Financial Management - Chapter 3

Subject: Financial Management

Chapter: 3 – Risk and Return

Chapter 3 – Risk and Return

Contents Risk and return go together Probability distribution of all possible outcomes in terms of return Measuring risk so as to expect adequate return – Weighted average return, Standard deviation and the Co-efficient of variation Risk in a portfolio context – introduction to a portfolio of securities Types of risk associated with investment in a portfolio – systemic and non-systemic Concept of Beta and Capital Asset Pricing Model Volatility and Risk Some concerns about Beta and the CAPM Numerical exercises in risk and return

At the end of the chapter the student will be able to Determine standard deviation and co-efficient of variation for a set of returns Measure degree of risk associated with an investment through volatility in returns over a period of time of a chosen investment Determine the diversifiable and non-diversifiable risks in the context of “portfolio” Apply Capital Asset Pricing Model and find out the cost of equity in a chosen stock through “Beta”

Introduction – Risk and Return go together One of the fundamentals in Finance is – “Risk and Return go together”. Recall what we learnt in Chapter 2 under “4 tier structure for interest rates”. We saw that from tier 2 onwards the rate of interest starts progressively increasing. Why? This is because in each successive tier, the risk is higher than the immediately preceding tier. For example, we saw that the loan given by a bank carries more risk than the deposit kept with the bank. This is so as the bank is much more broad based with so many customers than the borrower to whom the loan is given. We mean that the chances of failure of an individual business are more than the chances of failure of a larger bank. Similarly the rate of return from a project is the highest at Tier no. 4, as entrepreneurial risk is the highest risk in any economy – the risk of running a business enterprise. Please recall the factors considered by us while concluding that the rate of return from a project should be the highest. We repeat here for facilitating recall. ♦

The project owner’s investment does not have the backing of assets. A lender, on the contrary, has backing of assets for his loan.

♦

The enterprise pays the lender interest periodically. The owners on the contrary, get return in the form of dividend. This is not certain.

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Chapter: 3 – Risk and Return ♦

Besides interest, the enterprise should also have sufficient surplus after paying interest to repay the loan amount

♦

Risk of project failure affects the owners more than the lenders for the same reason as mentioned in the first bullet point

Thus we prove the point mentioned at commencing this chapter namely “risk and return go together”. The question relevant here is that “can we define risk?’ Let us make an attempt here. We make an investment in bank’s fixed deposit at 8% p.a. We have an agreement with the bank that if the market rate comes down the rate of interest offered on the deposit would also come down. Is there a risk here? Definitely, if the market rate comes down. What is this risk? The risk of not getting the expected return of 8%. Thus the first definition of “risk” is the “uncertainty”. Uncertainty relating to what? In the given example, uncertainty relates to “outcome” of an “activity”, i.e., investment. Is the “outcome” stated? Yes. Right in the beginning when we contracted with the bank to get 8% return. So, we build up the definition of “risk”. We can define risk in general as “uncertainty relating to a stated outcome of a specific activity”. The activity could be anything and the outcome automatically gets related to this. For example, undergoing a post graduation course in “Management” could be the activity and the risk could be relating to the stated outcome of landing oneself in a well-paid job. In finance terms, the “risk” obviously relates to the activity of investment and the stated outcome relating to this would be the “return” on this investment. Thus going back to our example of investment in a bank deposit, the activity is “investment in a bank deposit”. The risk relates to the outcome of return on this investment namely interest not coming down from the expected rate of 8%.

Is risk related only to possible reduction in rate of return? Or in other words, is there no risk in case the return is higher than the expected rate of return? Suppose the bank deposit referred to above fetches us higher return than expected rate of 8%. Is there no risk? There apparently is no risk from the point of view of the depositor. However this is not the correct picture. The very fact that the return is higher than the expected rate due to increase in market rate of interest could also bring the rate down in future any time. Thus going by the accepted definition of “risk” relating to investment, it relates to uncertainty of the return from the investment and not specifically to whether the deviation (fluctuation) is positive (return being higher than expected) or negative (return being less than expected). In both the cases of deviation or fluctuation from the expected rate of return, risk exists. Let us examine the following graph.

