Today Risk and Return Reading Portfolio Theory Capital Asset Pricing Model Reading Brealey, Myers, and Allen, Chapters 7 and 8

Measuring Risk Variance - Average value of squared deviations from mean. A measure of volatility. Standard Deviation - Average value of squared deviations from mean. A measure of volatility. Variance measures ‘Total Risk’

Measuring Risk Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.” Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.” Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. 18

Measuring Risk 21

Portfolio Risk The variance of a two stock portfolio is the sum of these four boxes 19

Portfolio Risk Example Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The expected return on your portfolio is: 19

Portfolio Risk Example Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. 19

Portfolio Risk Example Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. 19

Portfolio Return and Risk 19

Portfolio Risk To calculate portfolio variance add up the boxes The shaded boxes contain variance terms; the remainder contain covariance terms. 1 2 3 4 5 6 N To calculate portfolio variance add up the boxes STOCK STOCK

Copyright 1996 by The McGraw-Hill Companies, Inc Beta and Unique Risk 1. Total risk = diversifiable risk + market risk 2. Market risk is measured by beta, the sensitivity to market changes beta Expected return market 10% - + +10% stock Copyright 1996 by The McGraw-Hill Companies, Inc -10%

Beta and Unique Risk Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stock’s return to the return on the market portfolio.

Beta and Unique Risk Covariance with the market Variance of the market

Markowitz Portfolio Theory Combining stocks into portfolios can reduce standard deviation, below the level obtained from a simple weighted average calculation. Correlation coefficients make this possible. The various weighted combinations of stocks that create this standard deviations constitute the set of efficient portfolios.

Markowitz Portfolio Theory Price changes vs. Normal distribution Coca Cola - Daily % change 1987-2004 Proportion of Days Daily % Change

Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment A % probability % return

Markowitz Portfolio Theory Standard Deviation VS. Expected Return Investment B % probability % return

Markowitz Portfolio Theory Expected Returns and Standard Deviations vary given different weighted combinations of the stocks Expected Return (%) Coca Cola 40% in Coca Cola Exxon Mobil Standard Deviation

Efficient Frontier Each half egg shell represents the possible weighted combinations for two stocks. The composite of all stock sets constitutes the efficient frontier Expected Return (%) Standard Deviation

Efficient Frontier T rf S Lending or Borrowing at the risk free rate (rf) allows us to exist outside the efficient frontier. Expected Return (%) T Lending Borrowing rf S Standard Deviation

Efficient Frontier Example Correlation Coefficient = .4 Stocks s % of Portfolio Avg Return ABC Corp 28 60% 15% Big Corp 42 40% 21% Standard Deviation = weighted avg = Standard Deviation = Portfolio = Return = weighted avg = Portfolio =

Efficient Frontier Let’s Add stock New Corp to the portfolio Example Correlation Coefficient = .4 Stocks s % of Portfolio Avg Return ABC Corp 28 60% 15% Big Corp 42 40% 21% Standard Deviation = weighted avg = Standard Deviation = Portfolio = Return = weighted avg = Portfolio = Let’s Add stock New Corp to the portfolio

Efficient Frontier NOTE: Higher return & Lower risk Example Correlation Coefficient = .3 Stocks s % of Portfolio Avg Return Portfolio 28.1 50% 17.4% New Corp 30 50% 19% NEW Standard Deviation = weighted avg = NEW Standard Deviation = Portfolio = NEW Return = weighted avg = Portfolio = NOTE: Higher return & Lower risk How did we do that? DIVERSIFICATION

Efficient Frontier Return B A Risk (measured as s)

Efficient Frontier Return B AB A Risk

Efficient Frontier Return B N AB A Risk

Efficient Frontier Return B ABN N AB A Risk

Efficient Frontier Goal is to move up and left. Return WHY? B ABN N AB Risk

Efficient Frontier Return Low Risk High Return High Risk High Return Low Return High Risk Low Return Risk

Efficient Frontier Return Low Risk High Return High Risk High Return Low Return High Risk Low Return Risk

Efficient Frontier Return B ABN N AB A Risk

. Security Market Line rf Return Market Return = rm Efficient Portfolio Risk Free Return = rf Risk

. Security Market Line rf Return Market Return = rm Efficient Portfolio Risk Free Return = rf 1.0 BETA

. Security Market Line rf Return Risk Free Return = Security Market Line (SML) rf BETA

Security Market Line rf SML Equation = rf + β ( rm - rf ) Return SML BETA 1.0 SML Equation = rf + β ( rm - rf )

Capital Asset Pricing Model R = rf + β ( rm - rf ) CAPM

Beta vs. Average Risk Premium Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1931-2002 30 20 10 SML Investors Market Portfolio Portfolio Beta 1.0

Beta vs. Average Risk Premium Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1931-65 SML 30 20 10 Investors Market Portfolio Portfolio Beta 1.0

Beta vs. Average Risk Premium Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1966-2002 30 20 10 SML Investors Market Portfolio Portfolio Beta 1.0

Arbitrage Pricing Theory Alternative to CAPM Expected Risk Premium = r - rf = Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + … Return = a + bfactor1(rfactor1) + bf2(rf2) + …

Arbitrage Pricing Theory Estimated risk premiums for taking on risk factors (1978-1990)