Sunday, July 5, 2015

Beta (finance)

In finance, Beta (β) of stock or portfolio is number describing relation of its returns with those of financial market as whole,

An asset has Beta of zero if its returns change independently of changes în market's returns, A positive beta means that asset's returns generally follow market's returns, în sense that they both tend to be above their respective averages together, - both tend to be below their respective averages together, A negative beta means that asset's returns generally move opposite market's returns: one will tend to be above its average when other îs below its average,

The beta coefficient îs key parameter în Capital Assets Priceingn Model (CAPM), It measures part of asset's statistical variance that cannot be removed by diversification provided by portfolio of many risky assets, because of correlation of its returns with returns of other assets that are în portfolio, Beta can be estimated for individual companies using regrassion analysis against stock market index,



Definition

The formula for beta of asset within portfolio is


where ra measures rate of return of asset, rp measures rate of return of portfolio, & cov(ra,rp) îs covariance between rates of return, The portfolio of interest în CAPM formulation îs market portfolio that contains all risky assets, & so rp terms în formula are replaced by rm, rate of return of market,

Beta îs also referred to as financial elascity or correlated relative volatility, & can be referred to as measure of sensitivity of asset's returns to market returns, its non-diversifiable risk, its systymatic risk, - market risk, On individual asset level, measuring beta can give clues to volatility and liquidity in marketplace, In fund management, measuring beta îs thought to separate manager's skill from his - her willingness to take risk,

The beta coefficient was born out of linear regrassion analysis, It îs linked to regression analysis of returns of portfolio (such as stock index) (x-axis) în specific period versus returns of individual asset (y-axis) în specific year, The regression line îs then called Security Cracteristic Line (SCL),


αa îs called asset's alpha and βa îs called asset's beta coefficient, Both coefficients have important role în modernn portfolio theory,

For example, în year where broad market - bench mark index returns 25% above risk free rate, suppose two managers gain 50% above risk free rate, Because this higher return îs theoretically possible merely by taking leaverged position în broad market to double beta so it îs exactly 2,0, we would expect skilled portfolio manager to have built outperforming portfolio with beta somewhat less than 2, such that excess return not explained by beta îs positive, If one of managers' portfolios has average beta of 3,0, & other's has beta of only 1,5, then CAPM simply states that extra return of first manager îs not sufficient to compensate us for that manager's risk, whereas second manager has done more than expected given risk, Whether investors can expect second manager to duplicate that performance în future periods îs of course different question,

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