1. Chapter 13. Risk & Return in Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models Portfolio Theory Managing Risk Asset Pricing Models

2. I. Portfolio Theory how does investor decide among group of assets? assume: investors are risk averse additional compensation for risk tradeoff between risk and expected return how does investor decide among group of assets? assume: investors are risk averse additional compensation for risk tradeoff between risk and expected return

3. goalgoal efficient or optimal portfolio for a given risk, maximize exp. return OR for a given exp. return, minimize the risk efficient or optimal portfolio for a given risk, maximize exp. return OR for a given exp. return, minimize the risk

4. toolstools measure risk, return quantify risk/return tradeoff measure risk, return quantify risk/return tradeoff

5. return = R = change in asset value + income initial value Measuring Return R is ex post based on past data, and is known R is typically annualized R is ex post based on past data, and is known R is typically annualized

6. example 1 Tbill, 1 month holding period buy for $9488, sell for $9528 1 month R: Tbill, 1 month holding period buy for $9488, sell for $9528 1 month R: 9528 - 9488 9488 =.0042 =.42%

7. annualized R: (1.0042) 12 - 1 =.052 = 5.2%

8. example 2 100 shares IBM, 9 months buy for $62, sell for $101.50 $.80 dividends 9 month R: 100 shares IBM, 9 months buy for $62, sell for $101.50 $.80 dividends 9 month R: 101.50 - 62 +.80 62 =.65 =65%

9. annualized R: (1.65) 12/9 - 1 =.95 = 95%

10. Expected Return measuring likely future return based on probability distribution random variable measuring likely future return based on probability distribution random variable E(R) =SUM(R i x Prob(R i ))

11. example 1 RProb(R) 10%.2 5%.4 -5%.4 E(R) =(.2)10% + (.4)5% + (.4)(-5%) = 2%

12. example 2 RProb(R) 1%.3 2%.4 3%.3 E(R) =(.3)1% + (.4)2% + (.3)(3%) = 2%

13. examples 1 & 2 same expected return but not same return structure returns in example 1 are more variable same expected return but not same return structure returns in example 1 are more variable

14. RiskRisk measure likely fluctuation in return how much will R vary from E(R) how likely is actual R to vary from E(R) measured by variance (    standard deviation  measure likely fluctuation in return how much will R vary from E(R) how likely is actual R to vary from E(R) measured by variance (    standard deviation 

15.   = SUM[(R i - E(R)) 2 x Prob(R i )]  SQRT(  

16. example 1   = (.2)(10%-2%) 2 =.0039 + (.4)(5%-2%) 2 + (.4)(-5%-2%) 2  = 6.24%

17. example 2   = (.3)(1%-2%) 2 =.00006 + (.4)(2%-2%) 2 + (.3)(3%-2%) 2  =.77%

18. same expected return but example 2 has a lower risk preferred by risk averse investors variance works best with symmetric distributions same expected return but example 2 has a lower risk preferred by risk averse investors variance works best with symmetric distributions

19. symmetricasymmetric E(R) R prob(R) R E(R)

20. II. Managing risk Diversification holding a group of assets lower risk w/out lowering E(R) Diversification holding a group of assets lower risk w/out lowering E(R)

21. Why? individual assets do not have same return pattern combining assets reduces overall return variation Why? individual assets do not have same return pattern combining assets reduces overall return variation

22. two types of risk unsystematic risk specific to a firm can be eliminated through diversification examples: -- Safeway and a strike -- Microsoft and antitrust cases unsystematic risk specific to a firm can be eliminated through diversification examples: -- Safeway and a strike -- Microsoft and antitrust cases

23. systematic risk market risk cannot be eliminated through diversification due to factors affecting all assets -- energy prices, interest rates, inflation, business cycles systematic risk market risk cannot be eliminated through diversification due to factors affecting all assets -- energy prices, interest rates, inflation, business cycles

24. exampleexample choose stocks from NYSE listings go from 1 stock to 20 stocks reduce risk by 40-50% choose stocks from NYSE listings go from 1 stock to 20 stocks reduce risk by 40-50%

25.  # assets systematic risk unsystematic risk total risk

26. measuring relative risk if some risk is diversifiable, then  is not the best measure of risk σ is an absolute measure of risk need a measure just for the systematic component if some risk is diversifiable, then  is not the best measure of risk σ is an absolute measure of risk need a measure just for the systematic component