Return On investment

Expected rate of return

Duration of investment

The above graph shows returns deviating from the expected rate of return both positively and negatively. Does it mean that when it deviates positively there is no risk for us? There is a risk of uncertainty that the returns could go down and be less than the expected rate of return. Conclusion: The higher the uncertainty the higher the risk. The higher the risk the higher the return expectation. This is because the investors are risk averse and would expect a higher return in case the risk increases. In terms of probability of Punjab Technical University, Online Virtual Campus

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Chapter: 3 – Risk and Return return, the higher the probability, the less the uncertainty and less the risk. Conversely the less the probability, the more the uncertainty and higher the risk. In this chapter, we are going to study the return on investment in stock markets, i.e., in shares and bonds and not any other investment as these are subject to market risk and fluctuations. This enhances the risk associated with investment into equity market and bond market. We will examine as to what kind of risk can be minimized and what cannot be minimized. We are also going to see how the risk of an individual stock (share) can be minimized by including the same in a bunch of securities (investment instruments) that is called “portfolio”.

Probability of distribution of outcome (return) for a given investment Example no. 1 Suppose we invest Rs.1000/- in shares of a limited company. The different expected returns on this investment and the probabilities assigned to them are as under: 14% = 35% 16% = 22% 13% = 43% The weighted average rate of return expected from this investment is: 0.14 x 35 = 4.9 0.16 x 22 = 3.52 0.13 x 43 = 5.59 Wt. Av. = 14.01%. This is referred to as the expected rate of return from this investment.

What is return from share investment? What is return from our share investment of Rs.1000/- in the above example? Is it dividend or something more than dividend?

Example no. 2 Date of purchase of the above share = Dec. 2001 Dividend for the year ended 31-03-2002 = 100/Date of sale = Dec. 2002 Market value = Rs. 1030/The total return on investment = Amount received on sale of investment – Amount invested at T0 ----------------------------------------------------------------------------------------------------------------

Amount invested at T0 Thus the return on our investment for a period of one year = 130/1000 = 13% p.a1. Return on investment in shares = dividend + market appreciation during the period of holding the security (difference between selling and purchase prices). Suppose the holding period is two years, the return is determined cumulatively for a period of 2 years and divided by 2 to arrive at annual return.

Standard deviation 1

Return is always expressed on annual basis. For example if the return for holding a security is 13% for a period of six months, the annualised return would be 26% = 2 x 13% Punjab Technical University, Online Virtual Campus

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Chapter: 3 – Risk and Return Investment is about selection of one stock (share or bond) in preference over another, after due consideration of the risks associated with them respectively. Let us say for example investment in shares of two limited companies A and B. In this case we should understand the implication of probability distribution of expected returns for a given period for both the stocks. Let us examine the probability distribution and understand the concept of risk. We are examining below the expected value of return and standard deviation of return for a chosen stock. Possible return (Ri)

Probability

of

- 0.10

0.05

-0.005

(-0.10 – 0.09) x (0.05)

-0.02

0.10

-0.002

(-0.02 – 0.09) x (0.10)

0.04

0.20

0.008

(-0.04 – 0.09) x (0.20)

0.09

0.30

0.027

(-0.09 – 0.09) x (0.30)

0.14

0.20

0.028

(-0.14 – 0.09) x (0.20)

0.20

0.10

0.020

(-0.20 – 0.09) x (0.10)

0.28

0.05

0.014

(-0.28 – 0.09) x (0.05)

occurrence (Pi)

(Ri) x (Pi)

∑ = .090 = R

Total = 1.00

2

(Ri – R) x (Pi)

2

2

2

2

2

2

2

2

σ = 0.00703 and σ = 0.0838

th

Where Ri is the return for the i possibility, Pi is the probability of that return occurring and n is the total number of possibilities. Thus the expected value of return is simply a weighted average of the possible returns, with the weights being the probabilities of occurrences. For the above distribution of possible returns, the expected weighted average return is 9% and the standard deviation of the return is 0.0838 or 8.38%. We can easily see that the higher the standard deviation the higher the risk; the higher the risk, the higher the expected rate of return in future. Thus the standard deviation is a simple measure of risk based on the distribution of returns in the past by assigning probabilities to them. The probabilities represent the % times the return has been so. In this case the probability is 10% for 20% return, this means that 10% of the times, the return has been 20%.

