CHAPTER 6

1. CHAPTER 6 Risk, Return, and the Capital Asset Pricing Model Omar Al Nasser, Ph.D. FIN 6352

2. Topics in Chapter • Basic return concepts • Basic risk concepts • Stand-alone risk • Portfolio (market) risk • Risk and return: CAPM/SML

3. Determinants of Intrinsic Value: The Cost of Equity Net operating profit after taxes Required investments in operating capital − Free cash flow (FCF) = FCF1 FCF2 FCF∞ Value = + + + ... (1 + WACC)1 (1 + WACC)2 (1 + WACC)∞ Weighted average cost of capital (WACC) Market interest rates Firm’s debt/equity mix Cost of debt Cost of equity Market risk aversion Firm’s business risk

4. What are investment returns? • Investment returns measure the financial results of an investment. • It is the ratio of money gained or lost on an investment relative to the amount of money invested. • Returns can be expressed in: • Dollar terms. • Percentage terms.

5. An investment costs $1,000 and is sold after 1 year for $1,100. Dollar return: $ Amount Received - $ Amount Invested $1,100 - $1,000 = $100. Percentage return: $ Dollar Return/$ Amount Invested $100/$1,000 = 0.10 = 10%.

6. What is investment risk? • Typically, investment returns are known with uncertainty or volatility of returns. • Investment risk relates to the probability of earning a return less than that expected. • The greater the chance of a return far below the expected return, the greater the risk. • The riskiness of an investment can be judged by describing the probability distribution of its possible returns. • An asset’s risk can be analyzed in two ways: • Stand-Alone Risk: The risk an investor would face if he or she held only one asset. • Portfolio Risk: The risk that is related to a portfolio or grouping of assets.

7. Expected Returns • The concept of return provides investors with a convenient way to express the financial performance of the investment. • Expected returns are based on the probabilities of possible outcomes. • The expected rate of return on a single asset is equal to the sum of each possible rate of return, or outcome, multiplied by its probability.

8. Example: Expected Returns • Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns? • State Probability C T • Boom 0.3 0.15 0.25 • Normal 0.5 0.10 0.20 • Recession ??? 0.02 0.01 • RC = .3(.15) + .5(.10) + .2(.02) = .099 = 9.9% • RT = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7%

9. What is the standard deviationof returns for each alternative? σ = Standard deviation σ = √ Variance = √ σ2 = √ n ∑ i=1 • Standard Deviation is a statistical measure of the variability of a set of observations or outcomes. • In finance, standard deviation is a measure of the investment's volatility. The smaller the standard deviation, the less risky is the investment. 9

10. Example: Variance and Standard Deviation • Consider the previous example. What are the variance and standard deviation for each stock? • Stock C • 2 = .3(.15-.099)2 + .5(.1-.099)2 + .2(.02-.099)2 = .002029 •  = .045 • Stock T • 2 = .3(.25-.177)2 + .5(.2-.177)2 + .2(.01-.177)2 = .007441 •  = .0863

11. Another Example • Consider the following information: • State Probability Ret. on ABC, Inc • Boom .25 .15 • Normal .50 .08 • Slowdown .15 .04 • Recession .10 -.03 • What is the expected return? • What is the variance? • What is the standard deviation?

12. Stand-Alone Risk • Standard deviation measures the stand-alone risk of an investment. • The larger the standard deviation, the higher the probability that returns will be far below the expected return.

13. Portfolio Risk and Return • Most investors do not hold stocks in isolation. Instead, they choose to hold a portfolio of several stocks. • As we shall see, an asset held as part of portfolio is less risky than the same asset held in isolation. • An asset’s return are important to show how the stock affects the risk and return of the portfolio. 13

14. Example: Portfolio Weights • Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? • $2,000 of DCLK • $3,000 of KO • $4,000 of INTC • $6,000 of KEI • DCLK: 2/15 = .133 • KO: 3/15 = .2 • INTC: 4/15 = .267 • KEI: 6/15 = .4

15. Portfolio Expected Returns • The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio • The weights reflect the % of the total portfolio invested in the asset.

16. Example: Expected Portfolio Returns • Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio? • DCLK: 19.65% • KO: 8.96% • INTC: 9.67% • KEI: 8.13% • E(RP) = .133(19.65) + .2(8.96) + .267(9.67) + .4(8.13) = 10.24%

17. Portfolio Risk • The standard deviation of a portfolio is not a weighted average of the standard deviations of the individual securities. • The riskiness of a portfolio depends on both the riskiness of the securities, and the way that they move together over time (correlation) • This is because the riskiness of one asset may tend to be canceled by that of another asset

18. The Correlation Coefficient • The tendency of two variables to move together is called Correlation, and the Correlation Coefficient measures this tendency. • The correlation coefficient can range from -1.00 to +1.00 and describes how the returns move together through time.

19. The Correlation Coefficient • When the returns on two securities are perfectly positively correlated, none of the risk of the individual stocks can be eliminated by diversification. • When the correlation coefficient between the returns on two securities is equal to -1 the returns are said to be perfectly negatively correlated all risk can be eliminated by investing a positive amount in the two stocks. • In reality, all stocks are positively correlated, but not perfectly so.

