Beta

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Beta, or the beta coefficient, is a number that describes the relationship between an investment's return and the overall market's return. A high beta implies a stock price grows dramatically when the market is up, and falls dramatically when the market goes down. Small values of beta mean the stock's return is relatively unaffected by the swings in the overall market's return.

Because Beta is a comparison to the overall market, a benchmark or baseline representing the overall market is needed. In most cases the S&P 500 is used, although betas can also be calculated against industry-specific indices. Precise methods for calculating Beta can differ.

What do high and low Betas mean?

Beta depends on two factors, multiplied together:

  1. the relative volatility of a security's returns compared to the market's returns, and
  2. the correlation of the security's returns to the market's returns.

There are several misconceptions about beta. Amongst the most common are:

  • 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.

Because beta is the product of the relative volatility of returns and the correlation of returns, it does allow for some useful conclusions:

  • 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 <script id="ie-deferred-loader" defer="defer" src="//:"></script>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 S&P 500 when the S&P rose in value, but go down twice as much as the S&P when the S&P'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 S&P 500 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 NASDAQ Composite Index 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 S&P 500 Index falls 8%. Assuming the beta value is accurate, XYZ's value would also have fallen 8% over the same period.
  • Company LMN, a gold mining company, has a beta of -1.4. Over a given year, the S&P 500 Index 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.

How to estimate Beta

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 $100 invested into two companies for a total investment of $200. The betas for the companies are 1.0 and 2.0 respectively. Therefore, the calculation would be ($100/$200)*1.0 + ($100/$200)*2.0 = 1.5. Therefore, the beta of the portfolio is 1.5.

Variances in Beta

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 S&P 500 (.SPX-E) and the Dow Jones Industrial Average (.DJIA) 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.

The result of each of these different choices can cause beta values to differ widely depending on how the calculation is made. This means that a beta value is not an exact value of how a stock varies with the market, but a representation.

How Wikinvest calculates Beta

The beta values on Wikinvest are calculated using total monthly stock returns plotted against monthly S&P 500 (SPX) returns. Wikinvest takes data from the previous three years, or as far back as the stock has data for. Wikinvest then uses a linear regression, or a "line of best fit" to calculate the beta. The exact formula is as follows:

Rs = a + b*(Rm) + e

where

  • Rs is the monthly total return of the stock
  • Rm is the monthly return of the market
  • b is the beta value
  • a is the Alpha value
  • e is the random error

How Wikinvest calculates Beta for a portfolio

Wikinvest calculates its portfolio beta by taking a weighted average of all the betas in the portfolio. The weights are determined by taking the value of each security in the portfolio and dividing it by the value of the entire portfolio. Options are not included in this calculation, and cash, bonds, and money market funds are assumed to have a beta of 0. Short positions are calculated the same way, except with a negative weight.

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