NationMaster - Encyclopedia: Beta coefficient

The Beta coefficient, in terms of finance and investing, is a measure of a stock (or portfolio)’s volatility in relation to the rest of the market. Beta is calculated for individual companies using regression analysis. (See Investing below) Finance studies and addresses the ways in which individuals, businesses, and organizations raise, allocate, and use monetary resources over time, taking into account the risks entailed in their projects. ... Invest redirects here. ... In finance, a portfolio is a collection of investments held by an institution or a private individual. ... Volatility most frequently refers to the standard deviation of the change in value of a financial instrument with a specific time horizon. ... This article does not cite any references or sources. ... The Beta coefficient, in terms of finance and investing, is a measure of a stock (or portfolio)â€™s volatility in relation to the rest of the market. ...

The beta coefficient is a key parameter in the capital asset pricing model (CAPM). It measures the part of the asset's statistical variance that cannot be mitigated by the diversification provided by the portfolio of many risky assets, because it is correlated with the return of the other assets that are in the portfolio. An estimation of the CAPM and the Security Market Line (purple) for the Dow Jones Industrial Average over the last 3 years for monthly data. ... This article is about mathematics. ... Diversification in finance involves spreading investments around into many types of investments, including stocks, mutual funds, bonds, and cash. ... Positive linear correlations between 1000 pairs of numbers. ...

For example, if every stock in the New York Stock Exchange was uncorrelated with every other stock, then every stock would have a Beta of zero, and it would be possible to create a portfolio that was nearly risk free, simply by diversifying it sufficiently so that the variations in the individual stocks' prices averaged out. This would be like owning a casino: essentially none of the business risk of owning a casino comes from the uncertain outcomes of the games of chance played by the customers, because those are uncorrelated, and average out over any significant period of time. In reality, investments tend to be correlated, more so within an industry, or when considering a single asset class (such as equities), as was demonstrated in the Wall Street crash of 1929. This correlated risk, measured by Beta, is what actually creates almost all of the risk in a diversified portfolio. The New York Stock Exchange (NYSE), nicknamed the Big Board, is a New York City-based stock exchange. ... This article or section does not adequately cite its references or sources. ... Crowd gathering on Wall Street. ...

The formula for the Beta of an asset within a portfolio is $beta_a = frac {mathrm{Cov}(r_a,r_p)}{mathrm{Var}(r_p)}$ ,

where

r a

measures the rate of return of the asset,

r p

measures the rate of return of the portfolio of which the asset is a part and

Cov(r a, r p)

is the covariance between the rates of return. In the CAPM formulation, the portfolio is the market portfolio that contains all risky assets, and so the

r p

terms in the formula are replaced by

r m

, the rate of return of the market. In probability theory and statistics, the covariance between two real-valued random variables X and Y, with expected values and is defined as: where E is the expected value. ...

Beta is also referred to as financial elasticity or correlated relative volatility, and can be referred to as a measure of the asset's 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. On a portfolio level, measuring beta is thought to separate a manager's skill from his or her willingness to take risk. In economics, elasticity is the ratio of the proportional change in one variable with respect to proportional change in another variable. ... Volatility most frequently refers to the standard deviation of the change in value of a financial instrument with a specific time horizon. ... This article is about the business definition. ... Lets talk about risk control strategies, anyone with more information and willing to share, please do so. ... A systemic risk is a risk faced by a system, in contrast to a specific risk or unique risk. ... Volatility most frequently refers to the standard deviation of the change in value of a financial instrument with a specific time horizon. ... Market liquidity is a business or economics term that refers to the ability to quickly buy or sell a particular item without causing a significant movement in the price. ...

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. However, it 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 to be confused with the attractiveness of the investment.

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). In statistics, linear regression is a regression method that models the relationship between a dependent variable Y, independent variables Xi, i = 1, ..., p, and a random term Îµ. The model can be written as Example of linear regression with one dependent and one independent variable. ... Capital Market Line Modern portfolio theory (MPT) proposes how rational investors will use diversification to optimize their portfolios, and how a risky asset should be priced. ...

α a

is called the asset's alpha coefficient and

β a

is called the asset's beta coefficient. Both coefficients have an important role in Modern portfolio theory. The alpha coefficient () is a parameter in the Capital Asset Pricing Model. ... Capital Market Line Modern portfolio theory (MPT) proposes how rational investors will use diversification to optimize their portfolios, and how a risky asset should be priced. ...

