The Beta coefficient, or financial elasticity (sensitivity of the asset returns to market returns, relative volatility), is a key parameter in the Capital asset pricing model (CAPM).

Beta can also be defined as the risk of the stock to a diversified portfolio. Therefore the beta of a stock will be much lower than its (the stock's) standard deviation. The formula for the Beta of an asset is $\backslash beta\_a\; =\; \backslash frac\; \{Cov(r\_a,r\_m)\}\{Var(r\_m)\}$

The β coefficient measures the asset's non-diversifiable risk, also called systematic risk or market risk, $r\_m$ measures the rate of return of the market and $r\_a$ measures the rate of return of the asset. On an individual asset level, measuring beta can give clues to volatility and liquidity in the marketplace. On a portfolio level, measuring beta is thought to separate a manager's skill from his willingness to take risk.

The beta movement should be distinguished from the actual returns of the stocks. For example a sector may be performing well and may have good prospects but the fact that its movement does not correlate well with the broader market index may decrease its beta. It however should not be taken as a reflection on the overall attractiveness or the loss of it for the sector or stock as the case may be. Beta is a measure of risk and not be confused with the attractiveness of investment.

The beta coefficient was actually borne out of regression analysis. It is linked to a regression analysis of the return of the stock index (x-axis) in a specific year versus the return of the market (y-axis) in a specific year. The regression line is then called the Security Characteristic Line (SCL).

$SCL\; :\; r\_\{it\}\; =\; \backslash alpha\_i\; +\; \backslash beta\_i\; r\_mt\; +\; \backslash epsilon\_\{it\}\; \backslash frac\{\}\{\}$

$\backslash alpha\_i$ is called the stock's alpha coefficient and $\backslash beta\_i$ is called the stock's beta coefficient. Both coefficients have an important role in Markowitz Portfolio Theory.

For example, in a year where the broad market or benchmark index returns 25%, suppose two managers gain 50%. Since this is theoretically possible merely by choosing a portfolio whose beta is exactly 2.0, we would expect a skilled portfolio manager to have built the portfolio with a beta somewhat less than 2, such that the excess return not explained by the beta is positive. If one of the managers has an average beta of 3.0 in his portfolio, and the other's is only 1.5, then the CAPM simply states that we are not being adequately compensated for the first manager's risk, whereas the second manager has done more than expected of him and appears capable of generating superior returns.

Multiple Beta Model

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The Arbitrage Pricing Theory (APT) has multiple betas in its model because unlike CAPM which has only one risk factor, namely the overall market, APT has multiple risk factors. Each risk factor has a corresponding beta indicating the responsiveness of the asset being priced to that risk factor.

Calculation of Beta

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To calculate Beta, one needs a list of (e.g., daily closing) prices for the asset and prices for the index, hopefully corrected for dividends. The first step is to calculate $r\_i$, the return for each period, for the asset and for the index. Next, a plot should be made, with the index returns on the x-axis and the asset returns on the y-axis, in order to check that there are no serious violations of the linear regression model assumptions. The fitted slope from the linear least-squares system is Beta. The y-intercept is "Alpha", a less commonly used term.

See also

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• The Capital Asset Pricing Model
• Treynor Ratio

External links

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• The Beta Coefficient at greekshares.com

Mathematical finance | Fundamental analysis

Betafaktor | Coefficient bêta | Beta系数