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

Please download to get full document.

View again

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
 3
 
  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
Share
Transcript
  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 0.20.40.60.821.21.41.61.8 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
Related Search
Similar documents
View more
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks
SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...

Sign Now!

We are very appreciated for your Prompt Action!

x