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The Capital Asset Pricing Model (CAPM) and the Security Market Line

Chapter Thirteen. The Capital Asset Pricing Model (CAPM) and the Security Market Line. Chapter Outline. Risk: Systematic and Unsystematic Diversification and Portfolio Risk Systematic Risk and Beta The Security Market Line The SML and the Cost of Capital: A Preview.

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The Capital Asset Pricing Model (CAPM) and the Security Market Line

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  1. Chapter Thirteen The Capital Asset Pricing Model (CAPM) and the Security Market Line

  2. Chapter Outline • Risk: Systematic and Unsystematic • Diversification and Portfolio Risk • Systematic Risk and Beta • The Security Market Line • The SML and the Cost of Capital: A Preview

  3. Total, Systematic & Unsystematic Risk • Total Risk (σ ) • Total risk = systematic risk + unsystematic risk • For well diversified portfolios, unsystematic risk is very small • Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk • Systematic Risk (Non- Diversifiable) . β • Risk factors that affect a large number of assets • Known as non-diversifiable risk market risk: • changes in GDP, inflation, interest rates, etc. • Unsystematic Risk (Diversifiable Risk) • Risk factors that affect a limited number of assets • Also known as unique risk and asset-specific risk • Includes such things as labor strikes, part shortages, etc.

  4. Example of Systematic & Unsystematic Risk Random portfolio from NYSE

  5. Figure 13.1

  6. Systematic Risk Principle • The expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away • Measuring Systematic Risk • How do we measure systematic risk? • We use the beta (β) coefficient to measure systematic risk • What does beta tell us? • A beta of 1 → the asset has the same systematic risk as the overall market • A beta < 1 → the asset has less systematic risk than the overall market • A beta > 1 → the asset has more systematic risk than the overall market

  7. Table 13.8 Β is defined as :

  8. Example- Total versus Systematic Risk • Consider the following information: σ Beta • Security C 20% 1.25 • Security K 30% 0.95 • Which security has more total risk? K • Which security has more systematic risk? C • Which security should have the higher expected return? C

  9. The Capital Asset Pricing Model (CAPM) • What is the CAPM? • A Theory about equilibrium of prices for risky assets -Developed in the 1960s ( Wiliam Sharp) • What is the risk premium on securities in equilibrium under some assumptions? • The assumptions of CAPM: • Investors care only about the mean and variance of their portfolio’s return. • Market are frictionless • Investors have homogenous believes all investors reach the same conclusions about means and SD of all feasible portfolios (you can’t beat the market”.

  10. Building up CAPM • CAPM say the optimal portfolio of risky assets is the market portfolio. • What is market portfolio ? • Suppose we have only 3 assets with the following market values :Ericsson stock= $66b Telia =$22b & risk-free asset = $ 12b. T. market value = 100b • How much should we hold of Ericsson, Telia and riskless) ? • Hold ( 66/22) or 3-1or 75% Ericsson&25% Telia • For riskless : depending on their risk aversion. • If 2 investor each with $100 000 to invest as follow:

  11. CAPM –Equations • In Equilibrium, the risk premium on any asset: • E(Rj)-RF = j (E(RM)-RF) SML- CAPM (1) • E(Rj)=RF +jE(RM)-RF) (2) • Pure time value of money • Reward for bearing systematic risk • Amount of systematic risk • The slope of SML (Rewards-risk Ratio): (3) • (3)

  12. Market Equilibrium & Security Market Line • The SML is the representation of market equilibrium • In equilibrium, all assets and portfolios must have the same reward-to-risk ratio • (4) • The slope of the SML could be also :(E(RM) –RF ) / M • Assume a company has E(R ) =20%  = 1.6 and RF = 8% • Slope of SML( R.T.R)=(E(RA)– Rf)/(A)=(20–8)/(1.6 ) = 7.5 • What if an asset has Reward-to-risk ratio of 8 (above the line)? • Undervalued • What if an asset has a reward-to-risk ratio of 7 (below the line)? • Overvalued

  13. Example–SML E(RA) Rf A

  14. Using CAPM in Portfolio Selection • For Portfolio Selection • Market portfolio on risky assets is efficient ( you can’t beat the market). • Be passive and do the following: • Diversify your holding of risky assets in proportion to market portfolio. • Mix this portfolio with riskless asset. • The CML provides a good benchmark for any portfolio • This passive called indexing ( SAX, S&P500…etc). • Advantages of passive portfolio according to CAPM: • Historically passive portfolio performed better than active. • It cost less ( costs for searching for mispriced stocks + Tr. costs).

