1. Slide 1 Risk and Rates of Return Remembering axioms Inflation and rates of return How to measure risk (variance, standard deviation, beta) How to reduce risk (diversification) How to price risk (security market line, CAPM)

2. Slide 2 Ten Axioms of Financial Management Risk-Return Tradeoff Save and invest for future consumption Investments should provide appropriate compensation for forgone consumption

3. Slide 3 Ten Axioms of Financial Management 90% Large-company stocks13.3%20.1 Small-company stocks17.633.6 Long-term corporate bonds5.98.7 Long-term government5.59.3 Intermediate-term government5.45.8 U.S. Treasury bills3.83.2 Inflation3.24.5 -90% 0% Series Average Return Standard Deviation Distribution

4. Slide 4 Interest Rates The real, risk-free rate is the rate which would exist on default-free (and free of other risks) obligations in an inflation-free environment (k*) Most economists believe that the real rate of interest is approximately one to three percent The Fisher equation indicates that the nominal rate of interest (k rf ) includes a component for inflation risk premium (IRP)

5. Slide 5 Interest Rates (Continued) Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation rate premium? (1.08) = (1.03) (1 + IRP) (1 + IRP) = (1.0485), so IRP = 4.85%

6. Slide 6 Term Structure of Interest Rates The pattern of rates of return for debt securities that differ only in the length of time to maturity

7. Slide 7 Term Structure of Interest Rates (Continued)

8. Slide 8 Term Structure of Interest Rates (Continued) http://www.smartmoney.com/onebond/index.cfm?story=yieldcurve http://www.stockcharts.com/charts/YieldCurve.html

9. Slide 9 Term Structure of Interest Rates (Continued) Expected Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc Required Return - the return that an investor requires on an asset given its risk and market interest rates

10. Slide 10 Treasury Securities Required Return The required return on Treasury securities is equal to risk-free rate of return Since Treasuries are essentially free of default risk, the rate of return on a Treasury security is considered the “risk-free” rate of return

11. Slide 11 Required Return on Risky Investments Required return on risky investments should take into account what investors can earn on riskless investments and the risk premium for the risky investment The problem is to determine how large of a risk premium we should require to buy a corporate security

12. Slide 12 Expected Return For each firm, the expected return on the stock is Return State of EconomyProbability (P)UtilityTech Recession0.204.00%-10.00% Normal0.5010.00%14.00% Boom0.3014.00%30.00%

13. Slide 13 Expected Return (Continued) For each firm, the expected return on the stock is Return State of EconomyProbability (P)UtilityTech Recession0.204.00%-10.00% Normal0.5010.00%14.00% Boom0.3014.00%30.00%

14. Slide 14 What is RISK? Based only on your expected return calculations, which stock would you prefer? Have you considered the RISK? The possibility that an actual return will differ from our expected return Uncertainty in the distribution of possible outcomes

15. Slide 15 How do we Measure Risk? A scientific approach is to examine the stock’s standard deviation of returns Standard deviation is a measure of the dispersion of possible outcomes The greater the standard deviation, the greater the uncertainty, and therefore, the greater the risk

16. Slide 16 Standard Deviation (Utility) ( 4% - 10%) 2 (0.20)= 7.2% (10% - 10%) 2 (0.50)= 0% (14% - 10%) 2 (0.30)= 4.8% Variance (Sum)= 12.0% Standard Deviation= Square Root of Variance (12.0%) = 3.46%

17. Slide 17 Standard Deviation (Tech) (-10% - 14%) 2 (0.20)= 115.2% ( 14% - 14%) 2 (0.50)= 0% ( 30% - 14%) 2 (0.30)= 76.8% Variance (Sum)= 192.0% Standard Deviation= Square Root of Variance (192.0%) = 13.86%

18. Slide 18 Which Stock Would You Prefer UtilityTech Expected Return10.00%14.00% Standard Deviation3.46%13.86% It depends on your tolerance for risk! Remember, there’s a tradeoff between risk and return

19. Slide 19 Portfolios Combining several securities in a portfolio can actually reduce overall risk How does this work? rate of return time kpkp kAkA kBkB

20. Slide 20 Diversification Investing in more than one security to reduce risk If two stocks are perfectly positively correlated, diversification has no effect on risk If two stocks are perfectly negatively correlated, the portfolio is perfectly diversified If you owned a share of every stock traded on the NYSE and NASDAQ, would you be diversified? – YES! Would you have eliminated all of your risk? – NO! Common stock portfolios still have risk

21. Slide 21 Types of Risk Market risk (systematic risk) is non-diversifiable. This type of risk cannot be diversified away Unexpected changes in interest rates Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle

22. Slide 22 Types of Risk Company-unique risk (unsystematic risk) is diversifiable. This type of risk can be reduced through diversification A company’s labor force goes on strike A company’s top management dies in a plane crash A huge oil tank bursts and floods a company’s production area

23. Slide 23 As you add stocks to your portfolio, company- unique risk is reduced

24. Slide 24 Do some firms have more market risk than others? Yes. For example: Interest rate changes affect all firms, but which would be more affected: Retail food chain Commercial bank As we know, the market compensates investors for accepting risk - but only for market risk. Company-unique risk can and should be diversified away So - we need to be able to measure market risk

25. Slide 25 This is why we have Beta Beta: a measure of market risk Specifically, beta is a measure of how an individual stock’s returns vary with market returns It’s a measure of the “sensitivity” of an individual stock’s returns to changes in the market

26. Slide 26 -5 -15 5 10 15 -15 -10 -5 5 10 15 XYZ Co. returns S&P 500 returns............. Calculating Beta Beta = slope = 1.20

27. Slide 27 The Market’s Beta is 1 A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market A firm with a beta > 1 is more volatile than the market (ex: technology firms) A firm with a beta < 1 is less volatile than the market (ex: utilities)

28. Slide 28 Summary We know how to measure risk, using standard deviation for overall risk and beta for market risk We know how to reduce overall risk to only market risk through diversification We need to know how to price risk so we will know how much extra return we should require for accepting extra risk

29. Slide 29 What is the Required Return? The return on an investment required by an investor given market interest rates and the investment’s risk. Required Return = Risk-free rate of return + Risk premium Risk premium is the compensation for holding the market risk Compensation per amount of market risk is the market risk premium or (k m – k rf ) Depending on the amount of market risk (Beta) some firms will have greater required return

30. Slide 30 What is the Required Return? (Continued) This linear relationship between risk and required return is known as the Capital Asset Pricing Model (CAPM)

31. Slide 31 k rf kmkm mm Security Market Line Note that the slope of SML is the market risk premium or (k m – k rf ) Security Market Line (SML)

32. Slide 32 Example Suppose the Treasury bond rate is 6%, the average return on the S&P 500 index is 12%, and Walt Disney has a beta of 1.2 According to the CAPM, what should be the required rate of return on Disney stock? k DIS = 0.06 + 1.2 (0.12 - 0.06) k DIS = 0.132 = 13.2% According to the CAPM, Disney stock should be priced to give a 13.2% return

33. Slide 33 SLM and Fair Pricing Theoretically, every security should lie on the SML If every stock is on the SML, investors are being fully compensated for risk If a security is above the SML, it is underpriced If a security is below the SML, it is overpriced

34. Slide 34 Return Calculations tt+1 $50$60