Chapter 5 Analysis of Risk and Return

1. Finance 311 1 Chapter 5Analysis of Risk and Return

2. Finance 311 2 Introduction This chapter develops the risk-return relationship for individual projects (investments) and a portfolio of projects.

3. Finance 311 3 RETURN - TERMINOLOGY Ex-Ante Returns Ex-Post Returns HPRs - covered previously Please annualize your returns You should consider compounding If a stock grew from $10 to $20 over 5 years, we do not say it grew by 100%

4. Finance 311 4 Expected Return  Given Probability Distribution 

5. Finance 311 5 Required return = Risk-free rate of return + Risk premium Risk-free rate (rf) = 1. Real rate of return + 2. Expected inflation premium Decreases in inflation rates normally leads to decreases in the required rate of return for all securities. The reverse is also true.

6. Finance 311 6 Expected Return A weighted average of the individual possible returns The symbol for expected return, r, is called �r hat.� r = Sum (all possible returns ? their probability)

7. Finance 311 7 Risk Premium Maturity risk premium Consider the Yield Curve (Slide # 13) and theories of the Term Structure of Interest Rates Default risk premium Seniority risk premium Marketability and liquidity risk premium

8. Finance 311 8 Risk Premium - Continued Business risk Variability of the firm�s operating earnings over time Financial risk Additional variability in a company�s earnings per share caused by the use of fixed-cost sources of funds, such as debt and preferred stock (�OPM�)

9. Finance 311 9 Risk and Return Risk refers to the potential variability of returns from a project or portfolio of projects Returns are cash flows Risk free returns are known with certainty For instance, US Treasury Securities

10. Finance 311 10 Risk-Return Relationship Required return = Risk-free return + Risk premium Real rate of return Risk-free rate Expected inflation premium

11. Finance 311 11 U.S. Treasury I Bonds The I Bond earnings rate is a combination of two separate rates: Fixed Rate of return A semiannual inflation rate based on the CPI-U For May 1, 2005 � October 30, 2005 Fixed Rate = 1.20% Inflation Rate = 1.79% Composite Rate = 4.80% http://publicdebt.treas.gov/sav/sbirate2.htm

12. Finance 311 12 Expected Inflation Premium Compensates investors for the loss of purchasing power due to inflation

13. Finance 311 13 Yield Curve � June 4, 2005, Source: Bloomberg

14. Finance 311 14 Explaining the Term Structure of Interest Rates Expectations theory Geometric Average of current and expected future short-term rates Liquidity Premium theory Liquidity Preference Market Segmentation theory Preferred Habitat Theory

15. Finance 311 15 MEASURING RISK Risk refers to the potential variability of returns from a project or portfolio of projects The possibility that actual cash flows (returns) will be different from forecasted cash flows Risk free returns are known with certainty US Treasury Securities

16. Finance 311 16 MEASURING RISK - Continued We can look at risk in two different ways In terms of an individual security In terms of a portfolio of securities One common way to measure total risk is to look at the variability of return by computing the standard deviation of the returns. Then calculate the Coefficient of Variation. Risk is typically an increasing function of time.

17. Finance 311 17 Standard Deviation Ex-Ante Data(probability distribution) Risk may be defined using some probability concepts.

18. Finance 311 18 Standard Deviation EX-Post Data or Equal Probability

19. Finance 311 19 More on the Standard Deviation The larger the standard deviation the larger the risk Standard Deviation is an absolute measure of risk Z score measures the # of standard deviations a particular return r is from the expected value r if the outcomes are normally distributed.

20. Finance 311 20 Coefficient of Variation Coefficient of variation v is a relative measure of risk Calculated by dividing the standard deviation by the mean or expected return It is better to use coefficient of variation to measure total risk when comparing investments of different sizes

21. Finance 311 21 Calculating the Z Score Z score = What�s the probability of a loss on an investment with an expected return of 20 percent and a standard deviation of 17 percent? (0% � 20%)/17% = �1.18 rounded From Table V (page 762 of your text) = 0.1190 or 11.90 percent probability of a loss

22. Finance 311 22 Diversification It has been shown that by constructing a portfolio of approximately 15-20 common stocks, unsystematic (diversifiable) risk can be virtually eliminated. (Some studies have shown as few as 10 randomly selected stocks will do it.)

23. Finance 311 23 Diversification Portfolio effect is the risk reduction accompanying diversification

24. Finance 311 24 Mathematics of Portfolios  Portfolio Returns = weighted average of the returns of the individual stocks in the portfolio. For a two stock portfolio:

25. Finance 311 25 Mathematics of Portfolios -- continued. The risk or standard deviation of a portfolio is more complicated. It depends on the standard deviation of the individual stocks, the amount invested in the stocks or weights, and the correlation between returns of the individual stocks. The portfolio effect is the risk reduction accompanying diversification.

26. Finance 311 26 Mathematics of Portfolios -- continued. For a two stock portfolio:

27. Finance 311 27 Correlation and Risk Reduction If the securities are perfectly positively correlated, there is no reduction in risk from forming a portfolio. When the correlation between returns is less than +1.0, there are risk reduction benefits. Diversification can reduce the risk of the portfolio below the weighted average of the total risk of the individual securities. The maximum risk reduction is achieved when the returns on two securities move exactly opposite each other so their correlation is -1.0.

