1. copyright © 2003 McGraw Hill Ryerson Limited 9-1 prepared by: Carol Edwards BA, MBA, CFA Instructor, Finance British Columbia Institute of Technology Fundamentals of Corporate Finance Second Canadian Edition

2. copyright © 2003 McGraw Hill Ryerson Limited 9-2 Chapter 9 Introduction to Risk, Return and the Opportunity Cost of Capital Chapter Outline  Rates of Return: A Review  Seventy-five Years of Capital Market History  Measuring Risk  Risk and Diversification  Thinking about Risk

3. copyright © 2003 McGraw Hill Ryerson Limited 9-3 Rates of Return: A Review Measuring Rate of Return  The returns on an investment come in two forms: Income (dividend or interest payments). Capital gains (or losses).  You have learned two ways to measure the total rate of return on an investment: Percentage Return = Dividend Yield+Capital Gain(%) Percentage Return = Dividend + Capital Gain Share Price

4. copyright © 2003 McGraw Hill Ryerson Limited 9-4 75 Years of Capital Market History Can the past tell us about the future?  By looking at the history of security returns, you can get some idea of the return that investors might reasonably expect from various types of securities.  You could look at individual securities. But there are thousands of such investments!  Thus financial analysts tend to rely on market indexes to summarize the return on different classes of securities.

5. copyright © 2003 McGraw Hill Ryerson Limited 9-5 75 Years of Capital Market History Can the past tell us about the future?  There are many kinds of market indexes you could study.  In this chapter, you will look at the historical performance of the following portfolios: A portfolio of 91 day government securities, known as Treasury bills (t-bills). A portfolio of long-term Canadian government bonds. A portfolio of common shares of large companies.

6. copyright © 2003 McGraw Hill Ryerson Limited 9-6 75 Years of Capital Market History Can the past tell us about the future?  These portfolios are not equally risky.  The t-bill portfolio is a safe holding. You are sure to get your money back from the government. Because of its short maturity, the price of the t-bill portfolio is quite stable and predictable.  The common stock portfolio is the riskiest of the three types of portfolios. There is no promise you will get your money back. The portfolio’s price is uncertain and not easily predicted.

7. copyright © 2003 McGraw Hill Ryerson Limited 9-7 75 Years of Capital Market History Can the past tell us about the future?  The portfolio of long-term bonds falls between the t-bill portfolio and the common stock one in its level of risk. You are certain to get your money back at maturity. However, the price of the holdings before maturity will be uncertain and not easily predicted.  The price of the bond holdings will fluctuate in response to interest rate changes.  When rates fall, bond prices rise, and vice versa.

8. copyright © 2003 McGraw Hill Ryerson Limited 9-8 75 Years of Capital Market History Can the past tell us about the future?  Look at Figure 9.1 on page 276 and you can see how much a $1 investment made in 1926 would have grown to by the end of 2000. You should see that the performance of the portfolios fits our risk ranking:  Common stocks were the most risky and also offered the greatest gains.  T-bills had the lowest risk and the lowest return.  Long-term bonds provided a return between the returns of t-bills and common stocks.

9. copyright © 2003 McGraw Hill Ryerson Limited 9-9 75 Years of Capital Market History Can the past tell us about the future?  We can summarize the average rates of return for each of the investment classes for the period 1926 – 2000 as follows: * Avg. Risk Premium = The extra return as versus a t-bill Average AnnualAverage PortfolioRate of ReturnRisk Premium* Treasury Bills4.8% - Gov’t Bonds6.4% 1.6%capitals Common Stocks11.8%7.0%capitals

10. copyright © 2003 McGraw Hill Ryerson Limited 9-10 75 Years of Capital Market History Can the past tell us about the future?  Common stock and government bonds both had a higher rate of return than t-bills. On average, investors demanded 7% more on a common stock portfolio than they did on t-bill portfolio. They demanded 1.6% more on a bond portfolio.  This excess return, over and above the risk free rate, is called the risk premium. It is the compensation investors demand for taking on extra risk.

