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S. D. Bala

WHAT sort of investor rationally views the beta of a security as the security's proper measure of risk? While risk is broken into diversifiable and non-diversifiable portions, the market will not reward an investor for holding diversifiable risk.

The logic is simple: the investor is expected to diversify them away. By not diversifying he is not being efficient. The market, therefore, rewards an investor only for the non-diversifiable risk. Hence, the only relevant risk is the non-diversifiable risk. Therefore, an investor must know how much non-diversifiable risk he is taking. This is measured in terms of beta.

An investor therefore, views the beta of a security as a proper measure of risk, in evaluating how much the market will reward him for the non-diversifiable of element of risk that he is assuming in respect of a security. An investor who is evaluating the "non-diversifiable element" of risk, that is, extent of deviation of returns vis-à-vis the market, will therefore consider beta as a proper measure of risk.

The concept of beta: The total risk of a stock is measured by its standard deviation. In relation to a market, it is its co-variance with the market. If this covariance is standardised for the covariance of the market we get the beta value, which. Beta value is a standardised measure of covariance of return of an asset and that of the market.

Beta is a measure of non-diversifiable risk. We can say that the beta of a stock measures the sensitivity of the stock with reference to a broad based market index.

The broad based index for instance, in India, could be the Sensex. We can understand what beta indicates by considering a few numbers. For instance, a beta of 1.2 for a stock would indicate that this stock is 20 per cent riskier than the Index. Similarly, a beta of 0.9 would indicate that this stock is 10 per cent (100-90) less risky than the Index. And, of course, a beta of one would mean that the stock is as risky as the stock market index.

This has two simple implications:

a) Beta is the measure of a stock's volatility with reference to the market index. Put another way, this would mean that the beta of a stock indicates the sensitivity of a stock to changes in the returns from the stock market. If the stock market as a class (measured by the Index) changes by 5 per cent, a stock with a beta of 1.2 should change by 5 x 1.2 = 6 per cent

b) Expected risk premium of any stock is beta times the market risk premium: An investor gets extra reward for taking risk. This is called risk premium. If the stock market as a class (measured by the Index) gives a risk premium of, say, 10 per cent and the beta of a stock is 1.2 the risk premium from this stock ought to be 1.2 times, that is, 12 per cent.

The beta value of a stock can be any number. If the beta value is greater than one, we call it a high beta stock. Such stocks are riskier than the "stock market". They move faster than the movement in the stock market. If the market goes up, this stock goes up faster. If the market falls, this stock falls faster.

If the beta value is less than one, we call it a low beta stock. Such stocks are less risky than the "stock market". They move slower than the movement in the stock market. If the market goes up, this stock goes up slower. If the market falls down, this stock falls slower.

Stocks with a beta value of one are called unity stocks. Such stocks mimic the market. They move in tandem with the market. If the market goes up by a certain percentage, this stock too moves up by the same percentage. If the market falls by a certain percentage, this stock too falls by the same percentage.

There are a few alternative ways of computing beta (see Table 1).

Beta of a portfolio: Beta of a portfolio of securities is computed as the weighted average return of the investments in the portfolio. This is because, a portfolio consists of a well-diversified set of securities and since systematic risk cannot be diversified away, the beta of a portfolio is the value-weighted beta of the securities constituting the portfolio. The beta of a portfolio depicts the systematic risk of the portfolio itself.

Capital rationing

IN A pure capital budgeting decision, we must select projects with positive NPV. Between two mutually exclusive projects, we must select the one with the higher NPV. These presupposed that we would have enough resources to undertake any and every project.

However, when money is in short supply, we must lay out a mechanism by which we will be able to maximise wealth within the framework of the money available.

Situation of limited availability of funds, to be invested in one or more alternative projects, is called capital rationing. Two issues are relevant.

Issue No. 1: Types of capital rationing. Money could be in short supply either in year 0 only or in more than one year. When it is in short supply in one year only it is called single period capital rationing; when it is in short supply in more than one year it is called multi period capital rationing. Money is said to be in short supply if the availability of money is less than the requirement of money. Such a short supply can arise, either in a single period (single period capital rationing) or in more than one period (multi period capital rationing).

This is explained with a brief example: The total requirement in respect of five projects that can be accepted is Rs 100 lakh in year 0.

Three of the projects also require additional investment in year 1 to the extent of Rs 50 lakhs. The monies available in the two years are Rs 90 lakh and Rs 40 lakh. We have to identify whether there is any capital rationing.

Hence, multi-period capital rationing exists.

Issue No. 2: Nature of projects. A project may be either a divisible project or an indivisible one. Divisible projects permit fractional investments, that is, they can be taken up in parts. Indivisible projects do not permit fractional investments, that is, they have to be taken in full or dropped.

For example: A project for constructing a 10-storeyed apartment complex is a divisible project.

If we have money only for constructing seven storeys we could do so; that is, undertake 0.7 of the project. A project for buying a lorry is an indivisible project because if we do not have enough money you cannot buy 0.7 of a lorry.

Where the short supply of cash resources is on account of factors beyond the control of an entity, it is known as "hard-rationing", and when, on account of internal policy decisions, for example, not to invest funds beyond a pre-determined level for purposes of dividend distribution, and so on, it is known as "soft rationing".

Under the decision tree

A FIRM has an investment proposal requiring an outlay of Rs 80,000. The investment proposal is expected to have two years' economic life with no salvage value.

In Year 1, there is a 0.4 probability that cash inflow after tax will be Rs 50,000 and 0.6 probability that cash inflow after tax will be Rs 60,000. The probability assigned to cash inflow after tax, for the year-2 are as shown in Table 2

The firm uses a 10 per cent discount rate for this type of investment.

Required: Construct a decision tree for the proposed investment project, and calculate the expected NPV.

What NPV will the project yield, if the worst outcome is realised, and what is the probability of occurrence of this NPV.

What will be the best and the probability of its occurrence? Will the project be accepted?

The decision tree diagram is presented in the chart. Identifying the various paths and outcomes, and the computation of various paths/outcomes and NPV of each path are presented in Tables 3, 4 and 5 respectively.

Conclusions: The aggregate net present values of all the paths, after reckoning the joint probability of occurrence of each path, is positive at Rs 6,223.

The expected worst possible outcome would be a loss of Rs 1,178 (path 1). The probability of the outcome is 0.08 (or 8 per cent)

The expected best possible outcome would be a profit of Rs 4,752. The probability of its occurrence is 0.3 (or 30 per cent)

The project will be accepted as it gives a positive NPV of Rs 6,773 based on joint probability.

Future lies here

THE following data relates to ABC Ltd's share prices: a) current price per share, Rs 180; b) price per share in the futures market six months, Rs 195.

It is possible to borrow money in the market for securities transactions at the rate of 12 per cent per annum.

Required: i) Calculate the theoretical minimum price of a six-month forward contract; and ii) explain if any arbitraging opportunities exist.

Solution: Currently, there is no system of booking "forward" contracts for purchase or sale of shares. It is assumed that the computation is for a "futures" contract, and not a forward contract.

The computation of theoretical minimum six-months futures price is presented in Table 6. As per computations shown, theoretical price of a six months futures contract is Rs 191.13.

Arbitrage opportunity: The decision rule to identify arbitrage opportunity is as shown in Table 7. The value of arbitrage benefit is computed as shown in Table 8.

(To be continued)

(Suggested answers to the CA Final (May 2004) MAFA paper.)

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