Coefficient of Variation The standard deviation can at times be misleading in comparing the risk, or uncertainty relating to the alternative returns, if they differ in size. Consider two alternative investment opportunities, A and B, whose normal probability distributions of one-year returns have the following characteristics:

____________________________________ Investment A

B

____________________________________ Expected Return R

0.08

0.24

Standard deviation σ

0.06

0.08

Co-efficient of variation CV 0.75

0.33

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Chapter: 3 – Risk and Return We have mentioned earlier that higher the standard deviation, the higher the risk and vice-versa. Now looking at the above table, can we say that since the standard deviation of stock B is more than that of stock A, the risk associated with it is higher? Yes and No. Yes if the sizes of investment is the same in both the stocks. This is best explained by taking two persons having widely different incomes with the same standard deviation. Let us assume that the average monthly income of the first person is Rs.10,000/- while that of the second person is Rs. 1,00,000/-. Both of them are having standard deviation of say 3,000/-. We can very easily see that while this standard deviation would affect the first person much more than it does the second person. This is what establishes the need for determining the co-efficient of Variation. How does one do it? To adjust for scale or size, the standard deviation can be divided by the expected value of return to compute the coefficient of variation (CV). Co-efficient of variation (CV) = σ/R. This in the above table gives us the values of 0.75 = 0.06/0.08 for stock A and 0.33 = 0.08/0.24 for stock B. Thus using the co-efficient of variation (CV) we find that the riskiness of stock A is more than the riskiness of stock B while by standard deviation method, we would have found stock B to be more risky than stock A.

Risk and Return in a portfolio context So far we have seen measure of risk associated with single investment or investment in one stock in preference to another. However usually the investment is not in single stock but in a combination of stocks that is called a “portfolio”. A portfolio is defined as “mixed bag of securities”. This is best understood by taking the example of “Mutual Funds”. The students would have heard of “mutual funds” in India, like Franklin Templeton Mutual Funds, Allianz Mutual Funds, Unit Trust of India, Kotak Mahindra Mutual Fund etc. These funds invest in: Different industries (also called sectors) Different time periods (also called maturities) Different units in the same industry (example in the Cement sector, ACC and Birla Cements) Different instruments of finance – debt instruments like bond and debentures or share capital instruments like equity share capital or preference share capital or even short-term instruments called money market instruments2 The above is to spread the risk of investment but at the same time optimizing the return from the investment and not minimising it. Therefore we need to understand the concept of “risk” and “return” in the context of a portfolio.

Portfolio Return The expected return of a portfolio is simply the weighted average of the expected returns of the securities constituting that portfolio. The weights are equal to the proportion of total funds invested in each security (the total of weights must equal to 100 percent). The general formula for the expected return of a portfolio Rp is as follows: m Rp = ∑ Aj x Rj J=1 Where Aj is the proportion of total funds invested in security j; Rj is the expected return for the security j and m is the total number of different securities in the portfolio. The expected return and standard deviation of the probability distribution of possible returns for two securities are shown below:

2

Security A

Security B

Expected return Rj

14.0%

11.5%

Standard deviation σj

10.7

1.5

For details of different markets and instruments, please refer to the chapter on “Financial Sources”

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Chapter: 3 – Risk and Return If equal amounts of money are invested in these two securities, the expected return of the portfolio containing two securities namely A and B is 0.5 x 14% + 0.5 x 11.5% = 12.75%.

