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Unformatted text preview: Comm371 Chapter 7: CAPM Chapter March 2011 Textbook Readings Textbook Chapter 8: Chapter Section 8.1, 8.2, 8.3 Section Chapter 9: Chapter Section 9.3, 9.6, 9.9 and 9.10 Section Outline Outline Beta and systematic risk The CAPM CML and SML Applications APT I. Beta and systematic risk I. Limits to diversification Limits The standard deviation of a portfolio The tends to decrease as more risky assets are added to the portfolio are
Std. Deviation Of Portfolio Firmspecific Risk Market (systematic) Risk Number of Securities 5 Diversification Diversification
Example of firmspecific risk CEO is killed in an auto accident A strike in one of the firm’s plant A firm finds oil on its property Example of market risk A unexpected recession in the US The subprime mortgage crisis is worse than expected Long term interest rates increase unexpectedly The Fed loses credibility on inflation control 6 What is beta? What
Systematic (market) risk vs unsystematic Systematic risk risk Reaction of individual assets (stocks, Reaction portfolios) to general market swings portfolios)
β= i
Cov ( RM , Ri ) Var ( RM ) 7 What is beta? What
Beta=1 for a broad market index (S&P 500) Beta>1 is aggressive and beta<1 is defensive Beta>1 aggressive defensive Portfolio beta is a weighted average of the Portfolio betas for the individual stocks in the portfolio β P = wA β A + wB β B
8 Beta for some assets Beta Asset WILSHIRE 5000TOTAL MARKET  PRICE INDEX MICROSOFT GEN.ELEC. Ford Motor YAHOO LOCKHEED MARTIN CORP S&P 500 Gold Bullion $/Troy Ounce Beta 19972002 1 1.36 1.22 0.93 2.25 0.33 0.99 0.05 9 II. The CAPM II. CAPM in a nutshell CAPM Portfolio I: 50 stocks, beta=1 for each and Portfolio very high specific risk for each Portfolio II: 50 stocks, beta=1 for each and Portfolio very low specific risk for each very Old theory vs CAPM
11 CAPM Assumptions CAPM Investors buy/sell all securities at competitive market prices (No taxes and no transactions costs) and can borrow and lend at the riskfree interest rate. interest Investors hold only efficient portfolios of Investors traded securities: portfolios that yield the maximum expected return for a given level of volatility. volatility. Investors have homogeneous expectations Investors regarding the volatilities, correlations, and expected returns of securities. expected Portfolio Theory Portfolio
CAL Portfolio Frontier Tangency Portfolio
n r u R d t c e p x E Standard Deviation 13 Tangency portfolio and market Portfolio Tangency Aggregate demand: tangency portfolio (or Aggregate efficient portfolio) Aggregate Supply = Market portfolio In equilibrium, this tangency portfolio is the In market portfolio market The market portfolio includes all stocks The weight of each asset equals: The Market Value of Stock Weight = Market Value of All Stocks
14 CAPM theory and the CML CAPM
CML Portfolio Frontier Expected Return Market Portfolio Standard Deviation 15 Risk and return of the market portfolio portfolio
E ( RM ) =RF +∑ i ( E ( Ri ) −RF ) w
i= 1 N Var ( RM ) = Cov ( RM , RM ) = Cov (∑wi Ri , RM )
i =1 N = ∑wi Cov ( Ri , RM )
i =1 N 16 All riskreturn tradeoffs are equal In equilibrium, the reward to risk ratio In (bang for the buck ratio) has to be the same for all assets: same
E ( R j ) − RF E ( Ri ) − RF E ( RM ) − RF = = Cov ( RM , Ri ) Cov ( RM , R j ) Var ( RM ) Reshuffling terms gives the CAPM formula
17 CAPM formula CAPM The CAPM determines the expected The return of a stock return
E ( Ri ) = RF + β i [ E ( RM ) − RF ] The expected return depends linearly The on the systematic risk of the asset on
Cov ( RM , Ri ) βi = Var ( RM ) Notice that beta also takes the form
βi = ρiM σi σM
18 Economic implications of the CAPM CAPM Using the market portfolio as a Using benchmark: benchmark:
Calculate the required return of a security Cost of capital of an investment Measure the performance of fund managers
Beta and risk Beta
oTotal stock return variance= Market variance + firm specific variance oMarket risk is related to beta:
