Beta is also referred to as financial elasticity or correlated relative volatility, and can be referred to as a measure of the sensitivity of the asset's returns to market returns, its non-diversifiable risk, its systematic risk, or market risk. On an individual asset level, measuring beta can give clues to volatility and liquidity in the marketplace. In fund management, measuring beta is thought to separate a manager's skill from his or her willingness to take risk.
The beta coefficient was born out of linear regression analysis. It is linked to a regression analysis of the returns of a portfolio (such as a stock index) (x-axis) in a specific period versus the returns of an individual asset (y-axis) in a specific year. The regression line is then called the Security characteristic Line (SCL).
- Beta < 0: Negative Beta - not likely.
- Beta = 0: Cash in the bank.
- Beta Between 0 and 1: Low-volatility
- Beta = 1: Matching the market.
- Beta > 1: More volatile than the market
Example of use: A fund with a beta of 1 is deemed to have the same volatility as the Nifty; therefore a fund with a beta of 4 is four times more volatile than the Nifty, and a fund with a beta of .25 is 25% as volatile as the Nifty.
This means that a fund with a beta of 4 would rise 40% if the Nifty rose 10% (the same is true of a drop).
For individual companies, beta can be estimated using regression analysis (line of best fit) against a stock market index. It is one of the required inputs to the Capital Asset Pricing Model (CAPM), which is used to calculate the expected return of an asset based on its beta and expected market returns. Essentially, to calculate beta for an individual security you take total stock returns for a given period, and simply plot it against the benchmark returns, and then fit a least squares regression line (line of best fit) through the data points. The slope of the line would then be your beta.
The beta for a portfolio of securities is simply the weighted average of each of the individual securities. The weight of each security is the value invested in that security divided by the value of the entire portfolio. A quick example would illustrate the concept. Assume you have Rs. 100 invested into two companies for a total investment of Rs. 200. The betas for the companies are 1.0 and 2.0 respectively. Therefore, the calculation would be (Rs.100/Rs.200)*1.0 + (Rs. 100/200)*2.0 = 1.5. Therefore, the beta of the portfolio is 1.5.
The two most widely used methods of estimating beta are:
1. Pure-Play Method
When using the pure-play method, a company seeks out companies with a product line that is similar to the line for which the company is trying to estimate the beta. Once these companies are found, the company would then take an average of those betas to determine its project beta.
2. Accounting-Beta Method
When using the accounting-beta method, a company would run a regression using the company's return on assets (ROA) against the ROA for market benchmark, such as the S&P 500. The accounting beta is the slope coefficient of the regression.
Different types of Beta - Explained by various financial scholars
This means that a fund with a beta of 4 would rise 40% if the Nifty rose 10% (the same is true of a drop).
The three basic interpretations of Beta are as follows:
- Econometric Beta: The primary risk factor for the CAPM. Relevant to pricing and not valuation.
- Graphical Beta: The slope coefficient of the characteristic line.
- Statistical Beta: The measure of systematic risk in the CAPM.
Beta depends on two factors, multiplied together:
- the relative volatility of a security's returns compared to the market's returns, and
- the correlation of the security's returns to the market's returns.
- Beta measures the relative volatility of a security's price compared to the price of the market. Beta is a measure that compares returns, not prices; a security with a positive beta can have a price that decreases while the market's price increases. The key is whether the security's returns are above or below its mean return when the market's returns are above or below its mean return; whether the security's mean return is positive or negative is not relevant to its beta.
- Beta measures the relative volatility of a security's returns compared to the volatility of the market's returns. Beta has two components: relative volatility of returns, and correlation of returns. Unless the correlation of returns is +1.0 or -1.0, beta does not measure the relative volatilities of returns.
- A positive beta means that a security's returns and the market's returns tend to be positive and negative together; a negative beta means that when the market's return is positive the security's return tends to be negative, and vice versa. The calculation of beta involves deviations of the market's returns and the security's returns about their respective mean returns. A security with a negative mean return can have a positive beta, and a security with a positive mean return can have a negative beta.
- A beta of 1.0 means that the security's returns have the same volatility as the market's returns. This could be true, or the security's returns could be twice as volatile as the market's returns, but their correlation of returns is +0.5. Beta, by itself, does not describe the relative volatility of returns.
- A beta of 1.0 could mean that the security's returns have the same volatility as the market's returns and their correlation is +1.0, or it could mean that the relative volatility is 2.0 and the correlation is +0.5, or it could mean that the relative volatility is 5.0 and the correlation is +0.2. It is certain that the volatility of the security's returns is at least as great as the volatility of the market's returns, and that the correlation of returns between the security and the market is positive.
- A beta higher than 1.0 means that the security's returns have been more volatile than the market's returns, and that the correlation of returns is positive. For example, a beta of 2.0 means that the security's returns have at least twice the volatility of the market's returns, probably more. The value of beta gives a lower limit to the relative volatility of the security's returns compared to the market's returns.
- A beta lower than 1.0 can mean that the security's returns are less volatile than the market's returns, or it could simply mean that the security's returns and the market's returns have a low correlation.