11. copyright © 2003 McGraw Hill Ryerson Limited 9-11 75 Years of Capital Market History Can the past tell us about the future?  The historical record shows that investors have received a risk premium for holding risky assets.  They also show a relationship between risk and return: Average returns on high risk assets exceed those on low risk assets.  In summary: Rate of Return = Interest Rate + Market Risk on Any Security on T-bills Premium

12. copyright © 2003 McGraw Hill Ryerson Limited 9-12 75 Years of Capital Market History Estimating Today’s Cost of Capital  You learned in Chapter 6 that a project should be discounted at the opportunity cost of capital.  Measuring the cost of capital is easy if the project is riskless: Any project which is risk free should have a rate of return which matches the rate of interest on a t-bill, which is also risk free.  But what is the cost of capital on a project which is not risk free?

13. copyright © 2003 McGraw Hill Ryerson Limited 9-13 75 Years of Capital Market History Estimating Today’s Cost of Capital  Suppose you found an investment with a risk which exactly matched the risk on a market portfolio of common stocks. Instead of investing in your project, the shareholders could invest in a portfolio of common stocks. Thus the project’s opportunity cost of capital would be the market rate of return.  This is what the investors are giving up by investing in your project.

14. copyright © 2003 McGraw Hill Ryerson Limited 9-14 75 Years of Capital Market History Estimating Today’s Cost of Capital  Key Question: What is the market rate of return?  We could use the historical average rate of return. From Slide #9, we know this rate to be 11.8%.  Do you think this would be a good solution to our question?

15. copyright © 2003 McGraw Hill Ryerson Limited 9-15 75 Years of Capital Market History Estimating Today’s Cost of Capital  Using the average rate of 11.8% would not be a good solution: You know from the historical record that the rate of return on the market varies quite dramatically from year to year. Thus 11.8% would not be a good indicator of the market rate of return for this moment in time. Investors right now may want 11.8%, or more than 11.8%, or less than 11.8% on the market portfolio.  Can you see another solution?

16. copyright © 2003 McGraw Hill Ryerson Limited 9-16 75 Years of Capital Market History Estimating Today’s Cost of Capital  Historically, investors have demanded a 7% risk premium over the t-bill rate to hold common stocks.  So a better procedure for estimating the market rate of return would be to take the current interest rate on t-bills and add the normal risk premium of 7%: Expected = Interest Rate + Normal Risk Market Return on T-bills Premium

17. copyright © 2003 McGraw Hill Ryerson Limited 9-17 75 Years of Capital Market History Estimating Today’s Cost of Capital  You now know how to estimate the opportunity cost of capital for: A risk-free project … use the t-bill rate. A project with market risk (an “average risk” project) … use the rate of return on a market portfolio.  But, how should you handle a project that does not fit either of these two categories?

18. copyright © 2003 McGraw Hill Ryerson Limited 9-18 75 Years of Capital Market History Estimating Today’s Cost of Capital  You do know that the opportunity cost of an investment should reflect its risk.  Therefore, it is essential for you to understand how the risk of a project is measured.  Understanding this concept will allow you to understand how to estimate the required rate of return on a project.

19. copyright © 2003 McGraw Hill Ryerson Limited 9-19 Measuring Risk Variance and Standard Deviation  Which of the following two investments is riskier? Investment A has an average annual return of 8%, with a range of  2%.  Returns vary from 6% to 10% in any particular year. Investment B also has an average annual return of 8%, but with a range of  12%.  Returns vary from –4% to 20% in any particular year.

20. copyright © 2003 McGraw Hill Ryerson Limited 9-20 Measuring Risk Variance and Standard Deviation  You should recognize immediately that B is the riskier investment. There is much greater uncertainty about the possible outcome on Investment B.  Thus, intuitively, you know that risk depends on the dispersion or spread of the possible outcomes. The greater the dispersion, the greater the risk.  The critical question is: How do you measure the amount of dispersion?

21. copyright © 2003 McGraw Hill Ryerson Limited 9-21 Measuring Risk Variance and Standard Deviation  In financial analysis, we have two measures of risk on an investment: Variance  The average value of squared deviations from the the mean. Standard Deviation  The square root of the variance.  Both standard deviation and variance are measures of volatility of return.

