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[object Object],[object Object],[object Object],[object Object],[object Object],CHAPTER 2  Risk and Return: Part I
What are investment returns? ,[object Object],[object Object],[object Object],[object Object],[object Object]
What is the return on an investment that costs $1,000 and is sold after 1 year for $1,100? ,[object Object],[object Object],$ Received  -  $ Invested $1,100  -  $1,000  =  $100 . $ Return/$ Invested $100/$1,000  =  0.10  =  10% .
What is investment risk? ,[object Object],[object Object],[object Object]
Probability distribution Rate of return (%) 50 15 0 -20 Stock X Stock Y ,[object Object]
Assume the Following Investment Alternatives Economy Prob. T-Bill Alta Repo Am F. MP Recession 0.10 8.0% -22.0% 28.0% 10.0% -13.0% Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0 Average 0.40 8.0 20.0 0.0 7.0 15.0 Above avg. 0.20 8.0 35.0 -10.0 45.0 29.0 Boom 0.10 8.0 50.0 -20.0 30.0 43.0 1.00
What is unique about  the T-bill return? ,[object Object],[object Object]
Do the returns of Alta Inds. and Repo Men move with or counter to the economy? ,[object Object],[object Object]
Calculate the expected rate of return on each alternative. r = expected rate of return. r Alta  = 0.10(-22%) + 0.20(-2%)   + 0.40(20%) + 0.20(35%)   + 0.10(50%) =  17.4% . ^ ^
[object Object],[object Object],^ r Alta 17.4% Market 15.0 Am. Foam 13.8 T-bill 8.0 Repo Men 1.7
What is the standard deviation of returns for each alternative?
Alta Inds:    = ((-22 - 17.4) 2 0.10 + (-2 - 17.4) 2 0.20 + (20 - 17.4) 2 0.40 + (35 - 17.4) 2 0.20 + (50 - 17.4) 2 0.10) 1/2  = 20.0%.  T-bills  =  0.0%.  Alta  = 20.0%.  Repo = 13.4%.  Am Foam = 18.8%.  Market = 15.3%.
Prob. Rate of Return (%) T-bill Am. F. Alta 0 8 13.8 17.4
[object Object],[object Object],[object Object]
Expected Return versus Risk Expected Security return Risk,   Alta Inds. 17.4% 20.0% Market 15.0 15.3 Am. Foam 13.8 18.8 T-bills 8.0 0.0 Repo Men  1.7 13.4
Coefficient of Variation: CV = Expected return/standard deviation. ,[object Object],[object Object],[object Object],[object Object],[object Object]
Expected Return versus Coefficient of Variation Expected Risk: Risk: Security return  CV Alta Inds 17.4% 20.0% 1.1 Market 15.0 15.3 1.0 Am. Foam 13.8 18.8 1.4 T-bills 8.0 0.0 0.0 Repo Men  1.7 13.4 7.9
Return vs. Risk (Std. Dev.):  Which investment is best?
Portfolio Risk and Return Assume a two-stock portfolio with $50,000 in Alta Inds. and $50,000 in Repo Men. Calculate r p  and   p . ^
Portfolio Return, r p r p  is a weighted average: r p  = 0.5(17.4%) + 0.5(1.7%) =  9.6% . r p  is between r Alta  and r Repo . ^ ^ ^ ^ ^ ^ ^ ^ r p  =    w i r i  n i = 1
Alternative Method r p  = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40 + (12.5%)0.20 + (15.0%)0.10 =  9.6% . ^ Estimated Return (More...) Economy Prob. Alta Repo Port. Recession 0.10 -22.0% 28.0% 3.0% Below avg. 0.20 -2.0 14.7 6.4 Average 0.40 20.0 0.0 10.0 Above avg. 0.20 35.0 -10.0 12.5 Boom 0.10 50.0 -20.0 15.0
[object Object],[object Object],[object Object],[object Object],[object Object]
Two-Stock Portfolios ,[object Object],[object Object],[object Object],[object Object],[object Object]
What would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added? ,[object Object],^
Large 0 15 Prob. 2 1  1    35% ;   Large    20%. Return
# Stocks in Portfolio 10 20 30  40   2,000+ Company Specific (Diversifiable) Risk Market Risk 20 0 Stand-Alone Risk,   p  p  (%) 35
Stand-alone  Market  Diversifiable Market risk  is that part of a security’s stand-alone risk that  cannot  be eliminated by diversification. Firm-specific , or  diversifiable , risk is that part of a security’s stand-alone risk that  can  be eliminated by diversification. risk  risk  risk  =  +  .
Conclusions ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],Can an investor holding one stock earn a return commensurate with its risk?