2 Market variance = β i2σ M = ( ρ iM σ i ) 2 Market volatility = β i σ M = ρ iM σ i oSpecific risk: large for individual securities and small for indexes
2 2 firm specific variance = σ i2 − β i2σ m = σ i2 (1 − ρ iM ) 2 2 firm specific volatility = σ i2 − β i2σ m = σ i 1 − ρ iM 20 Question Question
Suppose the riskfree return is 4% and the market portfolio has an expected return of 10% and a volatility of 16%. Campbell Soup stock has a 26% volatility and a correlation with the market of 0.33. a) What is Campbell Soup’s beta with the market? b) Under the CAPM assumptions, what is its expected return c) Calculate Campbell stock’s firm specific volatility (assuming the CAPM holds) III. Capital market line (CML) and security market line (SML) and Decomposition of risk Decomposition CML and SML CML
E Rs −R E (( Rs))−R f f E R p =R + σ E (( R p))= R f f + σPP σ σSS E ( Ri ) = R f + β i [ E ( RM ) − RF ] SML and mispriced stocks: Alpha Alpha IV. Applications IV. Estimating expected return on equity equity
The SML gives a way to estimate expected return on equity We need: • Risk free rate: Current yield on 1 year Tbill • Market excess return: historical data • Beta: regression analysis or published in beta books (Merrill Lynch, Value Line)
27 E ( Ri ) − RF = β i [ E ( RM ) − RF ] Regression Techniques Regression
0.1 MSFT Excess Return 0 0.1 0.05 0 0.05 0.1 0.1
Market Excess Return 28 Linear Regression Linear The GM regression line equals: RGM − RF = α GM + β GM × [ RM − RF ] + ε GM We do not know αGM and βGM but we use We regression to estimate them regression We need historical returns
29 Regression output Regression
Coefficient Interpretation Estimate of βGM (call it b) The usual interpretation of beta βGM =Cov(RGM, RM)/Var(RM) How confident are you in the estimate b Standard error on the estimate of b call it sb Estimate of αGM Measure attractiveness of GM Should be 0 is CAPM holds: Alpha is called Abnormal return How confident are you in the estimate a Standard error on the estimate of a call it sa Estimates of the standard deviation of εGM call it s(εGM) R 2 = Var(βGM RM)/[Var(βGM RM) +s2(εGM)] =Explained variance/Total variance An estimate of firm specific risk How well future GM return are likely to be predicted by the market retrun Example. Monthly returns of GM and the S&P500 (Market): 11992 to 122006. S&P500 Regression output Regression
Coefficient Estimate Estimate of βGM (call it b) 1.047 Standard error on the estimate of b call it sb Estimate of αGM (monthly) 0.143 0.14% Standard error on the estimate of a call it sa Estimates of the standard deviation of εGM call it s(εGM) R 2 = Var(βGM RM)/[Var(βGM RM) +s2(εGM)] =Explained variance/Total variance 0.57% 8.36% 20% V. The APT V. Bye, bye beta Bye, 34 The Arbitrage Pricing Theory The The CAPM is a one factor model: Ri − RF = β i [ RM − RF ] + ε i The APT is a multifactor model:
Ri − RF = β i1 F1 + + β iN FN + ε i 35 The factors The
Macroeconomic: Inflation, GDPgrowth, interest Macroeconomic: rates, term premium, default premium, oil prices Stock related: Industry, Fama and French (HML, SMB and market) SMB Statistical factors, which do not have any Statistical economic meaning (principle components) economic
36 Example: 3Factor Model Example:
3Factor Model (FamaFrench) 1st factor: Market Premium (RM –
M • The difference between the market return and the riskfree rate 2nd factor (SMB): SmallStock Premium (RS –
S RF ) • The difference between the return of small and large The companies, measured according to their market capitalization capitalization 3nd factor (HML): ValueStock Premium (RV –
V RL ) • The difference between the return of value and growth The stocks. Value stocks are mature companies and growth stocks are companies with large growth potential stocks RG )
37 Example: IBM stock (Jan 1962 to Dec 2001) Dec Estimate the 3Factor model for Estimate IBM. You get the following betas: IBM.
Market beta: βM = 0.97 Market 0.97 Size beta: βS = 0.18 Size 0.18 Value beta: βV =  0.41 Value 0.41 Rsquare= 0.36 CAPM
Market beta= 1.17 Rsquare= 0.33
38 ...
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 Spring '08
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