22. copyright © 2003 McGraw Hill Ryerson Limited 9-22 Measuring Risk Standard Deviation for Various Securities  We can now add a column to the average rates of return for each of the investment classes for the period 1926 – 2000 : Average Annual Average Standard PortfolioRate of Return Risk Premium Deviation Treasury Bills4.8%- 4.3% Gov’t Bonds6.4% 1.6%capitals9.2% Common Stocks11.8%7.0%capitals18.6%

23. copyright © 2003 McGraw Hill Ryerson Limited 9-23 Measuring Risk Standard Deviation for Various Securities  You should see the risk-return trade-off: T-bills have the lowest average rate of return, and the lowest level of volatility.  The standard deviation of a t-bill is only 4.3% Stocks have the highest average rate of return and the highest level of volatility.  The standard deviation for a common stock portfolio is 18.6%. Bonds are in the middle, offering a “mid-level” return with a “mid-level” risk.

24. copyright © 2003 McGraw Hill Ryerson Limited 9-24 Risk and Diversification Diversification  If you look at Table 9.6 on page 286, you will see the standard deviation for some representative Canadian common stocks.  Remember, a market portfolio of Canadian common stocks has a standard deviation of about 19%. Do you see anything peculiar about the list in Table 9.6?

25. copyright © 2003 McGraw Hill Ryerson Limited 9-25 Risk and Diversification Diversification  Do the standard deviations look high to you?  The market portfolio’s standard deviation was about 19%. Yet you will discover that most stocks are substantially more variable than the market portfolio. Only a handful are less variable.  How is it possible for a market portfolio of individual stocks to have less variability than the average variability of its component parts?

26. copyright © 2003 McGraw Hill Ryerson Limited 9-26 Risk and Diversification Diversification  The answer to this question is: “diversification”  You will discover that diversification reduces variability.

27. copyright © 2003 McGraw Hill Ryerson Limited 9-27 Risk and Diversification Diversification  Suppose you are looking at investing in either a gold stock or an auto stock.  You have the following information about the two investments: Rate of Return ScenarioProbability Auto Stock Gold Stock Recession1/3-8.0%20.0% Normal1/3 5.0%3.0% Boom1/318.0%-20.0% Expected Return5.0%1.0% Standard Deviation10.6%16.4%

28. copyright © 2003 McGraw Hill Ryerson Limited 9-28 Risk and Diversification Diversification  You have to ask yourself: Why would anyone buy the gold stock?  It’s significantly more risky than the auto stock, yet it gives a smaller return. The gold stock looks like a lousy investment, by itself.  But, what do you think would happen if you were to put some of the gold stock in a portfolio with the auto stock?

29. copyright © 2003 McGraw Hill Ryerson Limited 9-29 Risk and Diversification Diversification  Let’s say you have $10,000 and decide to put $7,500 in autos and $2,500 in gold. First we need to calculate the expected return on this portfolio for each of the scenarios.  The portfolio return will be the weighted average of the returns on the individual assets. The weight will be equal to the proportion of the portfolio invested in each asset.

30. copyright © 2003 McGraw Hill Ryerson Limited 9-30 Risk and Diversification Diversification  That is for two assets: Portfolio Rate = fraction of portfolio x rate of return of return in 1 st asset on 1 st asset + fraction of portfolio x rate of return in 2 nd asset on 2 nd asset ( )

31. copyright © 2003 McGraw Hill Ryerson Limited 9-31 Risk and Diversification Diversification  Under the recession scenario you would calculate the portfolio rate of return as: Portfolio Rate = fraction of portfolio x rate of return of return in 1 st asset on 1 st asset + fraction of portfolio x rate of return in 2 nd asset on 2 nd asset ( ) = (0.75 x -8%) + (0.25 x 20%) = -1.0%

32. copyright © 2003 McGraw Hill Ryerson Limited 9-32 Risk and Diversification Diversification  Below we see the return table expanded to include the portfolio (75% auto stock and 25% gold): Rate of Return ScenarioProbability Auto Stock Gold Stock Portfolio Recession1/3-8.0%20.0% -1.0% Normal1/3 5.0%3.0%4.5% Boom1/318.0%-20.0%8.5% Expected Return5.0%1.0%4.0% Standard Deviation10.6%16.4%3.9%

