1 / 50

Try these problems

Try these problems. Ch 6 Problem 6 Problem 12 Problems 14-16 (see p 157) Ch 7 Problem 1 Problem 5. New York University/ING Barings. Portfolio Diversification and the Capital Asset Pricing Model. Prof. Ian Giddy New York University. Equity Risk and Return: Summary.

rudyard-tate
Télécharger la présentation

Try these problems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Try these problems • Ch 6 • Problem 6 • Problem 12 • Problems 14-16 (see p 157) • Ch 7 • Problem 1 • Problem 5

  2. New York University/ING Barings Portfolio Diversificationand theCapital Asset Pricing Model Prof. Ian Giddy New York University

  3. Equity Risk and Return: Summary • Investors diversify, because you get a better return for a given risk. • There is a fully-diversified “market portfolio” that we should all choose • The risk of an individual asset can be measured by how much risk it adds to the “market portfolio.”

  4. Capital Allocation Possibilities:Treasuries or an Equity Fund? Expected Return THE EQUITY FUND E(rP) =17% P 10% rf=7% 7% sP=27% Risk

  5. We Can Buy Some T-bills and Some of the Risky Fund... E(R) ONE PORTFOLIO: 30% Bills, 70% Fund E(R)=.3X7+.7X17=14% SD=.7X27=18.9% C.A.L. SLOPE=0.37 17% 14% rf=7% 18.9% 27% SD

  6. ...Or Buy Two Risky Assets E(r) A B

  7. k k k Diversification Portfolio of Assets F and G Asset F Asset G R e t u r n R e t u r n R e t u r n Time Time Time

  8. Portfolio Return... To compute the return of a portfolio: use the weighted average of the returns of all assets in the portfolio, with the weight given each asset calculated as (value of asset)/(value of portfolio). The portfolio return E(Rp) is: E(Rp) = (w1k1)+(w2k2)+ ... (wnkn) = S wj kj where wj = weight of asset j, kj = return on asset j

  9. ...and Risk (Standard Deviation) • Portfolio return is the weighted average of all assets’ returns, • But portfolio standard deviation is normally less than the weighted average of all assets’ standard deviations! • The reason: asset returns are imperfectly correlated.

  10. Measuring Portfolio Risk The variance of a 2-asset portfolio is: where wAand wBare the weights of A and B in the portfolio.

  11. Return and Risk, Generalized Portfolio return: where wi are the weights of each asset in the portfolio. (Expected return is simply the weighted sum of the individual asset returns.) Portfolio variance: When i = j, the term wiwjFiFjDijbecomes wi2Fi2.

  12. Covariance and Correlation The correlation coefficient scales the covariance to a value between -1 and +1:

  13. Risk and Return of Stocks,Bondsand a Diversified Portfolio

  14. The Correlation Between Stock and Bond Returns • Covariance = 0.3333(-7-11)(17-7) + 0.3333(12-11)(7-7) +0.3333(28-11)(-3-7) = -116.67 • Correlation= -116.66 / 14.3(8.2) = -0.99

  15. Portfolio Return and Standard Deviation

  16. Attainable Set of Risk/Return Combinations E(r) A B

  17. The Minimum-Variance Frontier of Risky Assets E(r) Efficient frontier Individual assets Global minimum-variance portfolio

  18. The Efficient Frontier of Risky Assets with the Optimal CAL E(r) CAL(P) Efficient frontier

  19. E(r) CAL(P) The Capital Asset Pricing Model (CAPM) CAPM Says: • The total risk of a financial asset is made up of two components. A. Diversifiable (unsystematic) risk B. Nondiversifiable (systematic) risk • The only relevant risk is nondiversifiable risk.

  20. Types of Risk TOTAL RISK P o r t f o l i o R i s k skp { DIVERSIFIABLE RISK } } NONDIVERSIFIABLE RISK 1 5 10 15 20 25 Number of Securities (Assets) in Portfolio

  21. The Model: CAPM The CAPM (Capital Asset Pricing Model) links together nondiversifiable risk and return for all assets: A. Beta Coefficient (b) is a relative measure of nondiversifiable risk; an index of the change of an asset's return in response to a change in the market return B. Market Return (km) is the return on the market portfolio of all traded securities

  22. Required Return, R(%) SML 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 } Rz = Rm = } Asset Z’s Risk Premium: 6% Market Risk Premium: 4% RF = 0 .50 1.0 1.5 2.0 . . . bm bz bRF Security Market Line Nondiversifiable Risk, b

  23. The Equation for the CAPM Rj = RF+ bj(Rm - RF) where: Rj = Required return on asset j; RF= Risk-free rate of return bj= Beta Coefficient for asset j; Rm = Market return The term [bj(Rm - RF)] is called the risk premium and (Rm-RF) is called the market risk premium