27. Beta,  variation in asset/portfolio return relative to return of market portfolio mkt. portfolio = mkt. index -- S&P 500 or NYSE index variation in asset/portfolio return relative to return of market portfolio mkt. portfolio = mkt. index -- S&P 500 or NYSE index  = % change in asset return % change in market return

28. interpreting  if  asset is risk free if  asset return = market return if  asset is riskier than market index   asset is less risky than market index if  asset is risk free if  asset return = market return if  asset is riskier than market index   asset is less risky than market index

29. Sample betas (monthly returns, 5 years back)

30. measuring  estimated by regression data on returns of assets data on returns of market index estimate estimated by regression data on returns of assets data on returns of market index estimate

31. problemsproblems what length for return interval? weekly? monthly? annually? choice of market index? NYSE, S&P 500 survivor bias what length for return interval? weekly? monthly? annually? choice of market index? NYSE, S&P 500 survivor bias

32. # of observations (how far back?) 5 years? 50 years? time period? 1970-1980? 1990-2000? # of observations (how far back?) 5 years? 50 years? time period? 1970-1980? 1990-2000?

33. III. Asset Pricing Models CAPM Capital Asset Pricing Model 1964, Sharpe, Linter quantifies the risk/return tradeoff CAPM Capital Asset Pricing Model 1964, Sharpe, Linter quantifies the risk/return tradeoff

34. assumeassume investors choose risky and risk-free asset no transactions costs, taxes same expectations, time horizon risk averse investors investors choose risky and risk-free asset no transactions costs, taxes same expectations, time horizon risk averse investors

35. implicationimplication expected return is a function of beta risk free return market return expected return is a function of beta risk free return market return

36. or is the portfolio risk premium where is the market risk premium

37. so if  portfolio exp. return is larger than exp. market return riskier portfolio has larger exp. return portfolio exp. return is larger than exp. market return riskier portfolio has larger exp. return > >

38. so if  portfolio exp. return is smaller than exp. market return less risky portfolio has smaller exp. return portfolio exp. return is smaller than exp. market return less risky portfolio has smaller exp. return < <

39. so if  portfolio exp. return is same than exp. market return equal risk portfolio means equal exp. return portfolio exp. return is same than exp. market return equal risk portfolio means equal exp. return = =

40. so if  portfolio exp. return is equal to risk free return = 0 =

41. exampleexample R m = 10%, R f = 3%,  = 2.5

42. CAPM tells us size of risk/return tradeoff CAPM tells use the price of risk CAPM tells us size of risk/return tradeoff CAPM tells use the price of risk

43. Testing the CAPM CAPM overpredicts returns return under CAPM > actual return relationship between β and return? some studies it is positive some recent studies argue no relationship (1992 Fama & French) CAPM overpredicts returns return under CAPM > actual return relationship between β and return? some studies it is positive some recent studies argue no relationship (1992 Fama & French)

45. other factors important in determining returns January effect firm size effect day-of-the-week effect ratio of book value to market value other factors important in determining returns January effect firm size effect day-of-the-week effect ratio of book value to market value

46. problems w/ testing CAPM Roll critique (1977) CAPM not testable do not observe E(R), only R do not observe true R m do not observe true R f results are sensitive to the sample period Roll critique (1977) CAPM not testable do not observe E(R), only R do not observe true R m do not observe true R f results are sensitive to the sample period

47. APTAPT Arbitrage Pricing Theory 1976, Ross assume: several factors affect E(R) does not specify factors Arbitrage Pricing Theory 1976, Ross assume: several factors affect E(R) does not specify factors

48. implications E(R) is a function of several factors, F each with its own  implications E(R) is a function of several factors, F each with its own 

49. APT vs. CAPM APT is more general many factors unspecified factors CAPM is a special case of the APT 1 factor factor is market risk premium APT is more general many factors unspecified factors CAPM is a special case of the APT 1 factor factor is market risk premium

50. testing the APT how many factors? what are the factors? 1980 Chen, Roll, and Ross industrial production inflation yield curve slope other yield spreads how many factors? what are the factors? 1980 Chen, Roll, and Ross industrial production inflation yield curve slope other yield spreads

51. summarysummary known risk/return tradeoff how to measure risk? how to price risk? neither CAPM or APT are perfect or free of testing problems both have shown value in asset pricing known risk/return tradeoff how to measure risk? how to price risk? neither CAPM or APT are perfect or free of testing problems both have shown value in asset pricing