Chapter 06 Risk and Return

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

1.Risk of financial asset is judged by the risk of its cash flow 2.Asset risk: Stand Alone basis vs. Portfolio Context 3.Portfolio context: Diversifiable Risk vs. Market Risk. 4.Investors in general are Risk Averse Important Notes

Stand alone risk: the risk an investor would face if she or he held only one particular asset. Investment risk pertains to the probability of actually earning a low or negative return. The greater the chance of low or negative returns, the riskier the investment. STAND ALONE RISK

r = expected rate of return. ^ Probability Distribution & Expected Rate of Return

Standard Deviation: a measure of the tightness of the probability distribution. The tighter the probability distribution, the smaller the Standard Deviation and the less risky the asset. Coefficient of Variation: Standard Deviation divided by return. It measures risk per unit of return, thus provides more standardized basis for risk profile comparison between assets with different return. Stand Alone Risk: Measurements

Standard Deviation Variance Standard Deviation

Probability distribution Expected Rate of Return Rate of return (%) Basic Foods Sale.com The larger the Standard Deviation: the lower the probability that actual returns will be close to the expected return hence the larger the risk

Historical Data to Measure Standard Deviation Standard Deviation

Standardized measure of dispersion about the expected value: Shows risk per unit of return. CV =  ^ r Coefficient of Variation (CV)

0 A B  A =  B, but A is riskier because larger probability of losses. = CV A > CV B.  ^ r

r p is a weighted average: ^ ^^ r p =   w i r i  n i = 1 Risk & Return in Portfolio Context Return Risk Correlation Coefficient to measure the tendency of two variables moving together

Portfolio Return

Portfolio Risk: Standard Deviation of 2-Asset-Portfolio Variance Covariance Standard Deviation

Portfolio Risk: Standard Deviation of 2-Asset-Portfolio The standard deviation of a portfolio is generally not a weighted average of individual standard deviations (SD). The portfolio's SD is a weighted average only if all the securities in it are perfectly positively correlated. Risk is not reduced at all if the two stocks have r = Where the stocks in a portfolio are perfectly negatively correlated, we can create a portfolio with absolutely no risk, or Portfolio’s SD equal to 0. Two stocks can be combined to form a riskless portfolio if r = -1.0.

Portfolio Risk: Perfectly Negative Correlation

Returns Distribution for Two Perfectly Negatively Correlated Stocks ( ρ = -1.0) and for Portfolio WM Stock WStock MPortfolio WM

Portfolio Risk: Perfectly Positive Correlation

Returns Distributions for Two Perfectly Positively Correlated Stocks ( ρ = +1.0) and for Portfolio MM’ Stock M Stock M’ Portfolio MM’

Portfolio Risk: Partial Correlation

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

24   stock ≈ 35%  Many stocks ≈ 20%

# Stocks in Portfolio ,000+ Company Specific Risk Market Risk 20 0 Stand-Alone Risk,  p  p (%) 35 Effects of Portfolio Size on Portfolio Risk 

Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification, and is measured by beta. Firm-specific risk is that part of a security’s stand-alone risk that can be eliminated by proper diversification.

Capital Asset Pricing Model (CAPM): relevant risk of individual stock is the amount of risk that the stock contributes to well-diversified stock portfolio, or the market portfolio. 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. Beta measures a stock’s market risk. It shows a stock’s volatility relative to the market. Beta shows how risky a stock is if the stock is held in a well-diversified portfolio. Beta can be calculated by running a regression of past returns on Stock i versus returns on the market. The slope of the regression line is defined as the beta coefficient. If beta > 1.0, stock is riskier than the market. If beta < 1.0, stock less risky than the market. Capital Asset Pricing Model & The Concept of Beta

28 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.

Beta - Illustration

30 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.

Beta - Calculation

32 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.

r i = Required return on Stock i r RF = Risk-free return (r M -r RF ) = Market risk premium b i = Beta of Stock i r i = r RF + (r M – r RF )b i. ^ Security Market Line (SML) Relationship between required rate of return and risk r i = r RF + RP M b i.

34 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: r i = r RF + (RP M )b i. Assume r RF = 8%; r M = r M = 15%. RP M = (r M - r RF ) = 15% - 8% = 7%.

35 SML 1 Original situation r (%) SML Risk, b i New SML  I = 3% Impact of Inflation Change on SML

36 SML 1 Original situation r (%) SML 2 After change Risk, b i  RP M = 3% Impact of Risk Aversion Change

Portfolio Theory and Asset Pricing Models

^ Efficient Portfolio 2-asset case: risk & return

^ Efficient Portfolio 2-asset case: risk & return Positive Correlation

^ Efficient Portfolio 2-asset case: risk & return Zero Correlation

^ Efficient Portfolio 2-asset case: risk & return Negative Correlation

Efficient Set of Investments Financial Management - Reza Masri42

Optimal Portfolios Financial Management - Reza Masri43

Efficient Set of Investments + Risk-Free Asset Financial Management - Reza Masri44

Optimal Portfolio with Risk-Free Asset Financial Management - Reza Masri45

Security Market Line (SML) & Capital Market Line (CML)

Alternative Theories/Models Arbitrage Pricing Theory (APT) Include more factors to specify the equilibrium risk/return relationship Based on complex mathematical & statistical theory Practical Usage has been limited Fama-French Three –Factor Model Include 2 more factors to CAPM: size of the company & book-to- market ratio More use by academic researchers than corporate managers Necessary data generally not accessible by public Behavioral Finance Stocks may have short term momentum Blending psychology & finance: “people don’t always behave rationally including in investments”