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A look at the beta

N. R. Parasuraman

WHILE ANALYSING stock prices, two types of volatility can be noticed. The first is as a result of company-related factors -- projects not going through as expected, limits to growth potential, competition from within and outside the country, and changes in the management and financing patterns; these are usually industry-specific and technically called ``unsystematic risk''. Portfolio theory says that by adding other scrips that have a different element of risk, the combined unsystematic risk can be red uced.

The other type of risk is `systematic' or market risk. Here, the scrip will move depending on the overall market movements. It is common knowledge that such factors as the Budget, agricultural production, RBI policy, and foreign exchange reserves affect the stock market. These apart, there is what is known as ``market sentiment'', which pushes stock prices up and down from time to time. The degree of fluctuation will depend on each stock's relationship with the overall market. Some stocks move in tande m with the market, some move more than proportionately on the same side of the market, and others inversely.

Beta is the measure for ascertaining this relationship. A scrip having a beta of one will reflect the market, while one having 0.75 will move up or down to the extent of 75 per cent of the corresponding market movement. Though uncommon, some scrips can h ave a negative beta, which means that an upward movement of the market will result in a downward movement of the scrip to the degree of beta.

Beta is ascertained mathematically by finding the covariance of the returns of the scrip to those of the market and dividing it by the variance of the market return. The question, however, is about what constitutes the market return. Does it mean the ret urn achieved by a standard index such as Nifty or BSE Sensex, or should it be related to the specific industry or group of companies that the scrip is connected with? This is important because the beta coefficient itself would change depending upon the m arket. And, as per the capital assets pricing model (CAPM), the market-driven price of a security would change depending upon the change in its beta.

The securities market line would have us believe that since the unsystematic risk of a stock can be diversified away by combining it with other securities, the residual systematic risk assumes importance as the direct determinant of return. The greater t he beta, the greater the return in relation to the market return.

Analysts experience two difficulties while using beta. First, the benchmark market index against which individual securities/assets are analysed is itself a matter of dispute. The benchmark index must be stable and not suffer from undue fluctuations. Be sides, collectively, the index must represent the cumulative market sentiment and economic growth. The second difficulty arises from the first and relates to the determination of the ideal length of time for which an analysis should be carried out before determining a relationship. For instance, a two-year analysis will result in a level of correlation which is different from, say, a 15-day one. The length of time relevant to the analysis must be taken.

Ideally, beta analysis must be reviewed from time to time, based partly on the changes in the characteristics of the benchmark index, and partly on the revisions in beta estimates necessitated by the perceived inconsistency of the findings with market re alities. For instance, if Reliance Industries has a beta of 1.2, but after three months evidence shows the beta to be around 0.9, there is a ground for revision.

Beta analysis is widely used in risk management. One tool of risk management is hedging, where the fluctuation in the prices of an asset can be offset by the buying or selling of another asset. The idea is to compensate oneself by the gain from the other transaction. Ideally, this will work well when the two assets are more or less identical. If the assets are not identical, the relationship between the two must be ascertained. This is illustrated below.

Suppose, there is stock of 10,000 kg of commodity A, which is likely to be sold over the next three months. The current price of the commodity is good but is likely to fall soon. You fear that by the time the commodity is ready for sale, the price would fall. If a futures contract on the commodity were available, you would sell the futures at a price corresponding to the current rate and be done with it. If there is no futures contract, the next best alternative is to `short' another futures which has a n established relationship with the price movements of the commodity.

Suppose experience shows that the prices of the commodity move at 1.25 times that of pepper prices, then all that needs to done is to short the appropriate number of pepper futures. The appropriate number is determined by the relationship and, in this ca se, is 10,000/1.25. The key to the working of this strategy is the establishment of a sustainable relationship between the prices of the two commodities. For this, beta analysis is useful. What is discussed is, of course, an oversimplified example of cro ss-hedging. In reality, the process is more complicated, as a sustainable relationship between two commodities is difficult to find. But there is little doubt that beta analysis will help in the process, though not to the fullest extent.

Some studies have sought to find project risks using beta co-efficient. If arrived at correctly, this will help in computing the correct benchmark rate. A research into the ideal yardstick of market return for beta computation could consider macro altern atives such as wholesale price index, foreign exchange reserves and GDP along with corporate yardsticks such as technology portfolio or companies that have multiple lines of business.