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Risk Aversion and Capital Allocation to Risky Asset

Risk Aversion and Capital Allocation to Risky Asset. Chapter 6. Risk and Risk Aversion. Risk, Speculation, and Gambling Risk Aversion and Utility Values Estimating Risk Aversion . Risk and Risk Aversion. Risk, Speculation, and Gambling

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Risk Aversion and Capital Allocation to Risky Asset

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  1. Risk Aversion and Capital Allocation to Risky Asset Chapter 6 Bodi Kane Marcus Ch 5

  2. Risk and Risk Aversion • Risk, Speculation, and Gambling • Risk Aversion and Utility Values • Estimating Risk Aversion

  3. Risk and Risk Aversion • Risk, Speculation, and Gambling • Risk: The chance that an investment's actual return will be different than expected. • Speculation: the assumption consider-able investment risk to obtain commensurate gain • Considerable = the risk is sufficient to affect the decision • Gamble = bet or wager on an uncertain outcome • Speculation gambling

  4. Risk and Risk Aversion • Risk Aversion and Utility Values

  5. Risk and Risk Aversion • Risk Aversion and Utility Values Portfolio L U = E ( r ) – ½ A 2

  6. Risk and Risk Aversion • Risk Aversion and Utility Values Portfolio M U = E ( r ) – ½ A 2

  7. Risk and Risk Aversion • Risk Aversion and Utility Values Portfolio H U = E ( r ) – ½ A 2

  8. Risk Aversion and Utility Values • The Trade-off Risk and Return P I II E(r p) III IV p

  9. Risk Aversion and Utility Values Indifference Curve • Indifference Curve Q E(r p) P p

  10. Risk and Risk Aversion • Estimating Risk Aversion

  11. Risk and Risk Aversion • Rate of Return r (loss) = -1 (i.e., -100%) p 1-p r (no loss) = 0 E (r ) = p x (-1) + (1-p) x 0 = -p

  12. Risk and Risk Aversion • Variance and Standard Deviation -1 – (-p) = p-1 p 1-p 0- (-p) = p 2 ( r ) = p (1-p) (6.3)

  13. Capital Allocation across Risky and Risk-Free Portfolios • The risk of long-term Bonds > the risk of T-Bills

  14. Portfolios of One Risky Asset and a Risk-Free Asset • The Expectation of the portfolio rate of return • E ( r C ) = The Complete portfolio • E ( r C ) = y.E( R p ) + (1-y) r f = rf + y [ E (rp) –rf ]= 7 + y ( 15-7) = 7 + 8y (6.8)

  15. Portfolios of One Risky Asset and a Risk-Free Asset • The Expectation of the Standard Deviation of portfolio • C = The Standard Deviation ofComplete portfolio • C = y p = 22y (6.9)

  16. Bodi Kane Marcus Ch 5 Portfolios of One Risky Asset and a Risk-Free Asset • If investor: • Invest solely in the risky asset; y = 1 ; the complete portfolio = P • Invest y = 0; (1-y) = 1; the complete portfolio = the risk free portfolio = F • The extra return per extra risk = 8/22 = .36

  17. Bodi Kane Marcus Ch 5 Portfolios of One Risky Asset and a Risk-Free Asset • The extra return per extra risk = 8/22 E ( r C ) = rf +y [ E (rp) –rf ] = rf + c /p [ E (rp) –rf] = 7 + 8/22 c (6.10)

  18. Bodi Kane Marcus Ch 5 Portfolios of One Risky Asset and a Risk-Free Asset CAL = Capital Allocation Line E(r p) =15% P E(r p )-r f = 8% r f = 7% F  p = 22%

  19. Bodi Kane Marcus Ch 5 Portfolios of One Risky Asset and a Risk-Free Asset Differential borrowing and lending rates CAL E(r p) =15% P S(y > 1) = .27 rBf = 9% S(y  1) = .36 r f = 7%  p = 22%

  20. Risk Tolerance and Asset Allocation Utility as function of allocation to the risky asset y .10 .05 0 Utility Allocation to risky asset 0.2 0.4 0.6 0.8 1

  21. Bodi Kane Marcus Ch 5 Indifference Curve A= 4 .60 .30 Highly risk averse A= 4 A= 2 A= 2 Slightly risk averse U =.09 U =.05 0 .10 .20 .30

  22. Bodi Kane Marcus Ch 5 Note Fig 6.7 • Steeper curve (kurva yang lebihcuram) menandakan investor menuntutpeningkatan expected return untuk setiap satu satuantambahanrisikoatau investor relatiflebihengganterhadaprisiko • The higher curve (kurvapadaposisilebihtinggi) menunjukkantingkatkepuasan yang lebihtinggi

  23. Bodi Kane Marcus Ch 5 Table 6.6 • Expected return of : • Given Risk Aversion (A) • Given Utility (U) • Certain Standard Deviation () • Higher risk (standard deviation)  higher Expected return • It is possible the same risk aversion (A= 4) has different Utility (U = .05 and U= .09)

  24. Bodi Kane Marcus Ch 5 Finding optimal complete portfolio CAL E(r p )= 15% E(r C= .1028 r f = 7%  C = .0902  p = .22

  25. Passive Strategies: The Capital Market Line • Menggambarkankeputusanbaik yang langsungatau tidak langsungberupayamenghindaripembuatananalisa • Tab 6.8 • Portofolio yang ditiru : S&P 500; T-Bills

  26. Bodi Kane Marcus Ch 5 Tugas Kelompok

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