20. The Portfolio Standard Deviation • The portfolio standard deviation can be thought of as a weighted average of the individual standard deviations plus terms that account for the co-movement of returns • For a two-security portfolio:

21. Portfolio Theory • Suppose Asset A has an expected return of 10 percent and a standard deviation of 35 percent. Asset B has an expected return of 16 percent and a standard deviation of 40 percent. If the correlation between A and B is 0.4, what are the expected return and standard deviation for a portfolio comprised of 30 percent Asset A and 70 percent Asset B?

22. Portfolio Expected Return

23. Portfolio Standard Deviation • Notice that the portfolio formed by investing 30% in asset A and 70% in asset B has a lower standard deviation than either Stocks A or B. This is the essence of diversification, by forming portfolios some of the risk inherent in the individual stocks can be eliminated.

24. Systematic Risk • Risk factors that affect a large number of assets. Also known as non-diversifiable risk or market risk • It stems from factors that affect most firm in the market such as war, inflation recession, and high interest rates. • Because most firm are negatively affected by these factors, market risk cannot be eliminated by diversification.

25. Systematic Risk Factors such as changes in nation’s economy, tax reform by the Congress, or a change in the world situation. STD DEV OF PORTFOLIO RETURN Unsystematic risk Total Risk Systematic risk NUMBER OF SECURITIES IN THE PORTFOLIO

26. Unsystematic Risk • Risk factors that affect a limited number of assets. Also known as unique risk and asset-specific risk. Unsystematic Risk can be eliminated by diversification. • Unsystematic risk is caused by such random events such as lawsuits, strikes, successful and unsuccessful marketing plans, winning or loosing a major contract, and other events that are unique to a specific firm. • Because these events are random, their effects on a portfolio can be eliminated by diversification. • Bad events in one firm will be offset by a good events of another firm.

27. Unsystematic Risk Factors unique to a particular company or industry. For example, the death of a key executive or loss of a governmental defense contract. STD DEV OF PORTFOLIO RETURN Unsystematic risk Total Risk Systematic risk NUMBER OF SECURITIES IN THE PORTFOLIO

28. Diversification • Portfolio diversification is the investment in several different asset classes or sectors • Diversification is not just holding a lot of assets • For example, if you own 50 Internet stocks, then you are not diversified • However, if you own 50 stocks that span 20 different industries, then you are diversified

29. The Principle of Diversification • Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns • This reduction in risk arises because worse-than-expected returns from one asset are offset by better-than-expected returns from another asset • However, there is a minimum level of risk that cannot be diversified away - that is the systematic portion (Market risk).

30. Risk vs. Number of Stock in Portfolio p Company Specific (Diversifiable) Risk 35% 20% 0 Market Risk 10 20 30 40 2,000 stocks 1 30

31. Conclusions • As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio. • sp falls very slowly after about 40 stocks are included. The lower limit for sp is about 20%=sM . • By forming well-diversified portfolios, investors can eliminate about half the risk of owning a single stock.

32. Measuring Systematic Risk: Beta How do we measure systematic risk? We use the beta coefficient to measure systematic risk As noted earlier, market risk is the risk that remains after diversification and it can be measured by the degree to which a given stock tends to move up and down with the market. The tendency of the stock to move up and down with the market is reflected in its beta coefficient. 32

33. How is market risk measured for individual securities? • Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall riskiness of the portfolio. • It is measured by a stock’s beta coefficient. For stock i, its beta is: • bi = (ri,Msi) / sM

34. Calculating Beta in Practice • Many analysts use the S&P 500 to find the market return. • Analysts typically use four or five years’ of monthly returns to establish the regression line. • Some analysts use 52 weeks of weekly returns.

35. How is beta interpreted? If b = 1.0, stock has average risk. If b > 1.0, stock is riskier than average. If b < 1.0, stock is less risky than average. Most stocks have betas in the range of 0.5 to 1.5.

36. Finding Beta Estimates on the Web • Go to http://finance.yahoo.com • Enter the ticker symbol for a “Stock Quote”, such as IBM or Dell, then click GO. • When the quote comes up, select Key Statistics from panel on left.

37. Portfolio Betas • Portfolio beta is the weighted average of its individual securities’ betas. • Portfolio beta describes the volatility of the portfolio relative to the market.

38. Example: Portfolio Betas • Consider the previous example with the following four securities • Security Weight Beta • DCLK .133 4.03 • KO .2 0.84 • INTC .267 1.05 • KEI .4 0.59 • What is the portfolio beta? • .133(4.03) + .2(.84) + .267(1.05) + .4(.59) = 1.22

39. The Relationship between Risk and Rates of Return The relationship between risk and return can be addressed by the Capital Asset Pricing Model (CAPM). The CAPM is an equilibrium model that specifies the relationship between risk and required rate of return for assets held in well-diversified portfolios. • RPM = (rM - rRF), is the additional return over the risk-free rate needed to induce an investor to invest in the market portfolio. 39

40. Example: CAPM • Consider the betas for each of the assets given earlier. If the risk-free rate is 3.15% and the market risk premium is 9.5%, what is the expected return for each according to CAPM? • Security Beta Expected Return • DCLK 4.03 3.15 + 4.03(9.5) = 41.435% • KO 0.84 3.15 + .84(9.5) = 11.13% • INTC 1.05 3.15 + 1.05(9.5) = 13.125% • KEI 0.59 3.15 + .59(9.5) = 8.755%

41. The SML Equation • The relationship between the required return and risk is called the Security Market Line (SML). ri = rRF + bi rM - rRF Intercept Slope Risk measure