RISK AND RETURNS. Challenges of Risk - creates anxiety - discourages investment - demands a greater cost, e.g. insurance, indemnity

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1 RISK AND RETURNS A risk is the probability that the outcome of a project may not be as expected. It implies that the project has clear-cut goals, and that information is available, but the future outcomes associated with each alternative are subject to change. Risk is not the same as uncertainty. An Uncertain situation is one in which there is little or no information in the first place, hence the outcome cannot be anticipated or predicted. All business ventures are subject to risk. In fact, risk should not be taken in an entirely negative context. It comes with benefits and challenges. Benefits of Risk - More effective management - More participation in the firm - The greater the risk is the greater the expected returns Challenges of Risk - creates anxiety - discourages investment - demands a greater cost, e.g. insurance, indemnity The extent to which risk may not be tolerated is called an aversion to risk. The risk taker or risk seeker will accept a highly risky investment. The risk averse investor will try to avoid or minimize the risk in the investment TYPES OF RISK Risk exists at all levels of the project and may be classified as 1 Physical Risks : those associated with carrying out of the activities in the firm. e.g. damages, malfunctioning equipment, earthquake, fire, flooding, drought, etc 2. Economic Risk : changes in the economic outlook due to inflation, government policies, new taxes, 3. Financial Risks : those associated with the investment, eg. changes in interest rates or in the policy of the bank 4. Business Risk : new entrants, increased competition, power of the suppliers, 5. Political Risk : nationalism, governmental sanctions, instability, wars, 6. Operational Risk : accidents, customer care, pilferage, 1

2 These categories of risk can be further summarized into two broad categories : i. firm specific risks : those associated with the business operation. They are called unsystematic risks, and can be controlled by effective management, and by diversification of the firms business portfolio. ii. market risk : these stems from factors that systematically affect all firms, such as government policies, national issues, war, terrorism, economic down turns. These cannot be eliminated by diversification. Illustrating the effectives of diversification on risks : Level Of Risk Company specific or Diversifiable risk Market risk : non-diversifiable & systematic Investment Portfolio PORTFOLIO THEORY One of the firm s best response to risk is to establish an investment portfolio. This is a collection of different portfolio that makes up the investor s total holding. This may be in the form of stocks and shares, or in new capital projects. Firms engaging in group of companies activities are classic examples of portolio. In most cases, one company in the group is critical to the success of another, or losses in one company is covered by the others. 2

3 e.g. Grace Group : agro-chemicals, agro-processing, shipping, financial, insurance, medical, consumables ATL Group : appliances & electronic, travel, hospitality and tourism, communications, RJR Communication Group: Radio 92, RJR 94FM, Fame 95, TVJ, Multimedia Ja., The Voice (UK) Based on the investment portfolio, the firm will have an expected return on the investments. This represents the weighted average expected return of all the investments in the portfolio. ONE ASSET PORTFOLIO In this situation, the firm must make one investment but there are more than one possible outcomes, thus giving rise to a probability of return for each outcome. The expected return on the investment would thus be : Kp = ka*pa + kb*pb + kc * pc Where ka = the returns from outcome A pa = the probability of outcome A occurring, etc e.g. The Lone Ranger is considering an investment as a private investigator. His market research indicate that this investment may either be Outcome Return Probability k p a) a flop 5% 0.2 b) moderately successful 10% 0.5 c) very successful. 20% 0.3 From these possible outcomes, the expected return is : Outcome Return x Probability = Expected Value (k) (p) (k*p) a) a flop 5% moderately successful 10% very successful. 20% Expected Return % 3

4 THE STANDARD DEVIATION Given the possible returns, and the expected return, we could compare the two by calculating the variance and the standard deviation, as follows Possible Expected Difference Square of Probability Product Returns Return (1-2) Difference ( 4 x 5 ) (7) (2) Variance ( sum of the product ) = Q Standard Deviation ( Square root of the variance ) = Q The standard deviation is a measure of risk in the investment The smaller the standard deviation is the less the probability of a variation in the returns, and generally the smaller the risk. Of course, the smaller the risk is the smaller the returns on the investment. Likewise the greater the risk is the greater the expected returns. ( $50,000 stashed away in a shoe box in your closet has virtually no risk. So at the end of the year, there is no return on the sum. The same amount lodged in a bank has just marginally more risk, so the returns at the end of the year is an interest of 10% or 12 %. However, using the entire sum to purchase lottery tickets for the $140 million jackpot has a very high risk of losing everything... ) THE COEFFICIENT OF VARIATION. Another measure of risk is the coefficient of variation. This is derived by Standard deviation Risk = Expected Return Return This represents the measure of risk per unit of return. It provides a more meaningful basis for comparing two or more alternatives, when the expected return on each is not the same as for the other. The greater the coefficient of variation is the greater the risk in the investment. 4