28. Finance 311 28 Characteristics of Securities Comprising a Portfolio Expected Return (r) Standard Deviation (sp) Correlation Coefficient (?) Learning Object Efficient Portfolio Efficient Frontier

29. Finance 311 29 Efficient Portfolio Has the highest possible return for a given ? Has the lowest possible ? for a given expected return

30. Finance 311 30 Capital Market Line (CML) The capital market line is a straight line starting at the risk-free rate and tangent to the efficient frontier. The efficient frontier is the set of risk-return choices associated with efficient portfolios.

31. Finance 311 31 Capital Asset Pricing Model (CAPM) An important theory about how assets are priced developed in the late 1960s and early 1970s Based upon portfolio mathematics and the relationship between diversification and risk From the CAPM came the security market line (SML) which gives us a theoretical relationship between risk and return.

32. Finance 311 32 Total Risk (Which we measure with the standard deviation (s)) can be divided into two components 1. Systematic Risk (also called undiversifiable or market risk) 2.Unsystematic Risk (also called diversifiable or company-specific risk)

33. Finance 311 33 Systematic risk caused by factors affecting the market as a whole: interest rate changes changes in purchasing power change in business outlook terrorist attacks Unsystematic risk caused by factors unique to a firm or industry: foreign competition government regulations management�s capabilities strikes

34. Finance 311 34 Since by diversifying an investor can eliminate unsystematic risk, we need to be able to measure the amount of systematic risk in a portfolioSystematic Risk is Measured by Beta (�)

35. Finance 311 35 Systematic Risk is Measured by Beta � ? A measure of the volatility of a security�s return compared to the Market Portfolio

36. Finance 311 36 Beta as a Measure of Risk Standardized measure of how the returns on an individual stock move with the �market� Calculating a stock�s beta: Regress time series of stock returns versus time series of market proxy returns Characteristic line is: kj = a + rm

37. Finance 311 37 More on Betas Beta = 1 has average risk. Risk equal to that of the market. B>1 more than average risk. B<1 less than average risk. Betas for many stocks are available from the Bridge System in the Trading Room, publications (e.g. Value Line) or on web sites Beta of a portfolio is a weighted average of the beta�s of the stocks in the portfolio

38. Finance 311 38 Important Points to Remember About Risk Measurement The standard deviation(s) and coefficient of variation are measures of total risk. Beta is a measure of systematic risk. An investor can construct a diversified portfolio by holding approximately 15-20 randomly selected stocks. A diversified portfolio is one where the diversifiable or unsystematic risk has been virtually eliminated.

39. Finance 311 39 Important Points to Remember About Risk Measurement -continued For an investor that holds a diversified portfolio thinking about adding a stock to their portfolio, which measure of risk should they consider? For an investor that holds only two stocks thinking about adding a stock to their portfolio, which measure of risk should they consider?

40. Finance 311 40 SML shows the relationship between r and � r rf

41. Finance 311 41 Beta � = Systematic risk Required rate of return k j = rf + � j ( rm - rf )

42. Finance 311 42 Beta

43. Finance 311 43 Required rate of return The required return for any security j may be defined in terms of systematic risk, �j , the expected market return, rm, and the expected risk free rate, rf

44. Finance 311 44 Risk Premium ( rm - rf ) = Market Risk Premium Slope of Security Market Line Will increase or decrease with uncertainties about the future economic and political outlook with the degree of risk aversion of investors

45. 45 SML is used to find a required rate of return. In equilibrium (an efficient market), the required rate of return = the expected rate of return.

46. Finance 311 46 CAPM Assumptions Investors hold well diversified portfolios Competitive markets Borrow and lend at the risk-free rate Investors are risk averse No taxes Investors are influenced by systematic risk Freely available information No brokerage charges Investors have homogeneous expectations

47. Finance 311 47 Major Problems in the Practical Application of the CAPM Estimating expected future market returns Determining an appropriate rf Determining the best estimate of future � Investors don�t totally ignore unsystematic risk Betas are frequently unstable over time Required returns are determined by macroeconomic factors such as inflation and interest rates

48. Finance 311 48 International Investing Appears to offer diversification benefits Returns from DMC�s tend to have high positive correlations Returns from MNC�s tend to have lower correlations Obtain the benefits of international diversification by investing in MNC�s or DMC�s operating in other countries

49. Finance 311 49 Risk of Failure is Not Necessarily Captured by Risk Measures Risk of failure especially relevant for undiversified investors Costs of bankruptcy Loss of funds when assets are sold at distressed prices Legal fees and selling costs incurred Opportunity costs of funds unavailable to investors during bankruptcy proceedings

50. Finance 311 50 High-Yield or High-Risk Securities Oftentimes called �Junk Bonds� Bonds with credit ratings below investment grade (BA or below) securities May be a �Fallen Angel� Have high returns relative to the returns available from investment grade securities Higher returns achieved only by assuming greater risk Ethical Issues � Next Slide

51. Finance 311 51 Ethical Issues High Risk Securities Savings and loan industry Insurance industry Executive Life Company Practices ENRON Health South World Com � MCI Adelphia Communications TYCO

52. Finance 311 52 Conclusion Risk vs. Return Yield Curve Systematic Risk Unsystematic Risk Efficient Portfolio Beta (�) Capital Asset Pricing Model Security Market Line