Chapter 11

Risk And Return

Risk is present in virtually every decision. When a production manager selects an equipment, or a marketing manager an advertising campaign, or a finance manager a portfolio of securities all of them face uncertain cash flows. Assessing risks and incorporating the same in the final decision is an integral part of financial analysis.

The objective in decision making is not to eliminate or avoid risk-- often it may be neither feasible nor necessary to do so -- but to properly assess it and determine whether it is worth bearing. Once the risk characterising future cash flows is properly measured, an appropriate risk-adjusted discount rate should be applied to convert future cash flows into their present values.

To estimate the risk-adjusted discount ratea task that we have glossed over so faryou should be able to measure and price financial risk. While the meaning of risk and return is grasped by almost every person, as a manager you need an explicit and quantitative understanding of these concepts and, more importantly, the nature of relationship between them. This chapter presents a framework that will help you in doing this. It is organised into five sections as follows:

Risk as variability in return Risk reduction through diversification Measurement of market risk Relationship between risk and return Implications

11.1 RISK AS VARIABILITY IN RETURN

The rate of return on an asset for a given period (usually a period of one year) is defined as follows:

Annual income + Ending price – Beginning priceRate of return =

Beginning price

To illustrate, consider the following information about a certain equity stock: * Price at the beginning of the year : Rs.60.00* Dividend paid at the end of the year : Rs.2.40* Price at the end of the year : Rs.69.00

The rate of return on this stock is calculated as follows:

2.40 + (69.00 – 60.00)= 0.19 or 19 per cent

60.00

It is sometimes helpful to split the rate of return into two components, viz., current yield and capital gains/loss yield as follows:

Annual income Ending price – Beginning price+

Beginning price Beginning price

Current yield Capital gains/loss yield

The rate of return of 19 per cent in our example may be broken down as follows:

2.40 (69.00 – 60.00)+ = 4 per cent + 15 percent

60.0 60.00Current Capital gainsyield yield

When you invest in a stock you know that its return can take various possible values. For example, it may be -5 percent, or 15 percent, or 35 percent. Further, the likelihood of these possible returns can vary.

Risk represents the variability of returns. It is commonly measured by variance or standard deviation of returns. To understand how it is calculated, let us consider the equity stock of Oriental Shipping. The return on the equity stock of Oriental Shipping depends on the state of the economy. The economy may be in three possible states, which is, boom, normal, and recession with probabilities of 0.30, 0.50, and 0.20. The probability distribution1 of the rate of return on the equity stock of Oriental Shipping is given in Exhibit 11.1.

1 The probability of an event represents the likelihood of its occurrence. When you define the probability of rate of return (or for that matter any other variable) remember that: The probability outcomes must be mutually exclusive and collectively exhaustive. The probability assigned to an outcome may vary between 0 and 1. The sum of the probabilities assigned to various possible outcomes is 1.Based on the probability distribution of the rate of return, you can compute two key parameters, the expected rate of return and the standard deviation of rate of return.

Exhibit 11.1Probability Distribution of the Rate of Return on Bharat Foods Stock and Oriental

Shipping Stock

Rate of Return (%)State of the Probability of Oriental Shipping

Economy Occurrence

Boom 0.30 40Normal 0.50 10Recession 0.20 -20

Given the probability distribution of the rate of return, we can calculate: n

E(R) = pi Ri

i=1

= pi {Ri – E (R)}2 1\2

where E(R) is the expected rate of return, Ri is the return for the i th possible outcome, pi

is the probability associated with Ri , and is the standard deviation of return.

E (R) and for the equity stock of Oriental Shipping are calculated in Exhibit 11.2.

Exhibit 11.2 Expected Return and Standard Deviation

Oriental Shipping Stock

i. State of the Economy pi Ri piRi Ri - E(R) (Ri - E(R))2 pi (Ri - E (R))2

1. Boom 0.30 50 15.0 27.0 729.0 218.7 2. Normal 0.50 20 10.0 -3.0 0.25 4.5 3. Recession 0.20 -10 -2.0 -33.0 1089.00 217.8

piRi = 23.0 pi (Ri – E (R))2 = 441.0

σ = [pi (Ri - E (R))2]1/2 = (441.0)1/2 = 21.0%

11.2 RISK REDUCTION THROUGH DIVERSIFICATION

By combining risky securities in a portfolio, you can reduce risk. Consider the example given in Exhibit 11.3. Suppose there are two firms, Company A and Company B, operating in a Caribbean island , where tourism is the main industry. Company A makes and sells suntan lotion. It does well in sunny years but poorly in rainy years. The return on its stock will vary from 30% to -10%, depending on weather conditions, as shown in Exhibit 11.3.

Company B makes and sells disposable umbrellas. It does well during rainy years but poorly in sunny years. The return on its stock varies between 30 percent and -10 percent depending on weather conditions, as shown in Exhibit 11.3.

If you buy the stock of only Company A or Company B, you are exposed to a lot of risk. However, if you split your funds equally across the stocks of A and B, you can enjoy a stable return of 10 percent as shown in the last column of Exhibit 11.3.

Exhibit 11.3Risk Reduction through Diversification

Weather

Conditions

Return on

Stock A, RA

Return on Stock B, RB

Return onPortfolio, RP

Sunny year 30% -10% 0.5(30) + 0.5(-10) = 10%

Normal year 10% 10% 0.5(10) + 0.5(10) = 10%

Rainy year -10% 30% 0.5(-10) + 0.5(30) = 10%

In this example, the returns on stocks A and B are perfectly negatively correlated. So, by appropriate diversification, it is possible to eliminate risk completely. In the real world, however, returns from most stocks tend to move together and hence it is not possible to eliminate risk completely. However, as long as returns on stocks do not move in a perfect lockstep, diversification reduces risk. In technical terms, diversification reduces risk if returns are not perfectly positively correlated.

The relationship between diversification and risk is shown graphically in Exhibit 11.4. When the portfolio has just one security, say stock 1, the risk of the portfolio, σp, is equal to the risk of single stock included in it, σ1. As a second security-say stock 2- is added, the portfolio risk decreases. As more and more securities are added, the portfolio risk decreases, but at a decreasing rate, and reaches a limit. Empirical studies suggest that the bulk of the benefit of diversification, in the form of risk reduction, is achieved by forming a portfolio of about ten securities. Thereafter, the gain from diversification tends to be negligible.

Exhibit 11.4Relationship Between Diversification and Risk

Risk

Unique Risk

Market Risk

1 5 10 No. of Securities

Market Risk versus Unique Risk

Notice that the portfolio risk does not fall below a certain level, irrespective of how wide the diversification is. Why? The answer lies in the following relationship which represents a basic insight of modern portfolio theory.

Total risk = Unique risk + Market risk

The unique risk of a security represents that portion of its total risk which stems from firm-specific factors like the development of a new product, a labour strike, or the emergence of a new competitor. Events of this nature primarily affect the specific firm and not all firms in general. Hence, the unique risk of a stock can be washed away by combining it with other stocks. In a diversified