5 TWO ASSETS PORTFOLIO The firm may be contemplating two investments, each with its own probability of return. From this we may calculate the expected return for each investment. Based on the proportion of each investment in the portfolio, the expected return on the portfolio can be derived : Kp = ka * wa + kb * wb Expected return on A x Proportion of A in the portfolio + Expected return on B x Proportion of B in the portfolio = Expected Return on Portfolio of A & B e.g. Gotham City is contemplating two investments, which showed the following expected returns Investment Expected Returns Possible Proportions of Investment Batman 18% 25% 50% 75% Robin 12% 75% 50% 25% Calculate the expected return on the portfolio, given the possible proportions of investment. Option Proportion of Batman x Expected Return on Batman = Expected Return + proportion of Robin x Expected Return on Robin of the Portfolio (0.25 x 18) + ( 0.75 x 12) = (0.50 x 18) + ( 0.50 x 12 ) = ( 0.75 x 18 + ( 0.25 x 12) = Here option 3 offers a better return on the portfolio CORRELATION COEFFICIENT The expected return in one investment generally have a bearing on that of the other investment. The measure of relationship between the one and the other is called the correlation coefficient. 5

6 Derived by applied statistical approach ( which you wont be asked to do! ) the correlation coefficient can range from + 1 to -1. These values are the extreme limits. Relationships may fall anywhere between the one and the other. The relationship established by the correlation coefficient can be interpreted to be a) Positive correlation, +1, which implies that the result of one investment is directly related to the result of the other. If one succeeds the other will succeed at the same proportion. Likewise if one fails, so will the other. E.g. an investment in sale of cellular phones and in phone cards, ceteris paribus. b) No correlation, 0, - the two investments have no perceived bearing on each other. E.g. an investment in cellular phones and in concrete nails c) Negative correlation, -1, where one investment is inversely proportion to the other. Thus, as the one succeeds, the other is likely to fail. E.g. an investment in Rastaman paraphernalia and in a pork shop, ceteris paribus, vice versa. When deriving the standard deviation of a portfolio, we use - the correlation coefficient - the proportion of each investment in the portfolio - the variance of each investment - the standard deviation of each investment Thus the standard deviation of a portfolio is based on the formula : Qp = [ Q 2 a * wa 2 ] + [ Q 2 b * wb 2 ] + [ 2 * wa * wb * Pab * Qa * Qb ] ٧ Where Qp Q 2 a Q 2 b Qa Qb = standard deviation of the portfolio = variance of the returns from investment in A = variance of the returns from investment in B = standard deviation of the returns from investment in A = standard deviation of the return from investment in B wa = the weight or proportion of investment A in the portfolio wb = the weight or proportion of investment B in the portfolio Pab = the correlation coefficient of returns from Investments A & B 6

7 e.g. Given that the investments by Gotham City included the following standard deviations Investment Expected Returns Standard Possible Proportions of Investment Deviation Batman 18% % 50% 75% Robin 12% % 50% 25% Calculate the standard deviation of the portfolio based on each investment option and assuming that there is a correlation coefficient of (a) +1, (b) 0, and (c) -1 SOLUTION COEFFICIENT PORTFOLIO INVESTMENT OPTIONS CORRELATION CAPITAL ASSET PRICING METHOD ( CAPM) The Capital Asset Pricing Method ( CAPM) is another approach to the calculation of risk and return. This is especially useful in a well diversified portfolio, whereby, the level of risk associated with a single investment is significantly minimized when it is held in a portfolio. The CAPM was first formulated for investments in stocks and shares on the market, rather than for companies investment in capital projects. It is based on a comparison of the systematic risk of individual investments and the risk of all shares in the market as a whole. A major assumption is that there is a linear relationship between the return obtained from an individual security and the average return from all securities in the market. The measure of risk under the CAPM involves the beta coefficient. Beta Coefficient is the relationship between the return on the investment and the movements in the market in general. 7

8 There are several approaches to the calculation of beta : i. COV jm PjmQj Q syst B= = = Q 2 m Qm Qm Where COVjm Q 2 m Pjm Q j Qm Q syst = Covariance of security j with the market = Variance of the market = Correlation of security j with the market = Standard deviation of the security j = Standard deviation of the market = Systematic risk of security j Beta values may range from 0.00 to beta value at 0.00 means that there is not relationship between the return on the investment and the return in the market - beta value at 0.50 means that the return on the investment is half as volatile as the return in the market - beta value at 1.00 means that the return on the investment is directly aligned to the return in market - beta value at 2.00 means that the return on the investment is twice as volatile as the return on the market Based on the CAPM, the expected returns on an investment can be derived as : E(rj) = rf + ( Erm - rf ) B Where E(rj) = the expected returns on an individual security rf = the risk free rate of return Erm = the expected return in the market B = the beta coefficient 8