- A beta of 0 means that the correlation of returns of the security and the market is 0.0; i.e., they tend to move independently.
- A negative beta means that the security's returns tend to move opposite the market's returns; i.e., their correlation of returns is negative. The absolute value of beta gives a lower limit to the relative volatility of the security's returns compared to the market's returns.
Applications of Beta
Beta is a commonly used tool for evaluating the performance of a fund manager. Beta is used in contrast with Alpha to denote which portion of the fund's returns are a result of simply riding swings in the overall market, and which portion of the funds returns are a result of truly outperforming the market in the long term. For example, it is relatively easy for a fund manager to create a fund that would go up twice as much as the Nifty when the Nifty rose in value, but go down twice as much as the Nifty when the Nifty's price fell - but such a fund would be considered to have pure Beta, and no alpha. A fund manager who is producing Alpha would have a fund that outperformed the Nifty in both good times and bad.
Beta can also be used to give investors an estimate on a stock's expected returns relative to the market return. Consider some examples:
Beta is a commonly used tool for evaluating the performance of a fund manager. Beta is used in contrast with Alpha to denote which portion of the fund's returns are a result of simply riding swings in the overall market, and which portion of the funds returns are a result of truly outperforming the market in the long term. For example, it is relatively easy for a fund manager to create a fund that would go up twice as much as the Nifty when the Nifty rose in value, but go down twice as much as the Nifty when the Nifty's price fell - but such a fund would be considered to have pure Beta, and no alpha. A fund manager who is producing Alpha would have a fund that outperformed the Nifty in both good times and bad.
Beta can also be used to give investors an estimate on a stock's expected returns relative to the market return. Consider some examples:
- Company ABC, a tech stock, has a beta of 1.8. Over a given year, the Nifty increases in value 17%. Assuming the beta value is accurate, ABC's value should have increased 30.1% or (1.8 x 17%) over the same time period.
- Company XYZ, a mid-sized oil company, has a beta of 1.0. Over a given year, the Nifty falls 10%. Assuming the beta value is accurate, XYZ's value would also have fallen 10% over the same period.
- Company LMN, a gold mining company, has a beta of -1.4. Over a given year, the Nifty increases in value 11%. Assuming the beta value is accurate, LMN's value would have declined 15.4% or (-1.4 x 11%) over the same period.
For individual companies, beta can be estimated using regression analysis (line of best fit) against a stock market index. It is one of the required inputs to the Capital Asset Pricing Model (CAPM), which is used to calculate the expected return of an asset based on its beta and expected market returns. Essentially, to calculate beta for an individual security you take total stock returns for a given period, and simply plot it against the benchmark returns, and then fit a least squares regression line (line of best fit) through the data points. The slope of the line would then be your beta.
The beta for a portfolio of securities is simply the weighted average of each of the individual securities. The weight of each security is the value invested in that security divided by the value of the entire portfolio. A quick example would illustrate the concept. Assume you have Rs. 100 invested into two companies for a total investment of Rs. 200. The betas for the companies are 1.0 and 2.0 respectively. Therefore, the calculation would be (Rs.100/Rs.200)*1.0 + (Rs. 100/200)*2.0 = 1.5. Therefore, the beta of the portfolio is 1.5.
The two most widely used methods of estimating beta are:
1. Pure-Play Method
When using the pure-play method, a company seeks out companies with a product line that is similar to the line for which the company is trying to estimate the beta. Once these companies are found, the company would then take an average of those betas to determine its project beta.
2. Accounting-Beta Method
When using the accounting-beta method, a company would run a regression using the company's return on assets (ROA) against the ROA for market benchmark, such as the S&P 500. The accounting beta is the slope coefficient of the regression.
Variances in Beta
Values of Beta can vary depending on how they are calculated. Specifically, the main varying components are:
Values of Beta can vary depending on how they are calculated. Specifically, the main varying components are:
- Different time frame: Depending on how far back into history the beta calculation goes, the values will differ. For example, if one calculation includes the stock prices for the trailing 12 months versus the trailing 60 months; the two values will be different.
- Different time intervals: Depending on the interval between the stock prices used, beta calculations can differ. For example, one calculation which uses the monthly stock prices will differ from another calculation which uses weekly or daily stock prices.
- Different index: Beta calculations can vary depending on which index is used to measure the overall value in the market. For example, using the Nifty and the SENSEX will result in different values.
- Inclusion or exclusion of dividends: Depending on whether dividends are included in the calculation of the returns of the stock, the beta calculations can differ.
1. Classic beta – This is related to the 'beta' as referred to in past decades, though now corrupted to mean precisely matching the market. In the new parlance the word beta is equivalent to a beta of 1 under the older definition. It effectively means just matching the market, whether the market is the US stock market, the UK FTSE 100, Indian Market Nifty or SENSEX or the global MSCI-EAFA. Standard index funds come under this category.
2. Bespoke beta – This refers to the same as 1 above except that the index no longer represents the broad market but particular sectors or other asset classes. For instance, the banking sector or a basket of commodities.
3. Alternative beta – The rationale is that there are systematic risk exposures which were previously not available to investors but which can be now accessed through ETFs. As an example, currency ETF linked to the price of the euro in terms of the dollar.
