Risk, Return, & the Capital Asset Pricing Model CHAPTER 6 Risk, Return, & the Capital Asset Pricing Model

Topics in Chapter Basic return concepts Basic risk concepts Stand-alone risk Portfolio (market) risk Risk and return: CAPM/SML 1

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) For value box in Ch 4 time value FM13. Market interest rates Firm’s debt/equity mix Cost of debt Cost of equity Market risk aversion Firm’s business risk

> Risk, > Return, (both + & -) Stand – Alone Risk Risk in Portfolio Context b. Market Risk Quantified by Beta & used in CAPM: Capital Asset Pricing Model Relationship b/w market risk & required return as depicted in SML Req’d return = Risk-free return + Mrkt risk Prem(Beta) SML: ri = rRF + (RM - rRF )bi a. Diversifiable

What are investment returns? Investment returns measure financial results of an investment. Returns may be historical or prospective (anticipated). Returns can be expressed in: ($) dollar terms. (%) percentage terms.

An investment costs $1,000 and is sold after 1 year for $1,100. Dollar return: $ Received - $ Invested $1,100 - $1,000 = $100 Percentage return: $ Return/$ Invested $100/$1,000 = 0.10 = 10% 2

What is investment risk? Typically, investment returns are not known with certainty. Investment risk pertains to the probability of earning a return less than expected. Greater the chance of a return far below the expected return, greater the risk. 2

Risk & Return Student Sue Student Bob Exam 1 70% X weight X 50% 80% X wt. X 50% ----------- Exam 2 x wt 100% x .50 ------- Final grade = 75 % Final grade = 75 %

Probability Distribution: Which stock is riskier? Why?

WedTech Co Normal 40% Return 20% = .08 Bad 30% Return 5% = .015 Good 30% Return 35% = .105 =Expected ave return = 20%

WedTech Co Standard Deviation: Measure of stand-alone risk Return-Exp Ret = Diff2 x Prob = Variance: SD:

Standard Deviation and Normal Distributions 1 SD = 68.26% likelihood 2 SD = 95.46% 3 SD = 99.74%

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

IBM Normal 80% Return 12% = .096 Bad 10% Return 4% = .004 Good 10% Return 20% = .02 =Expected ave return = 12% Standard deviation = measure of dispersion= 3.58%

IBM Graph

WedTech Co vs. IBM

WedTech Co & IBM in 2 stock Portfolio Ave Portfolio Return in 50%-50% split Ave Return %split Wedtech 20% x .5 = 10% IBM 12% x .5 = 6% Portf. Return = 16% Portfolio Standard Deviation

Portfolio Standard Deviation Consider returns of portfolio at various states of economy & associated probabilities Will diversify away risk at higher rate than simple average of securities standard deviation

WedTech Co & IBM in 2 stock Risk Averse Portfolio Ave Portfolio Return in 20%-80% split Ave Return %split Wedtech 20% x .2 = 4% IBM 12% x .8 = 9.6% Portf. Return = 13.6% With even lower standard deviation

WedTech Co & IBM in 2 stock Risk Taker Portfolio Ave Portfolio Return in 80%-20% split Ave Return %split Wedtech 20% x .8 = 16% IBM 12% x .2 = 2.4% Portf. Return = 18.4% But have greater Portfolio S.D. than other scenarios

WedTech Co & IBM & adding other stocks to Portfolio IBM WedTech Coke Microsoft

Historical Risk vs. Return Return: Hi – Lo Risk: Hi - Lo Small Co stock Large Co Stock LT Corp Bonds LT Treasuries ST T-Bills

Reward-to-Variabilty Ratio (Sharpe’s) Portfolio’s average return in excess of risk-free rate divided by standard deviation Rpf - Rrf S.D. Porftfolio

Comparing Different Stocks Coefficient of Variation: = S.D. / Return; or Risk / Return WalMart vs. Philip Morris 12% Return 12% 12 S.D. 24 = C.V. =

Expected Return versus Coefficient of Variation Security Expected Return Risk:  CV Alta Inds 17.4% 20.0% 1.1 Market 15.0 15.3 1.0 Am. Foam 13.8 18.8 1.4 T-bills 8.0 0.0 Repo Men 1.7 13.4 7.9

Comparing Different Stocks Correlation coefficient = r (rho): Measures tendency of 2 variables to move together. Rho (r) = 1 = perfect + correlation & variables move together in unison. Does not help with diversification

Two-Stock Portfolios Two stocks can be combined to form a riskless portfolio if r = -1.0. Risk is not reduced at all if the two stocks have r = +1.0. In general, stocks have r ≈ 0.35, so risk is lowered but not eliminated. Investors typically hold many stocks. What happens when r = 0? 22