33. copyright © 2003 McGraw Hill Ryerson Limited 9-33 Risk and Diversification Diversification  Are you surprised by the results? When you shifted funds from the auto stock to the more volatile gold stock, the variability of the portfolio actually decreased!  In fact, the volatility for the portfolio is much less than the volatility of either stock held separately.  This is the payoff from diversification. The gold stock offsets the swings in performance of the auto stock, reducing the best-case return, but improving the worst case return.

34. copyright © 2003 McGraw Hill Ryerson Limited 9-34 Risk and Diversification Diversification  Thus, addition of the gold stock stabilizes the returns on the portfolio.  Diversification reduces risk in a portfolio because the assets in the portfolio do not move in exact lock step with each other. When one stock is doing poorly, the other is doing well, helping to offset the negative impact on return of the stock with the poorer performance.

35. copyright © 2003 McGraw Hill Ryerson Limited 9-35 Risk and Diversification Diversification  Key Question: Can we quantify how much two assets move in lock step with each other?  Yes! The correlation coefficient is a measure of the degree to which any two variables move together.  Thus, it is a useful concept for understanding how stocks move relative to each other.

36. copyright © 2003 McGraw Hill Ryerson Limited 9-36 Risk and Diversification Correlation Coefficient  The correlation coefficient is always a number between -1 and +1. The closer the correlation coefficient is to either -1 or +1, the stronger the relationship between the two variables.

37. copyright © 2003 McGraw Hill Ryerson Limited 9-37 Risk and Diversification Correlation Coefficient If the correlation coefficient is greater than zero, then the two variables tend to move in the same direction.  They are said to be positively correlated. If it is less than zero, then the two variables tend to move in the opposite direction.  They are said to be negatively correlated. If it equals zero, then a change in one variable tells you nothing about the likely change in the other.  They are said to be uncorrelated.

38. copyright © 2003 McGraw Hill Ryerson Limited 9-38 Risk and Diversification Correlation Coefficient If the correlation coefficient equals 1, then the two variables are perfectly positively correlated.  They will move in lock step with each other. If the it equals -1, then two variables are perfectly negatively correlated.  They will move exactly opposite of each other.

39. copyright © 2003 McGraw Hill Ryerson Limited 9-39 Risk and Diversification Correlation Coefficient  We use the Greek letter “rho” (  ) to represent the correlation coefficient.  The standard deviation of a portfolio with two stocks, x and y, and a correlation between x and y of  xy, is calculated as:  p =  x 2  x + y 2  y + 2xy  xy  x  y 22

40. copyright © 2003 McGraw Hill Ryerson Limited 9-40 Risk and Diversification Correlation Coefficient  If you calculate the standard deviation of a portfolio,  p, you will find the following:  xy = 1  The stocks move in lock step and there is no benefit from diversification. The risk of the portfolio will equal the weighted average of the risk of the stocks.  xy = -1  The stocks move exactly opposite to each other. There is 100% benefit from diversification. It is possible to reduce the risk of the portfolio to zero.

41. copyright © 2003 McGraw Hill Ryerson Limited 9-41 Risk and Diversification Correlation Coefficient  If you calculate the standard deviation of a portfolio,  p, you will find the following: -1 <  xy < 1  There is a benefit from diversification and the standard deviation of a portfolio,  p, will be between zero and the weighted average of the the risk of the stocks.  The closer  xy is to -1, the greater the benefit from diversification, and the lower the risk of the portfolio.

42. copyright © 2003 McGraw Hill Ryerson Limited 9-42 Risk and Diversification Market Risk Versus Unique Risk  You will find that if you are holding only one stock, then you will be exposed to 100% of the risk of that stock’s price changes.  If you hold two stocks with a correlation coefficient less than 1, then the risk of the portfolio can be reduced below the risk of holding either stock by itself.  As you add stocks to the portfolio, the risk steadily falls as in the graph on the next slide.