4. Fundamental beta – There is now a raging debate as to whether indices constructed by weighting the constituent stocks by market capitalisation are the best proxies for the market. A strongly supported school has sprung up which claims that fundamental indices, in which the constituents are weighted by fundamental factors such as revenue or dividends, are much better. It is better to match these fundamental indices as fundamental beta.
5. Cheap beta – This refers to a situation where beta cannot be produced by investing in an index or ETF, but where beta is embedded in a complex basket of risks within one security. An example is a convertible bond. This has the following elements of risk embedded in it: interest rate risk, stock market risk, credit risk, and volatility risk. Players in convertible bonds are effectively getting indirect exposure to all these different betas. Interestingly, here we take beta as numbers rather than as the concept of matching the market.
6. Active beta – it refers to long-short funds such as 130/30, where the overall exposure of the portfolio matches the market but additionally there is 30% additional long exposure in favour of stocks, counterbalanced by short exposures in unattractive stocks.
7. Bulk beta – This refers to traditional equity portfolio management of the standard type, where portfolios consist of a large element of beta, i.e. market exposure, as well as the ability to generate alpha through stock selection.
That's the general formula for conversion, with Ub being the unlevered (or Asset) beta, Eb being the levered (or equity) beta, and Db being the debt beta. L is the leverage ratio. From this equation, you can see the "weighted average" quality of asset beta.
Basically, there is a ton of information about the relation between levered and unlevered betas. For valuation purposes, I think it is important to know that when using the betas of comparable companies to find a beta for your private company, you would want to unlever them to make them "free" of the comparable companies' capital structure. After doing this, you would then take the average (or whatever) and relever it using your company's leverage ratio to find the appropriate equity beta, and thus amount of return that you need to get on your equity (usingCAPM).
2. Bespoke beta – This refers to the same as 1 above except that the index no longer represents the broad market but particular sectors or other asset classes. For instance, the banking sector or a basket of commodities.
3. Alternative beta – The rationale is that there are systematic risk exposures which were previously not available to investors but which can be now accessed through ETFs. As an example, currency ETF linked to the price of the euro in terms of the dollar.
4. Fundamental beta – There is now a raging debate as to whether indices constructed by weighting the constituent stocks by market capitalisation are the best proxies for the market. A strongly supported school has sprung up which claims that fundamental indices, in which the constituents are weighted by fundamental factors such as revenue or dividends, are much better. It is better to match these fundamental indices as fundamental beta.
5. Cheap beta – This refers to a situation where beta cannot be produced by investing in an index or ETF, but where beta is embedded in a complex basket of risks within one security. An example is a convertible bond. This has the following elements of risk embedded in it: interest rate risk, stock market risk, credit risk, and volatility risk. Players in convertible bonds are effectively getting indirect exposure to all these different betas. Interestingly, here we take beta as numbers rather than as the concept of matching the market.
6. Active beta – it refers to long-short funds such as 130/30, where the overall exposure of the portfolio matches the market but additionally there is 30% additional long exposure in favour of stocks, counterbalanced by short exposures in unattractive stocks.
7. Bulk beta – This refers to traditional equity portfolio management of the standard type, where portfolios consist of a large element of beta, i.e. market exposure, as well as the ability to generate alpha through stock selection.
8. Levered beta = Risk of Equity. The beta of a company, including debt. The levered beta describes the capital structure of the company and volatility relative to the market.
9. Unlevered Beta = Risk of Entire Firm (Assets)
Unlevered Beta is basically a weighted average of the levered Beta and the debt Beta. Typically, the debt beta is thought to be 0, although it isn't always. The beta of a company after subtracting out the impact of its debt obligations. Unlevered beta removes the effects of the use of leverage on the capital structure of a firm, since the use of debt can result in tax rate adjustments that benefit a company. Removing the debt component allows an investor to compare the base level of risk between various companies.
Ub = [(1-L)Eb + (L)DB ]/ (1 - TL)
Unlevered Beta is basically a weighted average of the levered Beta and the debt Beta. Typically, the debt beta is thought to be 0, although it isn't always. The beta of a company after subtracting out the impact of its debt obligations. Unlevered beta removes the effects of the use of leverage on the capital structure of a firm, since the use of debt can result in tax rate adjustments that benefit a company. Removing the debt component allows an investor to compare the base level of risk between various companies.
Ub = [(1-L)Eb + (L)DB ]/ (1 - TL)
Basically, there is a ton of information about the relation between levered and unlevered betas. For valuation purposes, I think it is important to know that when using the betas of comparable companies to find a beta for your private company, you would want to unlever them to make them "free" of the comparable companies' capital structure. After doing this, you would then take the average (or whatever) and relever it using your company's leverage ratio to find the appropriate equity beta, and thus amount of return that you need to get on your equity (usingCAPM).
Practical Application of Levered and Unlevered Beta can be better understood by this research article:
Practical Application on Excel:
Great! A detailed information about Beta! thanx a lot :-)
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ReplyDeleteThe only article which gives complete information about Beta. Thank you so much Varun sir for such knowledgeable content about Beta at a single place.
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