[object Object],[object Object],[object Object],How is market risk measured for individual securities?
How are betas calculated?  ,[object Object]
Using a Regression to Estimate Beta ,[object Object],[object Object]
Use the historical stock returns to calculate the beta for PQU. Year Market PQU 1 25.7% 40.0% 2 8.0% -15.0% 3 -11.0% -15.0% 4 15.0% 35.0% 5 32.5% 10.0% 6 13.7% 30.0% 7 40.0% 42.0% 8 10.0% -10.0% 9 -10.8% -25.0% 10 -13.1% 25.0%
Calculating Beta for PQU r PQU = 0.83r M + 0.03 R 2 = 0.36 -40% -20% 0% 20% 40% -40% -20% 0% 20% 40% r M r KWE
What is beta for PQU? ,[object Object]
Calculating Beta in Practice ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],How is beta interpreted?
Finding Beta Estimates on the Web ,[object Object],[object Object],[object Object]
Expected Return versus Market Risk ,[object Object],Expected Security return Risk, b HT 17.4% 1.29 Market 15.0 1.00 USR 13.8 0.68 T-bills 8.0 0.00 Collections  1.7 -0.86
Use the SML to calculate each alternative’s required return. ,[object Object],[object Object],[object Object],[object Object],^
Required Rates of Return r Alta   =  8.0% + (7%)(1.29) =  8.0% + 9.0% =  17.0%. r M =  8.0% + (7%)(1.00) =  15.0%. r Am. F. =  8.0% + (7%)(0.68) =  12.8%. r T-bill =  8.0% + (7%)(0.00) =  8.0%. r Repo =  8.0% + (7%)(-0.86) =  2.0%.
Expected versus Required Returns ^ r  r Alta 17.4% 17.0% Undervalued  Market 15.0 15.0 Fairly valued Am. F. 13.8 12.8 Undervalued T-bills 8.0 8.0 Fairly valued Repo 1.7 2.0 Overvalued
. . Repo . Alta T-bills . Am. Foam r M   = 15 r RF  =  8 -1    0   1   2 . SML: r i  = r RF  + (RP M ) b i r i  = 8%   + (7%) b i r i  (%) Risk, b i SML and Investment Alternatives Market
Calculate beta for a portfolio with 50% Alta and 50% Repo b p = Weighted average = 0.5(b Alta ) + 0.5(b Repo ) = 0.5(1.29) + 0.5(-0.86) =  0.22 .
What is the required rate of return on the Alta/Repo portfolio? r p =  Weighted average r = 0.5(17%) + 0.5(2%)  =  9.5% . Or use SML: r p =  r RF  + (RP M ) b p = 8.0% + 7%(0.22) =  9.5% .
SML 1 Original situation Required Rate  of Return r (%) SML 2 0 0.5 1.0 1.5 2.0 18 15 11 8 New SML    I = 3% Impact of Inflation Change on SML
r M   = 18% r M   = 15% SML 1 Original situation Required Rate of Return (%) SML 2 After increase in risk aversion Risk, b i 18 15 8 1.0    RP M  = 3% Impact of Risk Aversion Change
Has the CAPM been completely confirmed or refuted through empirical tests? ,[object Object],[object Object],[object Object]

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Pk

  • 1.
  • 2.
  • 3.
  • 4.
  • 5.
  • 6. Assume the Following Investment Alternatives Economy Prob. T-Bill Alta Repo Am F. MP Recession 0.10 8.0% -22.0% 28.0% 10.0% -13.0% Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0 Average 0.40 8.0 20.0 0.0 7.0 15.0 Above avg. 0.20 8.0 35.0 -10.0 45.0 29.0 Boom 0.10 8.0 50.0 -20.0 30.0 43.0 1.00
  • 7.
  • 8.
  • 9. Calculate the expected rate of return on each alternative. r = expected rate of return. r Alta = 0.10(-22%) + 0.20(-2%) + 0.40(20%) + 0.20(35%) + 0.10(50%) = 17.4% . ^ ^
  • 10.
  • 11. What is the standard deviation of returns for each alternative?
  • 12. Alta Inds:  = ((-22 - 17.4) 2 0.10 + (-2 - 17.4) 2 0.20 + (20 - 17.4) 2 0.40 + (35 - 17.4) 2 0.20 + (50 - 17.4) 2 0.10) 1/2 = 20.0%.  T-bills = 0.0%.  Alta = 20.0%.  Repo = 13.4%.  Am Foam = 18.8%.  Market = 15.3%.
  • 13. Prob. Rate of Return (%) T-bill Am. F. Alta 0 8 13.8 17.4
  • 14.