Portfolio Risk The portfolio expected return is a straightforward weighted average of returns on the individual securities; the portfolio standard deviation is not the weighted average of individual security standard deviations. We should not ignore the relationship or correlation between the returns of two different securities in a portfolio. This correlation however has no impact on the portfolio’s expected return. Let us understand what we mean by “correlation” between securities. Suppose we have two stocks “A” and “B” in our portfolio. During a given period the return of “A” increases say by 1% while that of “B” increases by 0.5% in the same period. This means that both are moving positively in the direction of increasing returns. This is described as “positive” correlation. However the quantum of increase is not the same in both the cases. Hence this is imperfect but positive correlation. In case the quantum of increase is 1% in both the cases, then the correlation is said to be positive and perfect correlation. If the returns move in the opposite direction, say one increasing and the other decreasing, then the correlation is negative. Still the relationship could be perfect in the sense that the quantum of increase in return say in the case of “A” is the same in the case of “B” but in the opposite direction. This means that while stock “A” has increased its return, stock “B” has lost its return by the same percent. Let us try to put these in the form of equations. “Δ” represents the increase in return and (“Δ”) (within brackets indicate that the return is decreasing). Keeping these in mind let us attempt the following: Δ of stock A = 1% for a given period = Δ of stock B = perfect and positive correlation Δ of stock A = 1% for a given period; Δ of stock B = greater than or less than 1% but the return has increased and not decreased = positive but imperfect correlation Δ of stock A = 1% for a given period; (“Δ”) of stock B = 1%. Then stock A and stock B are said to have perfect but negative correlation. Δ of stock A = 1% for a given period; (“Δ”) of stock B less than or more than 1%. Then stock A and stock B are said to have imperfect and negative correlation. We have consciously omitted the fifth possibility of both the stocks A and B losing to the same percent during a given period. Any portfolio would avoid such stocks unless the future is going to be completely different in which case the past is not the basis on which stock selection is being made. We have also tried to present these concepts in as simple a manner as possible. The students are advised to go through these repeatedly to grasp the essence of the underlying concept in correlation between one stock and another. This is required because the concept of correlation is the fundamental based on which the selection of stocks for a portfolio is done. The students will appreciate that positive correlation between two stocks would mean increased risk especially if the relationship is perfect. Negative correlation stocks are not desirable. What is then left is positive but imperfect correlation. The risk-averse investors would invariably choose such stocks as show positive relationship between them (or among them in view of the number of stocks in a portfolio being more than 2, which is usually the case) but not perfect relationship. Then only the risk in a portfolio is reduced. For a given period, same degree of movement in return on different stocks in the same direction only increases the risk in a portfolio.

Now going back to the standard deviation of a portfolio, we will appreciate that it is not merely the weighted average of the standard deviation numbers for each stock in the portfolio. Suppose there are five stocks in a portfolio. We can appreciate that there are quite a few possible combinations of these five stocks depending upon the proportion of investment in each of them; for each combination, the weighted average of the standard deviation numbers has to be etermined first and then the ultimate average standard deviation should be found out for all possible combinations. This involves a very complicated calculation and hence not presented here.3 However before we end this topic it

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This is better explained by any standard textbook on “Security Analysis and Portfolio Management”. Any student interested on the topic of “Investment” is well advised to refer to any standard textbook on SAPM. Punjab Technical University, Online Virtual Campus

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Chapter: 3 – Risk and Return should be mentioned that the complicated calculation is worth the time invested in, as the ultimate result is reduction in the total risk of the portfolio. This is the very objective of a portfolio.

