27 May 2010

WHAT IS BETA ? How do we have to go about reading the market is simple beta calculation.

The beta compares the sensitivity of a stock’s price movement with the broader index. Higher the beta, higher will be the volatility in the stock price, and hence, riskier the investments. The beta of the index or the market is pegged at 1.

“Some of the clients had to liquidate positions at lower prices due to mark-to-market pressures. While until morning, there was no panic, the sentiment turned negative, after the Nifty and the Sensex fell from the psychological levels of 4800 and 16,000, respectively,” the dealer said. “We are asking some of our clients who are leveraged in the derivatives segment to either pay the additional margins to maintain the positions. We have liquidated positions of those who could not pay up on time,” said a dealer, who handles wealthy clients at a domestic broking firm.

Analysts advise caution while dealing with high-beta stocks. Gurudatta Dhanokar, technical and derivative strategist, Almondz Global Securities, says that the trend in the Nifty looks down only till the time the global markets are under pressure. “If someone wants to trade the high-beta space, he should do through buying out of the money calls as the premium is low. Investors are already ‘long’ should put stop losses in place, while those who want to create fresh position should do so only after waiting for the markets to stabilise.”

In finance, the beta (β) of a stock or portfolio is a number describing the relation of its returns with that of the financial market as a whole.[1]

An asset with a beta of 0 means that its price is not at all correlated with the market. A positive beta means that the asset generally follows the market. A negative beta shows that the asset inversely follows the market; the asset generally decreases in value if the market goes up and vice versa.[2]

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. Beta can be estimated for individual companies using regression analysis against a stock market index.


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 ra measures the rate of return of the asset, rp measures the rate of return of the portfolio, and Cov(ra,rp) is the covariance between the rates of return. The portfolio of interest in the CAPM formulation is the market portfolio that contains all risky assets, and so the rp terms in the formula are replaced by rm, the rate of return of the market.

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).

SCL : r_{a,t} = \alpha_a + \beta_a  r_{m,t} +  \epsilon_{a,t} \frac{}{}

αa is called the asset's alpha and βa is called the asset's beta coefficient. Both coefficients have an important role in Modern portfolio theory.

For an 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

 Security market line

: Security market line

The Security Market Line

The SML graphs the results from the capital asset pricing model (CAPM) formula. The x-axis represents the risk (beta), and the y-axis represents the expected return. The market risk premium is determined from the slope of the SML.

The relationship between β and required return is plotted on the security market line (SML) which shows expected return as a function of β. The intercept is the nominal risk-free rate available for the market, while the slope is E(Rm − Rf). The security market line can be regarded as representing a single-factor model of the asset price, where Beta is exposure to changes in value of the Market. The equation of the SML is thus:

 \mathrm{SML}: E(R_i) - R_f = \beta_i (E(R_M) -  R_f).~

It is a useful tool in determining if an asset being considered for a portfolio offers a reasonable expected return for risk. Individual securities are plotted on the SML graph. If the security's risk versus expected return is plotted above the SML, it is undervalued since the investor can expect a greater return for the inherent risk. And a security plotted below the SML is overvalued since the investor would be accepting less return for the amount of risk assumed.

Beta volatility and correlation

There is a simple formula between beta and volatility (sigma):

\beta = (\sigma / \sigma_m) r\,

That is, beta is a combination of volatility and correlation. For example, if one stock has low volatility and high correlation, and the other stock has low correlation and high volatility, beta can decide which is more "risky".

This also leads to an inequality (since |r| is not greater than one):

\sigma \ge |\beta| \sigma_m

In other words, beta sets a floor on volatility. For example, if market volatility is 10%, any stock (or fund) with a beta of 1 must have volatility of at least 10%.

Another way of distinguishing between beta and correlation is to think about direction and magnitude. If the market is always up 10% and a stock is always up 20%, the correlation is one (correlation measures direction, not magnitude). However, beta takes into account both direction and magnitude, so in the same example the beta would be 2 (the stock is up twice as much as the market)



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