  24. Silicon Graphics Consider an investment in Silicon Graphics. It has a Beta of 2.0 (riskier than the average stock). If the T-bill rate is 5% and the S&P return is 10%, what is the required return for Silicon Graphics stock? kj = .05 + [2.0 x (.10-.05)] = .05 + [2.0 x (.05)] = .05 + .10 = .15 or 15%

  25. Graphic Depiction of CAPM Security Market Line REQUIRED RETURN } 15% Rj with bj = 2.0 10% Rm 5% RF Given: RF = 5%; Rm = 10% SML = Rj= .05 + bj(.10-.05) Stock’s Risk Premium: 10% } Market Risk Premium: 5% 0 .50 1.0 1.5 2.0 . . . Beta (Nondiversifiable Risk)

  26. Interpreting Beta • Market Beta = 1.0 = average level of risk • A Beta of .5 is half as risky as average • A Beta of 2.0 is twice as risky as average • A negative Beta asset moves in opposite direction to market

  27. Finding Beta: Example You have found the following data relative to the stock of the Telmex Corp. and current conditions: Required/expected return = 20% Market portfolio return = 11% Risk premium for market portfolio = 6% What is the Beta of Telmex stock?

  28. Determine the Risk-Free Rate Ri = Rf + bi(RM - Rf) Algebraic Solution Graphic Solution Rm - RF = .06 .11 - RF = .06 RF = .05 SML Rm =11% Rf = 5% } 6% } 5% 1.0 Beta

  29. Plug into SML Formula .20 = .05 + [Beta x (.11 - .05)] .15 = Beta x (.06) .15 = Telmex Beta 2.5 .06

  30. New York University/ING Barings Portfolio TheoryAssignment Prof. Ian Giddy New York University

  31. Try these problems • Ch 6 • Problem 6 • Problem 12 • Problems 14-16 (see p 157) • Ch 7 • Problem 1 • Problem 5

  32. BKM Chapter 6, Problem 6 E(r) Optimal CAL A. If rG,S<+1, gold is still an attractive asset to hold as part of a portfolio. P Stocks Gold E(r) Optimal CAL B. If rG,S=+1, a portfolio of stocks and bills only dominates a portfolio with gold in all instances P Stocks Gold

  33. BKM Chapter 6, Problem 12 RA-Rf A Since B’s error is small, diversification effect is less than for A, which has large unsystematic risk. RM-Rf Stock A has a large error term so would be very risky if all funds were in this one basket. B RB-Rf RM-Rf

  34. BKM, Chapter 6, Problem 14 Most diversification achieved with 1st 20 stocks By choosing low-correlated assets in the portfolio, risk may not be affected significantly. But would these be the best-return stocks? P o r t f o l i o R i s k skp 1 5 10 15 20 Number of Securities (Assets) in Portfolio

  35. BKM, Chapter 6, Problem 15 The risk/number of stocks relationship is nonlinear, so risk increases as number of stock is further reduced P o r t f o l i o R i s k skp 1 5 10 15 20 Number of Securities (Assets) in Portfolio

  36. BKM, Chapter 6, Problem 16 E(r) Hennessy’s portfolio Limiting Hennessy’s holdings may have little impact on the risk of the total portfolio

  37. BKM, Chapter 7, Problem 1 E(RP) = Rf + b[E(RM) - Rf] 20 = 5 + b(15-5) b =15/10 = 1.5

  38. BKM, Chapter 7, Problem 5

  39. BKM, Chapter 7, Problem 5 • ) The beta is the change in the stock return per change in the market return. Therefore:bAggressive= (2-32)/(5-20) = 2.00bDefensive = (3.5-14)/(5-20) = .70 • ) The expected return is an average of the two possible outcomes: E(RAgg.) = .5(2+32) = 17% E(RDef.) = .5(3.5+14) = 8.75%

  40. BKM, Chapter 7, Problem 5 • / The SML is determined by the market expected return of .5(20+5) = 12.5%, with a beta of 1, and the bill return of 8%. Therefore, the equation for the security market line is: E(R) = 8 + b(12.5 - 8)

  41. BKM, Chapter 7, Problem 5 E(r) SML A 17% M 12.5% D 8% b .7 1.0 2.0

  42. A SML E(r) M 12.5% aD D 8% .7 1.0 2.0 BKM, Chapter 7, Problem 5 • /

  43. BKM, Chapter 7, Problem 5 • / The hurdle rate is determined by the project beta .7. The correct discount rate is 11.15%, the fair return on the defensive stock.

  44. Equity Risk and Return: Summary • Investors diversify, because you get a better return for a given risk. • There is a fully-diversified “market portfolio” that we should all choose • The risk of an individual asset can be measured by how much risk it adds to the “market portfolio” • The CAPM tells us how the required return relates to the relevant risk.

  45. www.giddy.org

  46. www.giddy.org Ian Giddy NYU Stern School of Business Tel 212-998-0704; Fax 212-995-4220 igiddy@stern.nyu.edu http://www.giddy.org

More Related