9 e.g. the risk free rate of return is 9% and the expected market return is 13%. If the shares in the Prudent Company have a beta of 1.5 what is the expected return on these shares? E(rj ) = rf + ( Erm rj ) B = 9 + ( 13-9 ) 1.5 = 15% If the market returns fall by 3%, then the expected return on the company s shares would fall by 3 x 1.5 = 4.5, to 10.5 Hence E(rj) = 9 + ( 10 9 )1.5 = 10.5% DETERMINANTS OF THE RATES OF RETURN In general, the quoted interest rate on a debt is composed of a real risk free rate of interest, plus several premiums that reflect inflation or increased risk. The real risk free rate would exist on a security with a guaranteed payoff. It can be taken to be the interest rate on a government treasury bill. The quoted interest rate is thus derived by the formula : k = krf + DRP + LP + MRP where k = the nominal rate of return on a given security krf = the risk free rate of return, generally tied to a government s t-bill DRP = Default risk premium, on the assumption that the issuer will not pay principal or interest on the security on time LP = liquidity premium, charged by some lenders to reflect the fact that some securities cannot be converted to cash at short notice MRP = maturity risk premium, associated with decline in prices over time 9

10 TUTORIAL QUESTIONS 1. Explain the difference between risk and uncertainty 2. Explain the term risk aversion 3. What are systematic and unsystematic risks? 4. An investment in a newspaper business shows the following possible outcomes and returns : Outcomes Probability Returns a) Poor 0.2 8% b) Marginal c) Good d) Excellent Calculate : (1) the expected returns on the investment (2) the standard deviation of the returns (3) the correlation variation 5. An investment portfolio consist of two securities : telecommunications, which account for 80% with an expected returns of 15%; and the remainder in financial services which have an expected returns of 18%. Calculate the expected returns of the portfolio. 6. The Investment Times showed that there are two hot investments available with the following data Mayberry Investments JMMB Expected Returns 25% 20% Standard Deviation 15% 10% The two investments have a correlation coefficient of Calculate the expected returns and the standard deviation of a portfolio comprising a) 25% Mayberry and 75% JMMB b) 50% Mayberry and 50 % JMMB c) 75% Mayberry and 25% JMMB 10

11 7. An investor is reviewing two investments : imported cement and a local dairy farm. The two options showed the following data : Cement Dairy Expected Returns 10% 12% Standard Deviation 2% 4% The investor plans to put 60% in the local dairy business. Calculate the portfolio s expected returns, standard deviation, and coefficient of variation if the two investments have correlation coefficient of a) b) 0 c) Fantom Mojah is contemplating an investment as a dancehall promoter. The following outcomes are predicted from this line of business Outcomes Probability Expected Returns a) A Complete Failure 0.1 (10) % b) Pass the Worse 0.2 5% c) Barely Survive % c) Make it Big Time % Calculate (i) the expected returns (ii) the standard deviation (iii) the coefficient variation 9. Tricia Spence is contemplating two investment options, for which the following data is available Expected Returns Probability RJR s Wild Child 30% % % 0.3 Royal Palm s Neeka 50% % % 0.2 Assuming that there is no correlation between the two investments, calculate a) the expected returns and standard deviation for each investment separately b) the expected returns and standard deviation of a portfolio comprising 60% Wild Child and 40% Neeka 11

12 10. Dervan Malcolm is contemplating two investment options, for which the following data is available Expected Returns Probability Power106 News 30% % % 0.3 Barn Theatre 50% % % 0.2 It is assumed that the two investments have correlation coefficient of , and Dervan Malcolm plans a portfolio that consist of 70% in Power 106 News Required : Calculate the following a. the expected returns on each investment b. the standard deviation for each investment c. the coefficient of variation for each investment d. the expected returns on the portfolio e. the standard deviation of the portfolio 11. The summary of three investments are presented below : Investment Expected Return Standard Deviation Sandals Resorts 18% 20% ATL Motors 20% 20% Air Jamaica Express 20% 18% Discuss the best of the three options 12

13 12. Two investments showed the following data Probability Returns X Y 0.1 (10%) (35%) a) calculate the expected returns on X and Y b) calculate the standard deviation and the coefficient of variation for X and Y c) comment on the results. Which option would you chose as an investor? 13. Carberra Investments has a standard deviation of 8% and a correlation of 0.6 in relations to the market. The returns on the market is 13% with a standard deviation of 9%. Given that the risk free rate of return is 7%, use the CAPM to calculate ( a) the beta and (b) the returns on the Carberra Investments 14. Given the following : krf = 8%, km = 11%, and ka = 14% a) Calculate investment A s beta b) If Investment A s beta was 1.5 what would be A s new required rate of interest? 15. Given the following : krf = 9%, km = 14%, and beta x = 1.3 a) What is the required rate of return on Investment X? b) If the krf was to (i) increase to 10% or (ii) decrease to 8%, what would be the impact on the required rate of return on Investment X? c) if the krf did not change, but the km was to (i) increase to 16%, or (ii) decrease to 13%, what would be the impact on the required rate of return on Investment X? 13

Lecture 8 & 9 Risk & Rates of Return

Lecture 8 & 9 Risk & Rates of Return We start from the basic premise that investors LIKE return and DISLIKE risk. Therefore, people will invest in risky assets only if they expect to receive higher returns.