as follows:

bAct = bLong ∙ wDebt + bАК ∙ wАК, (3)

● bAkt - beta of the company's assets;

● bDebt - the beta of the company's debt;

● bАК - beta of the share capital of the company;

● wDebt - the share of debt in the ownership structure;

● wАК - the share of equity (reserve) capital in the ownership structure.

It should be noted that the higher the level of debt a company has, the greater the beta of equity. If a company has high debt levels, then a significant portion of the revenue will go to creditors, so the remaining cash flows attributable to shareholders will fluctuate greatly - their variability will be significantly higher than the variance of earnings. If the level of debt is small, then payments on loans have practically no effect on what goes to shareholders, i.e. variability in net income and variability cash flow in favor of shareholders will be approximately the same.

When calculating the weights of debt and equity, one must take into account important point- interest on loans is deducted from profit before calculating income tax, so the debt level is adjusted by the value (1-t), where t is the income tax rate. That is, the debt attracted for financing "costs" slightly less than its nominal value.

As a result, the formula looks like:

where D and E are the amount of debt and equity, respectively.

It is usually assumed that bDolt = 0, i.e. loan payments do not depend on general market factors. Although this is not always true (for example, the likelihood of bankruptcy increases with a crisis in the economy and a corresponding collapse in the market), in practice, in most cases, this assumption is made.

Thus, scholars disagree on how accurate the CAPM's risk-reward forecast is; the practical calculation of the beta coefficient seems to be a complex and time-consuming process, but these facts alone do not prove the inconsistency of the theory in practice.

Bibliographic reference

Podkopaev O.A. METHODS AND APPROACHES TO CALCULATING THE BETA COEFFICIENT FOR DETERMINING THE DISCOUNTING RATE OF FINANCIAL AND REAL INVESTMENTS // International Journal of Applied and basic research... - 2015. - No. 3-2. - S. 245-249;
URL: https://applied-research.ru/ru/article/view?id=6523 (date accessed: 25.02. We bring to your attention the journals published by the "Academy of Natural Sciences"

Beta coefficient (in English... beta)Is an indicator of the sensitivity of the stock price relative to the entire stock market (or broad stock index). Beta measures systematic risk, that is, risk, inherent in all financial system... Beta is an important component of a capital asset pricing modelCAPMwhen calculating the required rate of return. Mathematically, beta is the slope coefficient of the Securities Market Line (in English... Security Market Line).

Formula

The beta is calculated as the covariance between stock returns and market returns divided by the variance of market returns.

A slight modification of this formula will reveal another key relationship: beta is equal to the correlation coefficient multiplied by the standard deviation of stock returns divided by the standard deviation of market returns.

Analysis

A beta of 1 assumes that the stock has the same risk as the general market and that the stock's returns will be comparable to the market's returns. A ratio below one indicates lower risk and lower potential return relative to the market. On the other side, β above 1, higher risk of investing in a given stock.

In 2017 the actionChevron (ticker CVX)had a beta coefficient of 1.17. This indicates that the company's stock is slightly more risky than the stock index.S&P 50... Marathon Oil (NYSE ticker: MRO), on the other hand, has a β of 3.02. We can conclude that this stock is more risky than the market as a whole.

Beta coefficient calculation

If we do not have information on the standard deviation and correlation to calculate the beta coefficient, you need to follow these simple steps inExcel :

1) Find data on the historical dynamics of the stock price

2) Get the historical values of the corresponding index (for example, S & P500).

3) Determine the daily return on the stock price using the following formula:

Yield = (Closing Price - Opening Price) / Opening Price

4) Similarly, convert the index price values to returns.

5) We compare the received returns by dates.

6) Using the TILT function (in the English version -SLOPE)determine the slope coefficient between data sets. The final value is the beta coefficient..

One of critical indicators for a stock is the beta coefficient - it shows the change in the price of a stock relative to the market situation. With an increase in the β coefficient, we can talk about an increase in the price of an 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 this asset on the general market trend.

The beta coefficient can be calculated both for one share and for a selected set of shares. With the help of β, it is possible to assess the risks and profitability of both an individual asset and a selected investment portfolio relative to a similar portfolio. In other words, the beta of a stock shows the degree of risk for a selected portfolio or individual security.

Description

The first to propose using the beta coefficient of a portfolio to calculate systemic risk was the American economist Harry Markowitz, back in the early 1950s. First, he characterized such ratios as "indices of non-diversified 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 need the profitability of the stock itself and the profitability of the exchange 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 particular company or industry and the average profitability ratio of the entire industry.

If we get β = 1, then the conclusion will be simple: the non-diversified risk of a particular instrument coincides with the general market risk. If β = 0, which means that 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 part of the risk to be diversified for a specific investment object both in the case of macro- and microeconomics.

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

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Beta coefficient calculation

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

Ra, t = a + βаrp, е + Еt

To calculate the beta of a security:

βа = Cov (ra, rp): Var (rp)

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

ra is the profitability of the asset under consideration or the size of the assessment for which the asset is calculated;
rp - this value is used to compare the profitability of a security or market;
Cov - covariance of the estimated value and the reference;
Var - the value of the possible deviation of the indicator.

If a company does not trade stocks in the background market, the β-coefficient is calculated by comparing parameters with similar companies, but the general formula will change.

Basically, the beta is a single instance of the relationship of several variables. And the variables here are the securities of the selected company relative to the rest of the securities of the stock market.

What the beta coefficient will show

Upon obtaining the value β = 1, we can conclude that the risk of under-diversification for a given share is equal to the overall market risk indicator. If the beta is zero, then you are working with a risk-free asset. In general, the higher the beta value you get, the more risks the asset promises. In this way, you can analyze the distribution of investment risks for both micro- and macroeconomic levels.

To calculate the coefficient β, two quantities are needed:

The level of profitability of the company. It is the difference between the opening and closing of a company's stock on stock market for the selected period of time.
Average market level of profitability. it average level the profitability of all securities included in a specific investment portfolio. The portfolio can be stocked with shares of the company in question.