43. copyright © 2003 McGraw Hill Ryerson Limited 9-43 Risk and Diversification Diversification Reduces Risk 0 2 4 6 8 10 12 14 16 051015202530 Number of Securities Portfolio Standard Deviation Market Risk Unique Risk

44. copyright © 2003 McGraw Hill Ryerson Limited 9-44 Risk and Diversification Market Risk Versus Unique Risk  If you look at the graph, you should note: You cannot eliminate all risk from a portfolio by adding securities.  You get the greatest risk reduction by holding a few securities.  Once you get beyond 15 stocks, adding more stocks does very little to reduce the risk of the portfolio.  There always remains some risk in a portfolio from economy-wide perils that threaten all businesses.

45. copyright © 2003 McGraw Hill Ryerson Limited 9-45 Risk and Diversification Market Risk Versus Unique Risk  The risk which cannot be eliminated from a portfolio regardless of how much you diversify is known as market risk.  The risk which can be avoided by diversifying is known as unique risk. Unique risk exists because of the perils which are peculiar to any one company. If you held less than 15 securities in your portfolio, you should see on the graph that you would be exposed to unique risk. The fewer the securities you hold, the more unique risk you are exposed to.

46. copyright © 2003 McGraw Hill Ryerson Limited 9-46 Risk and Diversification Market Risk Versus Unique Risk  For a reasonably well diversified portfolio, unique risk is not an issue. Unique risk can be diversified away.  The only risk which matters in a well diversified portfolio is __________ market risk market risk.

47. copyright © 2003 McGraw Hill Ryerson Limited 9-47 Risk and Diversification Thinking About Risk  There are 3 messages which you want to take from this chapter: Message1: Some risks look big and dangerous but are really diversifiable.  If a risk is a unique risk, reflecting perils specific to a particular company, investors can avoid that risk by combining it in a diversified portfolio with many other assets or securities.  From an investor’s perspective, unique risk need not be a concern.

48. copyright © 2003 McGraw Hill Ryerson Limited 9-48 Risk and Diversification Thinking About Risk Message2: Market risks are macro risks.  Diversified portfolios are not exposed to the unique risks of individual holdings.  However, they are exposed to uncertain events which affect the entire securities market or the entire economy.  These macro factors include changes in interest rates, industrial production, inflation, exchange rates and energy cost.  When these macro factors are favourable, investors do well and vice versa when they go the other way.

49. copyright © 2003 McGraw Hill Ryerson Limited 9-49 Risk and Diversification Thinking About Risk Message3: Risk can be measured.  We can measure how risky a stock is by comparing its price fluctuations to those of the market as a whole.  This measure will be developed in the next chapter.

50. copyright © 2003 McGraw Hill Ryerson Limited 9-50 Summary of Chapter 9  You can estimate the opportunity cost of capital for a zero risk and an “average risk” project. A project with zero risk should be discounted at the t-bill rate. A project with average risk should be discounted at the return expected on a market portfolio of common stocks.  The market rate of return can be estimated by adding 7% to the t-bill rate.  You can measure the risk, or volatility, of a security by measuring the standard deviation, or variance, of its price over a period of time.

51. copyright © 2003 McGraw Hill Ryerson Limited 9-51 Summary of Chapter 9  Standard deviation and variance are measures of the volatility of a security’s price. The standard deviation on a market portfolio of common stocks has averaged 19% per year.  Diversification reduces risk because stocks do not move in exact lock step, meaning that poor performance by one stock can be offset by strong performance by another.  Risk which can be eliminated by diversification is known as unique risk.

52. copyright © 2003 McGraw Hill Ryerson Limited 9-52 Summary of Chapter 9  Risk which can’t be eliminated by diversification is called market risk. Even a well diversified portfolio can’t eliminate all risk.  When we talk about a risky stock, we are not talking about a stock held in isolation. We mean a stock which makes an above average contribution to the risk of a diversified portfolio. Investors do not have to worry about risk they can diversify away, but they do have to worry about risk that cannot be diversified. This non-diversifiable risk depends on a security’s sensitivity to macroeconomic factors.