Kinds of risk – diversifiable and non-diversifiable Diversifiable or non-systemic risks We have learnt that a portfolio aims at minimising the risk and optimising the returns. We have also learnt that any portfolio chooses the constituent stocks based on certain parameters and one of the important parameters is the correlation among the various stocks. We have also seen that a portfolio diversifies the risk by choosing stocks of: Different sectors, different units in the same sector, different maturities and different instruments including money market. Are there different kinds of risk associated with securities? Yes. Diversifiable and non-diversifiable risks. By choosing different sectors etc. we are diversifying the risks. This means that sector specific or industry specific or instrument specific or maturity specific risks are diversifiable. Let us explain this through examples. Your portfolio could contain stocks of Cement, Textiles, Software and Pharmaceuticals. This is called sector diversification. You will choose such sectors as are not having perfect correlation. Your portfolio could contain stocks of ACC, Larsen & Toubro and Dalmia Cements. This is called unit diversification in the same sector. You will choose again such units as are not having perfect correlation. Your portfolio could contain one-year investment (bond or debenture), more than one-year investment and longterm investment too. This is called maturity diversification. Here the relationship will rarely be perfect. Your portfolio could contain investment into equity shares, debt instruments and money market instruments. This is called instruments diversification. Here too the relationship will not be perfect as these relate to different segments of the Financial Markets. All the above are examples of diversifiable risks. One can use detailed analytical study of the past trends and knowledge about the various sectors and specific units for true diversification of stocks in a portfolio. Such diversifiable risks are often referred to as “non-systemic risks” or “specific risks” as such risks are not thrown in by the system.

Non-diversifiable or systemic risks Suppose we do all the above and arrive at a very good portfolio. The US and their allies decide to bomb IRAQ. All hell breaks loose. All the markets internationally are nervous. Can you and I do something about it besides feeling helpless about the whole thing? Such kind of risks could be specific to a country or economy or universal in its impact. The universality of market risks depends upon the degree of integration of different countries into the global system. The more they are integrated the higher will be the degree of uniformity of impact due to US bombing IRAQ. We cannot diversify this kind of risk at least within a country or system, although global investors are in a better position to diversify the country specific risk by pulling out of the country and reinvesting the amount in less risky markets. Typical example of a market risk in India – Sensex crashing from 6000 odd points in early 2000 to less than 3000 points in 2002. The markets becoming nervous on news of Indo-Pak war is another example.

Total risk of a portfolio = market risk of the portfolio + specific risk of the portfolio Concept of “Beta” and the Capital Asset Pricing Model (CAPM) Before we examine “Beta”, let us examine some fundamental concepts in the context of investment in securities like “risk free” investment, “risk premium”, “market portfolio” etc. Globally investment in Government securities is considered to be “risk free” investment. We may not agree with the statement that they are totally risk-free. In the absence of any better alternative that is 100% risk free, this has been accepted as “risk-free” investment. Suppose the average return from investment in Govt. securities in India say, is 6.5% p.a. Risk-averse investors would be induced to invest in market securities like shares or debentures or bonds only when they get what is known as “risk premium”. Let us assume this to be 6%. This means that the market investment should fetch us 6.5% + 6% = 12.5%. Unless we are sure of this return we will not invest in market securities. Punjab Technical University, Online Virtual Campus

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Chapter: 3 – Risk and Return Is there any readymade portfolio whose return represents the market return? Yes. The BSE sensex represents the market portfolio and the return on this for a given period is the market rate of return. The difference between this market rate of return (12.5%) and risk free rate (6.5%) represents the market premium (6%). Is BSE sensex the only portfolio? No. NSE’s 50 stock index is another one. However let us bear in mind that BSE sensex or NIFTY FIFTY does not include any debt instrument like debenture or bond or short-term money market instruments. Hence the parameter of market premium as applicable to BSE sensex etc. relates only to investment in equity shares.

