Professor XXXXX Course Name / Number Risk, Return, and CAPM Professor XXXXX Course Name / Number

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

Historical Approach for Estimating Expected Returns Assume that distribution of expected returns will be similar to historical distribution of returns. Using 1900-2003 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?

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% + 12.9% = 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

Probabilistic Approach for Estimating Expected Returns Identify all possible outcomes of returns and assign a probability to each possible outcome: 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 Return Probability Outcome GM Expected Return = 0.20(-30%) + 0.70(15%) +0.10(55%) = 10%

Risk-Based Approach for Estimating Expected Returns 1. Measure the risk of the asset 2. Use the risk measure to estimate the expected return 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 How can we capture the systematic risk component of a stock’s volatility?

Risk-Based Approach for Estimating Expected Returns 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 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.

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

ConAgra weekly returns Scatter Plot for Returns on ConAgra and S&P 500 ConAgra weekly returns S&P 500 weekly returns

Risk-Based Approach for Estimating Expected Returns 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. Beta measures systematic risk and links the risk and expected return of an asset.

Risk and Expected Returns • 18% • 14% ß = 1.5 • • • 10% “average” stock • 4% Risk-free asset • • • • • • • • • • 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Beta What is the expected return for stock with beta = 1.5?

Portfolio Expected Returns How does the expected return of a portfolio relate to the expected returns of the securities in the portfolio? The portfolio expected return equals the weighted average of the portfolio assets’ expected returns E(Rp) = w1E(R1)+ w2E(R2)+…+wnE(Rn) w1, w2 , … , wn : portfolio weights E(R1), E(R2), …, E(RN): expected returns of securities Expected return of a portfolio with N securities

Portfolio Expected Returns E(R) $ Invested Weights IBM 10% $2,500 0.125 GE 12% $5,000 0.25 Sears 8% Pfizer 14% $10,000 0.5 E(Rp) = (0.125)(10%) + (0.25)(12%) + (0.125)(8%) + (0.5)(14%) = 12.25% E(Rp) = w1E(R1)+ w2E(R2)+…+wnE(Rn)

Portfolio Risk Portfolio risk is the weighted average of systematic risk (beta) of the portfolio constituent securities. Portfolio Beta $ Invested Weights IBM 1.00 $2,500 0.125 GE 1.33 $5,000 0.25 Sears 0.67 Pfizer 1.67 $10,000 0.5 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

Portfolio composed of the following two assets: Security Market Line Portfolio composed of the following two assets: An asset that pays a risk-free return Rf, , and A market portfolio that contains some of every risky asset in the market. Portfolio E(R) Beta Risk-free asset Rf Market portfolio E(Rm) 1 Security market line: the line connecting the risk-free asset and the market portfolio

Security Market Line and CAPM The two-asset portfolio lies on security market line Given two points (risk-free asset and market portfolio asset) on the security market line, the equation of the line: E(Ri) = Rf + ß [E(Rm) – Rf] Return for bearing no market risk Portfolio’s exposure to market risk Reward for bearing market risk The equation represents the risk and return relationship predicted by the Capital Asset Pricing Model (CAPM)

The Security Market Line Plots relationship between expected return and betas 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.

The Security Market Line E(RP) SML • A - Undervalued • A Slope = E(Rm) - RF = Market Risk Premium RM • • • B RF • B - Overvalued •  =1.0 i

Much harder to create value through financial activities 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.

If asset prices unpredictable, then what is the use of CAPM? Efficient Markets If asset prices unpredictable, then what is the use of CAPM? CAPM gives analyst a model to measure the systematic risk of any asset. 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.

Decisions should be made based on expected returns. Risk, Return, and CAPM 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.