• Trade-Off Between Risk and Return | Capital Asset Pricing Model | Beta (Finance)

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  Review ã Trade-off between risk and return Risk, Return, and CAPM Finance 221 Summer 2006 ã What is the difference between systematic and unsytematic risk? ã Why are investors compensated only for systematic risk? ã What is a risk premium? 2 Average Return and St. Dev. for Individual Securities, 1994-2003 25 Review: Diversification ã Research suggests that investors are not as diversified as they should be ã Can also diversify across asset class: a portfolio composed of 80% stocks and 20% bo
  1 Risk, Return, and CAPM Finance 221Summer 2006 2 Review ãTrade-off between risk and returnãWhat is the difference between systematicand unsytematicrisk?ãWhy are investors compensated only forsystematic risk?ãWhat is a risk premium? 3  Average Return and St. Dev. forIndividual Securities, 1994-2003 05101520250 10 20 30 40 50 60  Average Return (%)Standard Deviation (%)Wal-Mart Anheuser-Busch Archer Daniels Midland American Airlines   Standard Deviation captures total risk  4 Review: Diversification ãResearch suggests that investors are not asdiversified as they should beãCan also diversify across asset class: a portfoliocomposed of 80% stocks and 20% bonds gets97% of S&P 500 return with 85% of the risk.ãInternational diversification; Correlation betweenUS and Brazil Markets –0.09 in late 1970s, 0.68in early 1990s. Home bias (Japan –98%).ãCampbell, Lettau, Malkieland Xu (2001): marketvolatility relatively constant over 1962-1997,firm-specific volatility doubled. Correlationsdeclined from 0.28 to 0.08 in the sample period. 5 Today: CAPM (Capital Asset Pricing Model) Nobel Prize in Economics, 1990, Awarded to Harry Markowitz, Merton Miller, and William Sharpe for “their pioneering work in the theory of financial economics”. ⇒  CAPM   A stock’s beta  ( β ) , a measure of how much astock’s returns vary in response to changes inthe overall market, is an importantdeterminant of the stock’s expected return  : aforecast of the return that an asset will earnover some period of time.   6 Expected Returns ãExpected returns reflect our estimate of how an investment will perform in thefuture. Think about the expected returnsof stocks vs. bonds.ãExpected returns are not observable  . Thismeans we need to develop methods toestimate expected returns.  2 7 Expected Returns Decisions must be based on expected returnsMethods used to estimate expected return Historical approachProbabilistic approach   Risk-based approach 8 Historical Approach forEstimating Expected Returns  Assumption: the distribution of expected returns willbe similar to historical distribution of returns.   Using 1900-2003 annual returns, the average risk premium for U.S. stocks relative to Treasury bills is7.6%. Treasury bills currently offer a 2% yield tomaturityExpected return on U.S. stocks: 7.6% + 2% = 9.6% Can historical approach be used to estimate the expected return of an individual stock?  9 Historical Approach forEstimating Expected Returns  Assume General Motors long-run average return is17.0%. Treasury bills average return over sameperiod was 4.1%GM historical risk premium: 17.0% -4.1% = 12.9%GM expected return = Current T-bill rate + GMhistorical risk premium = 2% + 12.9% = 14.9%Limitationsof historicalapproach forindividualstocksMay reflect GM’s past more thanits future   Many stocks do not have a longhistory to forecast expected return 10 Probabilistic Approach forEstimating Expected Returns Identify all possible outcomes of returns and assigna probability to each possible outcome:GM Expected Return = 0.20(-30%) + 0.70(15%)+0.10(55%) = 10%For example, assign probabilities for possible statesof economy: boom, expansion, recession and projectthe returns of GM stock for the three states 55%10%Boom15%70%Expansion-30%20%Recession GM ReturnProbabilityOutcome 11 Risk-Based Approach forEstimating Expected Returns 1. Measure the risk of the asset2. Use the risk measure to estimate the expectedreturn   How can we capture the systematic risk component of a stock’s volatility?  