What is “Beta” of a stock? We have learnt that the risk associated with a given stock can be measured either by standard deviation or the coefficient of variation. We have also learnt that the parameter of co-efficient of variation includes the scale of expected return unlike the standard deviation and hence is more comprehensive as a measure of risk. Let us extend whatever we have learnt to comparison of co-efficient of variation in returns of a given stock with the co-efficient of variation in returns of market portfolio during the same time. This comparison is called “Beta”. We examine the following example. Our investment in Reliance Industries Limited (RIL) has the co-efficient of variation as 10% for a given period of 6 months. Let us say that during the same period the co-efficient of variation of BSE sensex is 15%. Then the Beta for RIL stock is = 10%/15%. This gives us a number of 0.667. Thus “Beta” is the relationship between the co-efficient of variation of selected stock to the co-efficient of variation of market portfolio. At times students are confused with this concept and mistakenly identify as the relationship between the returns of selected stock and market portfolio. This is not the correct definition of “Beta”– please note.

Example no. 3 Let us say that the risk-free rate is 6.5% as assumed in the above paragraphs. Let us say that the market premium is also 6% as assumed before. The Beta of a given stock is 1.2. Then the expected rate of return from this stock is = R j = Risk free rate + (Beta of selected stock x market premium) = 6.5% + 6% x 1.2 = 13.7%. This means that the expected rate of return from selected stock is 13.7%. This equation is the famous equation called “Capital Asset Pricing Model (CAPM)” The higher the Beta, the higher the risk and the higher the risk premium in comparison with the market premium and vice-versa. In the preceding paragraph we saw that the Beta for RIL is less than 1. What does it mean? The risk associated with RIL stock is less than the risk associated with market portfolio. It is safer. Beta is a true measure of the relative volatility of the return of a given stock in comparison with the volatility of return of market portfolio.

Is Beta different from co-efficient of variation in the way in which it is determined? Yes. This exercise does consider not only the probability distribution of returns for a given stock but also the actual changes in the return due to movement of market price of the stock for a given period. The data 4 collected for a given period are subject to “regression analysis” for determining the Beta for a given stock. The students are well advised to attempt the numerical exercises given at the end of the chapter to familiarise themselves with this concept.

Please reproduce here graph as shown in the photocopy attached

Some concerns about Beta and CAPM 4

Datum is singular and data is a plural of datum. Hence data and are should be used and not data and is.

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Chapter: 3 – Risk and Return The CAPM model as detailed above is very useful without any doubt. However this has certain limitations. One of the most important limitations is that most of the times the trend in the past based on which Beta is determined may not influence the returns of the future. There could be other factors happening only in the future that could alter the rate of return expectation in a given stock either by reducing or increasing the risk associated with it. As a result of this, stocks’ Betas most of the times do not have any relationship with the returns in future. There have been successful attempts to overcome this constraint in the CAPM model and it is beyond the scope of this book to discuss these attempts. However before closing this point, it will be relevant to mention that two distinguished factors influence the market return of a selected stock. They are: The firm’s size – the smaller the size the higher the returns and Market value to book value ratio – the lower the ratio the higher the returns Let us conclude this topic by giving a formula for book value of equity share: Book value of equity share = Paid up capital + Reserves and Surplus Number of equity shares issued

Questions for reinforcement of learning and numerical exercises for practice 1.

How do you measure the risk associated with an investment in capital market?

2.

What are the components of return in the case of investment in a debt instrument like debenture or bond? Try to find out from general reading and answer this question.

3.

What are the components of return in the case of investment in equity shares? Suppose the market price of a given stock is very high then what will be practically the return on investment in such stocks?

4.

Explain the difference between standard deviation and co-efficient of variation with an example and which is more reliable?

5.

Can you name the various market portfolios besides the ones mentioned in the chapter?

6.

What are the sources of information on Beta, risk free rate and market premium? Find them out yourself.

7.

Beta measures the relationship between the return from a given stock with the return from market portfolio – Do you agree with the statement and if not explain the reasons with an example.

8.

Discuss the limitations of CAPM with an example.

9.

Find out the Betas for the following stocks along with market premium and risk-free rates and determine your expected rates of return from these stocks. Please explore the “Financial Dailies” and the “Financial Magazines” for getting the data for this. ACC Bombay Dyeing Indian Hotels Lupin Laboratories TISCO Ashok Leyland Infosys Wipro

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