For example, in a year where the broad market or benchmark index returns 25% above the risk free rate, suppose two managers gain 50% above the risk free rate. Since this higher return is theoretically possible merely by taking a leveraged position in the broad market to double the beta so it is exactly 2.0, we would expect a skilled portfolio manager to have built the outperforming 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' portfolios has an average beta of 3.0, and the other's has a beta of only 1.5, then the CAPM simply states that the extra return of the first manager is not sufficient to compensate us for that manager's risk, whereas the second manager has done more than expected given the risk. Whether investors can expect the second manager to duplicate that performance in future periods is of course a different question. A benchmark is a point of reference for a measurement. ... In finance, leverage (or gearing) is using given resources in such a way that the potential positive or negative outcome is magnified. ... The alpha coefficient () is a parameter in the Capital Asset Pricing Model. ...

Investing

By definition, the market itself has an underlying beta of 1.0, and individual stocks are ranked according to how much they deviate from the macro market (for simplicity purposes, the S&P 500 is usually used as a proxy for the market as a whole). A stock that swings more than the market (i.e. more volatile) over time has a beta above 1.0. If a stock moves less than the market, the stock's beta is less than 1.0. The S&P 500 is an index containing the stocks of 500 Large-Cap corporations, most of which are American. ...

More specifically, a stock that has a beta of 2 follows the market in an overall decline or growth, but does so by a factor of 2; meaning when the market has an overall decline of 3% a stock with a beta of 2 will fall 6%. (Betas can also be negative, meaning the stock moves in the opposite direction of the market: a stock with a beta of -3 would decline 9% when the market goes up 3% and conversely would climb 9% if the market fell by 3%.)

Higher-beta stocks mean greater volatility and are therefore considered to be riskier, but are in turn supposed to provide a potential for higher returns; low-beta stocks pose less risk but also lower returns. In the same way a stock's beta shows its relation to market shifts, it also is used as an indicator for required returns on investment (ROI). If the market with a beta of 1 has an expected return increase of 8%, a stock with a beta of 1.5 should increase return by 12%. In finance, rate of return (ROR) or return on investment (ROI), or sometimes just return, is the ratio of money gained or lost on an investment relative to the amount of money invested. ...

This expected return on equity, or equivalently, a firm's cost of equity, can be estimated using the Capital Asset Pricing Model (CAPM). According to the model, the expected return on equity is a function of a firm's equity beta (β_E) which, in turn, is a function of both leverage and asset risk (β_A):

$K_{E} = R_{F} + beta_E (R_{M} - R_{F} frac{}{})$

where: In finance, the cost of equity is the minimum rate of return a firm must offer shareholders to compensate for waiting for their returns, and for bearing some risk. ... An estimation of the CAPM and the Security Market Line (purple) for the Dow Jones Industrial Average over the last 3 years for monthly data. ...

because: The risk-free interest rate is the interest rate that it is assumed can be obtained by investing in financial instruments with no risk. ...

Multiple Beta Model

The Arbitrage Pricing Theory (APT) has multiple betas in its model. In contrast to the CAPM that 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. Arbitrage pricing theory (APT), in Finance, is a general theory of asset pricing, that has become influential in the pricing of shares. ... A risk factor is a variable associated with an increased risk of disease or infection but risk factors are not necessarily causal. ...

Estimation of Beta

To estimate Beta, one needs a list of returns for the asset and returns for the index; these returns can be daily, weekly or any period. 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 slope of the fitted line from the linear least-squares calculation is the estimated Beta. The y-intercept is the alpha. In statistics, linear regression is a regression method that models the relationship between a dependent variable Y, independent variables Xi, i = 1, ..., p, and a random term Îµ. The model can be written as Example of linear regression with one dependent and one independent variable. ... Linear least squares is a mathematical optimization technique to find an approximate solution for a system of linear equations that has no exact solution. ... The alpha coefficient () is a parameter in the Capital Asset Pricing Model. ...

Extreme and interesting cases

Treasury Securities are bonds issued by the U.S. Treasury. ... For other uses, see Cash (disambiguation). ... In statistics, the coefficient of determination R2 is the proportion of variability in a data set that is accounted for by a statistical model. ... In statistics, the coefficient of determination R2 is the proportion of variability in a data set that is accounted for by a statistical model. ... Positive linear correlations between 1000 pairs of numbers. ...

See also

The alpha coefficient () is a parameter in the Capital Asset Pricing Model. ... An estimation of the CAPM and the Security Market Line (purple) for the Dow Jones Industrial Average over the last 3 years for monthly data. ... The Treynor Ratio is a measurement of the returns earned in excess of that which could have been earned on a riskless investment (i. ... In corporate finance, Hamadaâ€™s Equation is used to separate the financial risk of a levered firm from its business risk. ...

