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Chapter 7

Chapter 7. Capital Asset Pricing. Outline. Beta: the market risk Relationship between risk and return: CAPM Security Market Line: graphic representation of CAPM. 1. Beta. Breaking down sources of risk. Stand-alone risk = Market risk + Firm-specific risk

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Chapter 7

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  1. Chapter 7 Capital Asset Pricing

  2. Outline • Beta: the market risk • Relationship between risk and return: CAPM • Security Market Line: graphic representation of CAPM

  3. 1. Beta

  4. Breaking down sources of risk Stand-alone risk = Market risk + Firm-specific risk • Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta. • Firm-specific risk – portion of a security’s stand-alone risk that can be eliminated through proper diversification.

  5. Beta • Measures a stock’s market risk, and shows a stock’s volatility relative to the market. • Indicates how risky a stock is if the stock is held in a well-diversified portfolio.

  6. Calculating betas • b = [COV(ri,rm)] / sm2 • Run a regression of past returns of a security against past returns on the market. • The slope of the regression line is defined as the beta coefficient for the security.

  7. Comments on beta • If beta = 1.0, the security is just as risky as the average stock. • If beta > 1.0, the security is riskier than average. • If beta < 1.0, the security is less risky than average. • Most stocks have betas in the range of 0.5 to 1.5. • Check beta in real world

  8. Creating a portfolio:Beginning with one stock and adding randomly selected stocks to portfolio • σp decreases as stocks added, because they would not be perfectly correlated with the existing portfolio. • Expected return of the portfolio would remain relatively constant. • Eventually the diversification benefits of adding more stocks dissipates (after about 10 stocks), and for large stock portfolios, σp tends to converge to  20%.

  9. sp (%) Company-Specific Risk 35 Stand-Alone Risk, sp 20 0 Market Risk 10 20 30 40 2,000+ # Stocks in Portfolio Illustrating diversification effects of a stock portfolio

  10. Portfolio beta • Since beta cannot be diversified away, Portfolio beta is the weighted average of individual stock beta. The weight is the proportion of individual stock to whole portfolio.

  11. 2. CAPM

  12. What risk do we care? • Stand alone? • Risk that can not be diversified?

  13. Capital Asset Pricing Model (CAPM) • Model based upon concept that a stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversification.

  14. Capital Asset Pricing Model (CAPM) • Model linking risk and required returns. CAPM suggests that a stock’s required return equals the risk-free return plus a risk premium that reflects the stock’s risk after diversification. ri = rRF + (rM – rRF) bi • Ri: required return of stock i • rM : Expected return of the market • Risk premium RP: additional return to take additional risk • The market (or equity) risk premium is (rM – rRF)

  15. Calculating required rates of return • Risk free rate:5.5%, market return:10.5%

  16. Calculating required rates of return • rHT = 5.5% + (5.0%)(1.32) = 5.5% + 6.6% = 12.10% • rM = 5.5% + (5.0%)(1.00) = 10.50% • rUSR = 5.5% + (5.0%)(0.88) = 9.90% • rT-bill = 5.5% + (5.0%)(0.00) = 5.50% • rColl = 5.5% + (5.0%)(-0.87) = 1.15%

  17. Applying CAPM • Computing other variables: risk free rate, market return, market risk premium • Computing the difference of return between two stocks. • Computing price in the future when current price is given

  18. 3. SML

  19. Security Market Line E(r) SML E(rM) rf ß ß = 1.0 M

  20. SML Relationships b = [COV(ri,rm)] / sm2 Slope SML = E(rm) - rf = market risk premium SML = rf + b[E(rm) - rf]

  21. Sample Calculations for SML E(rm) - rf = .08 rf = .03 bx = 1.25 E(rx) = .03 + 1.25(.08) = .13 or 13% by = .6 e(ry) = .03 + .6(.08) = .078 or 7.8%

  22. Graph of Sample Calculations E(r) SML Rx=13% .08 Rm=11% Ry=7.8% 3% ß .6 1.0 1.25 ß ß ß y m x

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