1 Risk Aversion and Capital Allocation to Risky

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

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

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

Risk and Risk Aversion • Risk Aversion and Utility Values Portfolio Risk Premium (%) Expected Return (%) Risk (SD) (%) L (Low Risk) 2 7 5 M (Medium Risk) 4 9 10 H (High Risk) 8 13 20

Risk and Risk Aversion • Risk Aversion and Utility Values Portfolio L U = E ( r ) – ½ A 2 Investor Risk Aversion (A) Utility Score Of Portfolio L [E(r) = 0. 07; = 0. 05] 2. 0 . 07 – ½ x 2 x. 052 . 0675 3. 5 07 – ½ x 3. 5 x. 052 . 0656 5. 0 07 – ½ x 5 x. 052 . 0638

Risk and Risk Aversion • Risk Aversion and Utility Values Portfolio M U = E ( r ) – ½ A 2 Investor Risk Aversion (A) Utility Score Of Portfolio L [E(r) = 0. 09; = 0. 10] 2. 0 . 09 – ½ x 2 x. 102 . 0800 3. 5 09 – ½ x 3. 5 x. 102 . 0725 5. 0 09 – ½ x 5 x. 102 . 0650

Risk and Risk Aversion • Risk Aversion and Utility Values Portfolio H U = E ( r ) – ½ A 2 Investor Risk Aversion (A) Utility Score Of Portfolio L [E(r) = 0. 13; = 0. 20] 2. 0 . 13 – ½ x 2 x. 202 . 09 3. 5 . 13 – ½ x 3. 5 x. 202 . 06 5. 0 . 13 – ½ x 5 x. 202 . 03

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

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

Risk and Risk Aversion • Estimating Risk Aversion Expected Return (E(r)) Standard Devi- Utility = E ( r ) - ½ A 2 ation ( ) . 10 . 200 . 10 -. 5 x 4 x. 04 . 02 . 15 . 255 . 02 . 20 . 300 . 02 . 25 . 339 . 02

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

Risk and Risk Aversion • Variance and Standard Deviation p -1 – (-p) = p-1 1 -p 2 ( r ) = p (1 -p) 0 - (-p) = p (6. 3)

Capital Allocation across Risky and Risk -Free Portfolios • The risk of long-term Bonds > the risk of T-Bills Ready Asset Money Market Fund Initial portfolio W to total $ 90, 000 Equities (30%) $ 113, 400 (54%) . 378 $ 300, 000 Risky Securities $ 210, 000 Long-Term bonds (70%) $ 96, 600 (46%) . 322. 70

Portfolios of One Risky Asset and a Risk -Free Asset The Risky rate of return of P The Expected rate of return Standard Deviation The rate of return 0 n the risk free asset Risk Premium rp E (r p) p rf E (r p)-r f 15% 22% 7% 8% Proportion risky portfolio Proportion risk free portfolio y 1 -y 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 + 8 y (6. 8)

Portfolios of One Risky Asset and a Risk -Free Asset The Risky rate of return of P The Expected rate of return Standard Deviation The rate of return 0 n the risk free asset Risk Premium rp E (r p) p rf E (r p)-r f 15% 22% 7% 8% Proportion risky portfolio Proportion risk free portfolio y 1 -y The Expectation of the Standard Deviation of portfolio C = The Standard Deviation of Complete portfolio C = y p = 22 y (6. 9)

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

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

Risk Tolerance and Asset Allocation Utility as function of allocation to the risky asset y Utility . 10 . 05 0 0. 2 0. 4 0. 6 0. 8 Allocation to risky asset 1

21 Bodi Kane Marcus Ch 5 Indifference Curve. 60 Highly risk averse A= 4 A= 2. 30 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 lebih curam) menandakan investor menuntut peningkatan expected return untuk setiap satuan tambahan risiko atau investor relatif lebih enggan terhadap risiko • The higher curve (kurva pada posisi lebih tinggi) menunjukkan tingkat kepuasan yang lebih tinggi

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

Passive Strategies: The Capital Market Line • Menggambarkan keputusan baik yang langsung atau tidak langsung berupaya menghindari pembuatan analisa • Tab 6. 8 • Portofolio yang ditiru : S&P 500; T-Bills

26 Bodi Kane Marcus Ch 5 Tugas Kelompok Klp RDPU RDPT RDC RDS Felix Bahana BNP Paribas Makinta Schroder Venny Schroders Panin Timothy Fortis Manulife Hilda Schroders Mandiri Mathew AXA Fortis Ivana GMT Gentry Batavia Danny Bahana