Adding Stocks to a Portfolio What would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added? sp would decrease because the added stocks would not be perfectly correlated, but the expected portfolio return would remain relatively constant. 25

s1 stock ≈ 35% sMany stocks ≈ 20%

Risk vs. Number of Stock in Portfolio 10 20 30 40 2,000 stocks Company Specific (Diversifiable) Risk Market Risk 20% Stand-Alone Risk, p p 35% 27

Stand-alone risk = Market risk + Diversifiable risk Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification. Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification. 29

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. 31

No. Rational investors will minimize risk by holding portfolios. Can an investor holding one stock earn a return commensurate with its risk? No. Rational investors will minimize risk by holding portfolios. They bear only market risk, so prices and returns reflect this lower risk. The one-stock investor bears higher (stand-alone) risk, so the return is less than that required by the risk. 32

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,M si) / sM 34

Beta Measurements In addition to measuring a stock’s contribution of risk to a portfolio, beta also measures the stock’s volatility relative to the market.

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

Using a Regression to Estimate Beta Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis. The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b. 35

Use the historical stock returns to calculate the beta for PQU. Year Market PQU 1 25.7% 40.0% 2 8.0% -15.0% 3 -11.0% 4 15.0% 35.0% 5 32.5% 10.0% 6 13.7% 30.0% 7 42.0% 8 -10.0% 9 -10.8% -25.0% 10 -13.1% 25.0%

Calculating Beta for PQU

Beta & PQU Co. Beta reflects slope of line via regression y = mx + b m=slope + b= y intercept Rpqu = 0.8308 rM + 0.0256 So, PQU’s beta is .8308 & y-intercept @ 2.56%

Beta & PQU Co. & R2 R2 measures degree of dispersion about regression line (ie – measures % of variance explained by regression equation) PQU’s R2 of .3546 means about 35% of PQU’s returns are explained by the market returns (32% for a typical stock) R2 of .95 on portfolio of 40 randomly selected stocks would reflect a regression line with points tightly clustered to it.

Calculating Beta in Practice Many analysts use the S7P 500 to find market return Analysts typically use 4 or 5 years of monthly returns to establish regression line. Some use 52 weeks of weekly returns.

Expected Return versus Market Risk: Which investment is best? Security Expected Return (%) Risk, b Alta 17.4 1.29 Market 15.0 1.00 Am. Foam 13.8 0.68 T-bills 8.0 0.00 Repo Men 1.7 -0.86

Capital Asset Pricing Model The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM). Return = Risk Free + Beta (RetMrkt –Rf) SML: ri = rRF + (RPM)bi . 43

Graph of Security Market Line

Use the SML to calculate each alternative’s required return. The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM). SML: return = risk-free return + Beta(Market risk premium) . Assume T-Bill = 7% =rRF; =Return on market =15%= rM Then: Market Risk premium =RPM = (rM - rRF) = 15% - 7% = 8%. 43

Use the SML to calculate each alternative’s required return. If company’s Beta = 1.25 Then: R = Rrf + B ( Rm – Rf). R = .07 + 1.25 (.08) = 17% Req’d return = 17% vs. Expected return of 13% Go / No Go ? No Go, it’s overvalued! 43

Required Rates of Return If t-bill =8%, & MRP = 7% Then required rates of return are: rAlta = 8.0% + (7%)(1.29) = 17%. rM = 8.0% + (7%)(1.00) = 15.0%. rAm. F. = 8.0% + (7%)(0.68) = 12.8%. rT-bill = 8.0% + (7%)(0.00) = 8.0%. rRepo = 8.0% + (7%)(-0.86) = 2.0%.

Expected versus Required Returns (%) Alta 17.4 17.0 Undervalued Market 15.0 Fairly valued Am. Foam 13.8 12.8 T-bills 8.0 Repo 1.7 2.0 Overvalued

SML: ri = rRF + (RPM) bi ri = 8% + (7%) bi . Repo Alta T-bills Am. Foam rM = 15 rRF = 8 -1 0 1 2 ri (%) Risk, bi Market 46

Calculate beta for a portfolio with 50% Alta and 50% Repo bp = Weighted average = 0.5(bAlta) + 0.5(bRepo) = 0.5(1.29) + 0.5(-0.86) = 0.22. 47

Required Return on the Alta/Repo Portfolio? rp = Weighted average r = 0.5(17%) + 0.5(2%) = 9.5%. Or use SML: rp = rRF + (RPM) bp = 8.0% + 7%(0.22) = 9.5%. 48

Impact of Inflation Change on SML Original situation r (%) SML2 0 0.5 1.0 1.5 Risk, bi 18 15 11 8 New SML  I = 3% 50

Impact of Risk Aversion Change SML1 Original situation r (%) SML2 After change Risk, bi 18 15 8 1.0  RPM = 3% 52

Has the CAPM been completely confirmed or refuted? No. The statistical tests have problems that make empirical verification or rejection virtually impossible. Investors’ required returns are based on future risk, but betas are calculated with historical data. Investors may be concerned about both stand-alone and market risk. 53