  • 15. Expected Return versus Risk Expected Security return Risk,  Alta Inds. 17.4% 20.0% Market 15.0 15.3 Am. Foam 13.8 18.8 T-bills 8.0 0.0 Repo Men 1.7 13.4
  • 16.
  • 17. Expected Return versus Coefficient of Variation Expected Risk: Risk: Security return  CV Alta Inds 17.4% 20.0% 1.1 Market 15.0 15.3 1.0 Am. Foam 13.8 18.8 1.4 T-bills 8.0 0.0 0.0 Repo Men 1.7 13.4 7.9
  • 18. Return vs. Risk (Std. Dev.): Which investment is best?
  • 19. Portfolio Risk and Return Assume a two-stock portfolio with $50,000 in Alta Inds. and $50,000 in Repo Men. Calculate r p and  p . ^
  • 20. Portfolio Return, r p r p is a weighted average: r p = 0.5(17.4%) + 0.5(1.7%) = 9.6% . r p is between r Alta and r Repo . ^ ^ ^ ^ ^ ^ ^ ^ r p =   w i r i  n i = 1
  • 21. Alternative Method r p = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40 + (12.5%)0.20 + (15.0%)0.10 = 9.6% . ^ Estimated Return (More...) Economy Prob. Alta Repo Port. Recession 0.10 -22.0% 28.0% 3.0% Below avg. 0.20 -2.0 14.7 6.4 Average 0.40 20.0 0.0 10.0 Above avg. 0.20 35.0 -10.0 12.5 Boom 0.10 50.0 -20.0 15.0
  • 22.
  • 23.
  • 24.
  • 25. Large 0 15 Prob. 2 1  1  35% ;  Large  20%. Return
  • 26. # Stocks in Portfolio 10 20 30 40 2,000+ Company Specific (Diversifiable) Risk Market Risk 20 0 Stand-Alone Risk,  p  p (%) 35
  • 27. Stand-alone Market Diversifiable Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification. Firm-specific , or diversifiable , risk is that part of a security’s stand-alone risk that can be eliminated by diversification. risk risk risk = + .
  • 28.
  • 29.
  • 30.
  • 31.
  • 32.
  • 33. Use the historical stock returns to calculate the beta for PQU. Year Market PQU 1 25.7% 40.0% 2 8.0% -15.0% 3 -11.0% -15.0% 4 15.0% 35.0% 5 32.5% 10.0% 6 13.7% 30.0% 7 40.0% 42.0% 8 10.0% -10.0% 9 -10.8% -25.0% 10 -13.1% 25.0%
  • 34. Calculating Beta for PQU r PQU = 0.83r M + 0.03 R 2 = 0.36 -40% -20% 0% 20% 40% -40% -20% 0% 20% 40% r M r KWE
  • 35.
  • 36.
  • 37.
  • 38.
  • 39.
  • 40.
  • 41. Required Rates of Return r Alta = 8.0% + (7%)(1.29) = 8.0% + 9.0% = 17.0%. r M = 8.0% + (7%)(1.00) = 15.0%. r Am. F. = 8.0% + (7%)(0.68) = 12.8%. r T-bill = 8.0% + (7%)(0.00) = 8.0%. r Repo = 8.0% + (7%)(-0.86) = 2.0%.
  • 42. Expected versus Required Returns ^ r r Alta 17.4% 17.0% Undervalued Market 15.0 15.0 Fairly valued Am. F. 13.8 12.8 Undervalued T-bills 8.0 8.0 Fairly valued Repo 1.7 2.0 Overvalued
  • 43. . . Repo . Alta T-bills . Am. Foam r M = 15 r RF = 8 -1 0 1 2 . SML: r i = r RF + (RP M ) b i r i = 8% + (7%) b i r i (%) Risk, b i SML and Investment Alternatives Market
  • 44. Calculate beta for a portfolio with 50% Alta and 50% Repo b p = Weighted average = 0.5(b Alta ) + 0.5(b Repo ) = 0.5(1.29) + 0.5(-0.86) = 0.22 .
  • 45. What is the required rate of return on the Alta/Repo portfolio? r p = Weighted average r = 0.5(17%) + 0.5(2%) = 9.5% . Or use SML: r p = r RF + (RP M ) b p = 8.0% + 7%(0.22) = 9.5% .
  • 46. SML 1 Original situation Required Rate of Return r (%) SML 2 0 0.5 1.0 1.5 2.0 18 15 11 8 New SML  I = 3% Impact of Inflation Change on SML
  • 47. r M = 18% r M = 15% SML 1 Original situation Required Rate of Return (%) SML 2 After increase in risk aversion Risk, b i 18 15 8 1.0  RP M = 3% Impact of Risk Aversion Change
  • 48.

Editor's Notes

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