Berlin, Fußzeile1 Professor Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics and Law Risk, Return, and CAPM

Berlin, Fußzeile2 Expected Returns Decisions must be based on expected returns Methods used to estimate expected return Historical approach Probabilistic approach Risk-based approach

Berlin, Fußzeile3 Historical Approach for Estimating Expected Returns Assume that distribution of expected returns will be similar to historical distribution of returns. Using annual returns, the average risk premium for U.S. stocks relative to Treasury bills is 7.6%. Treasury bills currently offer a 2% yield to maturity Expected return on U.S. stocks: 7.6% + 2% = 9.6% Can historical approach be used to estimate the expected return of an individual stock?

Berlin, Fußzeile4 Historical Approach for Estimating Expected Returns Assume General Motors long-run average return is 17.0%. Treasury bills average return over same period was 4.1% GM historical risk premium: 17.0% - 4.1% = 12.9% GM expected return = Current Tbill rate + GM historical risk premium = 2% % = 14.9% Limitations of historical approach for individual stocks May reflect GM’s past more than its future Many stocks have a long history to forecast expected return

Berlin, Fußzeile5 Probabilistic Approach for Estimating Expected Returns Identify all possible outcomes of returns and assign a probability to each possible outcome: GM Expected Return = 0.20(-30%) (15%) +0.10(55%) = 10% For example, assign probabilities for possible states of economy: boom, expansion, recession and project the returns of GM stock for the three states 55%10%Boom 15%70%Expansion -30%20%Recession GM ReturnProbabilityOutcome

Berlin, Fußzeile6 Risk-Based Approach for Estimating Expected Returns 1. Measure the risk of the asset 2. Use the risk measure to estimate the expected return How can we capture the systematic risk component of a stock’s volatility? 1. Measure the risk of the asset Systematic risks simultaneously affect many different assets Investors can diversify away the unsystematic risk Market rewards only the systematic risk: only systematic risk should be related to the expected return

Berlin, Fußzeile7  Collect data on a stock’s returns and returns on a market index  Plot the points on a scatter plot graph -Y–axis measures stock’s return -X-axis measures market’s return  Plot a line (using linear regression) through the points Risk-Based Approach for Estimating Expected Returns Slope of line equals beta, the sensitivity of a stock’s returns relative to changes in overall market returns Beta is a measure of systematic risk for a particular security.

Berlin, Fußzeile8 Scatter Plot for Returns on Sharper Image and S&P 500 S&P 500 weekly returns Sharper Image weekly returns

Berlin, Fußzeile9 Scatter Plot for Returns ConAgra and S&P 500 S&P 500 weekly returns ConAgra weekly returns

Berlin, Fußzeile10 R f Capital Market Line Risk Average Return Risk-Based Approach for Estimating Expected Returns rMrM MM Slope CML: Individual Stock A: CAPM

Berlin, Fußzeile11 The Security Market Line ii E(R P ) RFRF SML Slope = E(R m ) - R F = Market Risk Premium A - Undervalued RMRM  =1.0 B A B - Overvalued

Berlin, Fußzeile12 Risk-Based Approach for Estimating Expected Returns Beta measures systematic risk and links the risk and expected return of an asset. 2. Use the risk measure to estimate the expected return: Plot beta against expected return for two assets: -A risk-free asset that pays 4% with certainty, with zero systematic risk and -An “average stock”, with beta equal to 1, with an expected return of 10%. Draw a straight line connecting the two points. Investors holding a stock with beta of 0.5 or 1.5, for example, can find the expected return on the line.

Berlin, Fußzeile13 Risk and Expected Returns Security Market Line What is the expected return for stock with beta = 1.5 ? Expected returns 10% 1 Risk-free asset Beta 4% 18% 14% “average” stock ß = 1.5

14 Estimating the Risk Free Rate Extract of UK interest rate data from the Financial Times (17 February, 2005)

15 The Steps Towards the Estimation of Beta Using Ordinary Least Squares Regression

16 The Security Market Line

17 Arbitrage Drivers and the Linearity of the Security Market Line

Berlin, Fußzeile18 Portfolio Expected Returns The portfolio expected return equals the weighted average of the portfolio assets’ expected returns E(R p ) = w 1 E(R 1 )+ w 2 E(R 2 )+…+w n E(R n ) w 1, w 2, …, w n : portfolio weights E(R 1 ), E(R 2 ), …, E(R N ): expected returns of securities Expected return of a portfolio with N securities How does the expected return of a portfolio relate to the expected returns of the securities in the portfolio?

Berlin, Fußzeile19 Portfolio Expected Returns PortfolioE(R)$ InvestedWeights IBM 10%$2, GE 12%$5, Sears 8%$2, Pfizer 14%$10, E (R p ) = (0.125) (10%) + (0.25) (12%) + (0.125) (8%) + (0.5) (14%) = 12.25% E (R p ) = w 1 E (R 1 )+ w 2 E (R 2 )+…+w n E (R n )

Berlin, Fußzeile20 Portfolio Risk Portfolio risk is the weighted average of systematic risk (beta) of the portfolio constituent securities. PortfolioBeta$ InvestedWeights IBM1.00$2, GE1.33$5, Sears0.67$2, Pfizer1.67$10, ß P = (0.125) (1.00) + (0.25) (1.33) + (0.125) (0.67) + (0.50) (1.67) = 1.38 But portfolio volatility is not the same as the weighted average of all portfolio security volatilities

Berlin, Fußzeile21 Security Market Line PortfolioE(R)Beta Risk-free assetRfRf 0 Market portfolioE(R m )1 Portfolio composed of the following two assets: An asset that pays a risk-free return R f,, and A market portfolio that contains some of every risky asset in the market. Security market line: The line connecting the risk-free asset and the market portfolio

Berlin, Fußzeile22 The Security Market Line  In equilibrium, all assets lie on this line. If individual stock or portfolio lies above the line: -Expected return is too high. -Investors bid up price until expected return falls. If individual stock or portfolio lies below SML: -Expected return is too low. -Investors sell stock driving down price until expected return rises. Plots relationship between expected return and betas

Berlin, Fußzeile23 Efficient Markets Efficient market hypothesis (EMH): in an efficient market, prices rapidly incorporate all relevant information Financial markets much larger, more competitive, more transparent, more homogeneous than product markets Much harder to create value through financial activities Changes in asset price respond only to new information. This implies that asset prices move almost randomly.

Berlin, Fußzeile24 Efficient Markets CAPM gives analyst a model to measure the systematic risk of any asset. If asset prices unpredictable, then what is the use of CAPM? On average, assets with high systematic risk should earn higher returns than assets with low systematic risk. CAPM offers a way to compare risk and return on investments alternatives.

Berlin, Fußzeile25 Decisions should be made based on expected returns. Expected returns can be estimated using historical, probabilistic, or risk approaches. Portfolio expected return/beta equals weighted average of the expected returns/beta of the assets in the portfolio. CAPM predicts that the expected return on a stock depends on the stock’s beta, the risk-free rate and the market premium. Risk, Return, and CAPM