External links

Categories: Mathematical finance | Fundamental analysis | Financial ratios A stock market is a market for the trading of company stock, and derivatives of same; both of these are securities listed on a stock exchange as well as those only traded privately. ... For other uses, see Stock (disambiguation). ... Common stock, also referred to as common shares, are, as the name implies, the most usual and commonly held form of stock in a corporation. ... Preferred stock, also called preferred shares or preference shares, is typically a higher ranking stock than common stock, and its terms are negotiated between the corporation and the investor. ... Outstanding stock is common stock that has been authorized and issued by a corporation and purchased by investors. ... A treasury stock or reacquired stock is stock which is bought back by the issuing company, reducing the amount of outstanding stock on the open market (open market including insiders holdings). ... A market maker is a person or a firm which quotes a buy and sell price in a financial instrument or commodity hoping to make a profit on the turn or the bid/offer spread. ... A Floor Trader checking market prices A Floor Trader is a member of a stock or commodities exchange who trades on the floor of that exchange for his or her own account. ... A Floor Broker is a member of an exchange who is an employee of a member firm and executes orders, as agent, on the floor of the exchange for clients. ... This is a list of stock exchanges. ... There are several methods used to value companies and their stocks. ... Gordon growth model is a variant of the discounted dividend model, a method for valuing a stock or business. ... The dividend yield on a company stock is the companys annual dividend payments divided by its market cap, or the dividend per share divided by the price per share. ... Income per share is the bottom line net income divided by the number of shares outstanding. ... The book value of an asset or group of assets is sometimes the price at which they were originally acquired (historic cost), in many cases equal to purchase price. ... Earnings yield is the quotient of earnings per share divided by the share price. ... In finance, a financial ratio is a ratio of selected values on a enterprises financial statements. ... The price/cash flow ratio (also called price-to-cash flow ratio or P/CF), is a ratio used to compare a companys market value to its cash flow. ... In finance, the PE ratio of a stock (also called its earnings multiple, just multiple, or P/E) is used to measure how cheap or expensive share prices are. ... The PEG ratio is a valuation metric for determining the relative trade-off between the price of a stock, the earnings generated per share (EPS), and the companys expected future growth. ... Price-to-sales ratio, P/S ratio, or PSR, is a valuation metric for stocks. ... Price-to-book ratio or P/B ratio, is a ratio used to compare a stocks market value to its book value. ... The debt to equity ratio (D/E) is a financial ratio indicating the relative proportion of equity and debt used to finance a companys assets. ... Return on capital, also known as Return On Invested Capital (ROIC) is defined as NOPLAT / Invested Capital usually expressed as a percentage. ... Return on Equity (ROE, Return on average common equity) measures the rate of return on the ownership interest (shareholders equity) of the common stock owners. ... Dow Theory is a theory on stock price movements that provides a basis for technical analysis. ... It has been suggested that some of the information in this articles Criticism or Controversy section(s) be merged into other sections to achieve a more neutral presentation. ... Fundamental analysis of a business involves analyzing its income statement, financial statements and health, its management and competitive advantages, and its competitors and markets. ... Technical analysis is the study of market action, primarily through the use of charts, for the purpose of forecasting future price trends. ... In some stock markets, the Mark Twain effect is the phenomenon of stock returns in October being lower than in other months. ... The January effect (sometimes called year-end effect) is an unexplained financial phenomenon of most stock markets having significantly higher returns in January than in other months of the year. ... In finance, the efficient market hypothesis (EMH) asserts that financial markets are informationally efficient, or that prices on traded assets, e. ... Arbitrage pricing theory (APT), in Finance, is a general theory of asset pricing, that has become influential in the pricing of shares. ... It has been suggested that ex-dividend date be merged into this article or section. ... Stock split refers to a corporate action that increases the number of shares in a public company. ... Growth Stocks in finance, are stocks that appreciate in value and yield a high return on equity (ROE). ... Invest redirects here. ... Speculation involves the buying, holding, and selling of stocks, bonds, commodities, currencies, collectibles, real estate, derivatives or any valuable financial instrument to profit from fluctuations in its price as opposed to buying it for use or for income via methods such as dividends or interest. ... A Trade involves the buying, holding, selling, and short-selling of stocks, bonds, commodities, currencies, derivatives or any valuable financial instrument to profit from fluctuations in its price as opposed to buying it for use or for income via methods such as dividends or interest. ... Day trading refers to the practice of buying and selling financial instruments within the same trading day such that all positions will usually (not necessarily always) be closed before the market close of the trading day. ... A stock trader or a stock investor is an individual or firm who buys and sells stocks or bonds (and possibly other financial assets) in the financial markets. ...

Contents