  15. Usefulness of CAPM • 1- Gives portfolio selection ( ON SML) • 2- Used in judging of weather a stock is under/overvalued • 3- Finding the appropriate discount Rate (k). Valuation. • 4- Finding the correct risk free rate • 5- Finding the value of  • 6- Finding the portfolio's expected return and variance • 1- Finding overvalued or undervalued stocks • 1- Example1: Two assets:  E(R) • ABB 1.3 14% • Telia .8 10% Risk-free= 6%. • Calculate reward-to-risk ratio: • ABB = 14-6/1.3 = 6.15%. • Telia = 10-6/.8= 5% insufficient return (Overvalued)

  16. Usefulness of CAPM • 2- Using the CAPM to Calculate the appropriate Discount Rate (Expected rate of return); k • Example1 : assume the following for Telia: • D1= $5 Forevere div. per share grow at by 10% (g = 10%) • RF= .03 =1.5 E(RM) = .11 • Calculate the required rate of return, E ( R) , cost of equity capital • Price per Share for Telia • (a) • The Po = D1 / (k-g) perpetual • Po = 5 / (k-.10) perpetual • Using Equation (1) : E(R Telia)-RF =  TeliaE(RM)-RF), • E ( RTelia) = k = .03 + 1.5(.11-.03) = 15% • (b) • Po = 5 / (.15-.10) =$100 if correctly priced

  17. Usefulness of CAPM • Example 2. Consider the betas for each of the assets given below. If the risk-free rate is 4.5% and the market risk premium is 8.5%, what is the expected return for each?

  18. Usefulness of CAPM • Example 3. Suppose the risk-free rate is 4%, the market risk premium is 8.6% and a particular stock, say ABB, has a beta () of 1.3. Based on CAPM, what is the expected return on that stock? What is expected return be if the beta() were to double ? • First, if =1.3 • We know that E(R ABB) = RF + ABB(E(RM)-RF)* • where (E(RM)-RF) is the market risk premium • and (E(RM)-RF)* ABB (is ABB risk premium ) • Thus, the risk premium for ABB = 1.3 * 8.6% = 11.18% • E ( R) = 4% +11.18% = 15.18% if correctly priced • Second, if =2.6 • The risk premium for ABB = 2.6 * 8.6% = 22.36% • E ( R) = 4% +22.36% = 26.36%.

  19. Usefulness of CAPM • 5- Finding the value of  • Suppose the risk free rate is 8%. The expected return on the market is 16%. If a particular stock, say Telia, has a beta of 0.7, what is the expected return for Telia based on the CAPM? If another stock, say H&M, has an expected return of 24 %, what must its beta ( ) be? • We know that expected return according to CAPM is: • E(R i) = RF + (E(RM)-RF)* i • The market risk premium = 16% -8% = 8% • The expected return for Telia = 8% +.7 * 8% = 13.6 % • The risk premium for H & M = 24% -8% = 16% • According to CAPM : E(R i) = RF + i(E(RM)-RF) • 24% = 8% + (16%-8%) * i • i= 16% / 8% = 2.0

  20. Usefulness of CAPM • 5- Finding portfolio's systematic risk • Suppose that you invest 1/3 in stock (A) and 2/3 in stock (B). Assume also that βA=.50 and βB=1.5. Expected return for A= 14% and expected return for B = 15%. • What is the expected return of your portfolio? • E( R) P= 1/3(.14) + 2/3(.15)= • ΒP= 1/3(0.50) + 2/3( 1.5)= 1,17 • Finding portfolio's expected return & variance E(RP) = 0.10 (0.08) + 0.20(0.12) + 0.30(0.15)+ 0.40(0.18) = 14.9% BP= 0.10 (0.80) + 0.20(0.95) + 0.30(1.10)+ 0.40(1.40) = 1.16

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