1. Measure the risk of the asset ã Systematic risks simultaneously affect manydifferent assets ã Investors can diversify away the unsystematic risk  ã Market rewards only the systematic risk: onlysystematic risk should be related to the expectedreturn 12 ã Collect data on a stock’s returns and returns on amarket index ã Plot the points on a scatter plot graph  –  Y–axis measures stock’s return  – X-axis measures market’s return ã Plot a line (using linear regression) throughthepoints Risk-Based Approach forEstimating Expected Returns Slope of line equals beta, the sensitivity of a stock’sreturns relative to changes in overall market returns   Beta is a measure of systematic risk for a particularsecurity.  3 13 -30%-20%-10%0%10%20%30%-30% -20% -10% 0% 10% 20% 30% Slope =Beta = 1.44 Scatter Plot for Returns on SharperImage and S&P 500 S&P 500 weekly returns SharperImageweeklyreturns   14 -15%-10%-5%0%5%10%15%-15% -10% -5% 0% 5% 10% 15% Beta = 0.11 Scatter Plot for Returns on ConAgraand S&P 500 S&P 500 weekly returns ConAgraweeklyreturns   15 Beta Beta is a standardized measure of the systematic risk of an individual asset  Sharper Image – β = 1.44 ⇒ On average, if themarket’s return moves by 1%, the return for SharperImage moves in the same direction by 1.44% ⇒  Verysensitive to overall market movements.ConAgra –b = 0.11 ⇒ On average, if the market’sreturn moves by 1%, the return for ConAgra moves inthe same direction by 0.11% ⇒ Less sensitive tomarket movements.Which stock has the highest systematic risk? 16 Risk-Based Approach forEstimating Expected Returns   Beta measures systematic risk and links the risk and expected return of an asset. 2. Use the risk measure to estimate the expectedreturn: ã 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, withan expected return of 10%. ã Draw a straight line connecting the two points. ã Investors holding a stock with beta of 0.5 or 1.5,for example, can find the expected return on theline. 17 Risk and Expected Returns Expected returns ãã 10%1 Risk-free asset ã ã ã ã ã ã ã ã ã Beta ã 4% ã 18% ã 14%  “average” stock    What is the expected return for stock with beta = 1.5?  ß= 1.5  ãã 18 Portfolio Expected Returns The portfolio expected return equals the weightedaverage of the portfolio assets’expected returns E(R  p ) = w 1 E(R  1 )+ w 2 E(R  2 )+…+w n E(R  n ) ã w 1 , w 2 , …, w n : portfolio weights ã E(R  1 ), E(R  2 ), …, E(R  N ): expected returns of securitiesExpected 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?   4 19 Portfolio Expected Returns $10,000$2,500$5,000$2,500 $ Invested 0.1258%Sears0.514%Pfizer0.2512%GE0.12510%IBM WeightsE(R)Portfolio 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 ) 20 Short Selling ãPortfolio weights must sum up to oneãNot all weights have to be positive. A negativeweight ⇒ Short SellingRocket.comand BricksNMortarInc. both sell for $10per share. You expect returns on Rocket.comto be25%, but returns on BricksNMortarInc. to be only5%. You have $1,000 to invest.Borrow 50 shares of BricksNMortar---sellimmediately. Buy 150 shares of Rocket.com. %35%)25()5.1(%)5()5.0()( =×+×−=  p  R E  21 Short Selling $1,350Net Cash Earned($1,350-$1,000)/$1,000 = 0.35 = 35%Rate of Return =(price = $10.50)-$525Return BorrowedShares(price = $12.50)$1875Sell Rocket Shares End of Year (150 shares)$1500Rocket Shares(50 shares)$500Borrowed$1000Initial Investment Beginning of Year *This is called leveraging 22 Portfolio Risk  Portfolio risk is the weighted average of systematicrisk (beta) of the portfolio constituent securities. $10,000$2,500$5,000$2,500 $ Invested 0.1250.67Sears0.51.67Pfizer0.251.33GE0.1251.00IBM WeightsBetaPortfolio 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  23 Security Market Line 10 Beta E(R  m )Market portfolio R  f  Risk-free asset E(R)Portfolio Portfolio composed of the following two assets: ã  An asset that pays a risk-free return R  f, , and ã  A market portfolio that contains some of everyrisky asset in the market.Security market line: the line connecting the risk-free asset and the market portfolio   24 The Security Market Line β i E(R P )R F SML Slope = E(R  m ) -R  F =MarketRisk Premium ãã   ã R M β =1.0
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