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σ (r)

E(r). Expected return %. C. MVP. B. A. 10%. σ (r). 15%. Standard deviation of return. E(r). N. Expected return %. W. Consolidated. Q. MVP. Brown. Z. Acme. σ (r). 10% 20% 30% 40% 50%. Standard deviation of return. Portfolio weight in stock B.

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σ (r)

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  1. E(r) Expected return % C MVP B A 10% σ(r) 15% Standard deviation of return

  2. E(r) N Expected return % W Consolidated Q MVP Brown Z Acme σ(r) 10% 20% 30% 40% 50% Standard deviation of return

  3. Portfolio weight in stock B Portfolio weight in stock B XB XB Y’ Y’ 1.00 1.00 R Q Q L L U U T -1.00 -1.00 S S 1.00 1.00 XA XA 0 0 Portfolio weight in stock A Portfolio weight in stock A X X -1.00 -1.00

  4. Portfolio weight in stock B XB 1.00 1.00 XA 0 -1.00 Portfolio weight in stock A Isoexpected return line 10% 12% -1.00 16% 18% 20%

  5. Portfolio weight in stock B XB 30% W 28% 26% 21% 17% C MVP Portfolio weight in stock A 0 1.00 -1.00 XA X B

  6. XB 30% 28% 26% 21% 1.00 Isovariance ellipse N W 17% MVP Q Z Critical Line Y 0 XA -1.00 1.00 0.5 -0.5 F -0.5 E Isoexpected return line D -1.00 10% 12% 16% 20% 18%

  7. Portfolio weight in stock B XB 1.0 R Q Z -1.00 S T XA -.5 0 .5 1.0 Portfolio weight in stock A -1.00

  8. E(r) N Expected return % W Consolidated Q MVP Brown Z Acme σ(r) 10% 20% 30% 40% 50% Standard deviation of return

  9. Portfolio weight in stock B XB R B 1.0 Q Z S C T A XA -1.00 1.0 -.5 0 .5 E(r) N -1.00 Expected return % W CS Q MVP BR Z AT σ(r) 10% 20% 30% 40% 50% Standard deviation of return

  10. 資本市場線(CML) • 一個無風險資產， N個風險性資產(投資組合M)下的效率前緣

  11. CML v. s. SML(CAPM) • CML: • SML:

  12. FIGURE 8.8 CAPITAL MARKET LINE FIGURE 8.9 SECURITY MARKET LINE E (γ) E (γ) Capital market line 17.5% A M E (γM ) M 15% = E (γM ) Security market line E (γM) ﹣γF Expected return 10% =γF γF βM=1.00 σ (γ) β o o 1 1.5 Standard deviation Beta

  13. CAPM v.s.Market Model • 同:均與市場組合報酬有關 • 異:1.截距項 2.均衡概念(CAPM); 無 3.殘差項相關(CAPM); 獨立

  14. SML v.s. Characteristic line

  15. FIGURE 8.10 CHARACTERISTIC LINES UNDER THE CAPITAL ASSET PRICING MODEL γJ A B E(γA ) E(γB ) 10% =γF = E(γB ) C 5% γM o γF E(γM ) Market return -10%

  16. FIGURE 8.11 POSITIONS OF INDIVIDUAL STOCKS IN E(γ), σ (γ) SPACE E(γ) CML A A’ 17.5% β = 1.50 M 15% = E(γM ) β = 1.00 Expected return β = .50 10% =γF β = .00 σ (γ) 15% 22.5% 30% Standard deviation

  17. SML(CAPM) in (E (r), σ)

  18. FIGURE 8.12 POSITIONS OF STOCKS ACCORDING TO THEIR CORRELATION COEFFICIENTS E(γ) ρ = 1.00 Capital market line M ρ = .50 γF Expected return ρ = .00 ρ = -.50 σ (γ) o Standard deviation ρ = -1.00

  19. 資本資產定價模式(CAPM) • Where is the price?

  20. FIGURE 8.13 MARKET PRESSURE TO FORCE A STOCK TO ITS EQUILIBRIUM PRICE A E(γ) E(γ) Capital market line M’ B M 15% C’ γF= 10% C 5% σ (γ) o .10 Standard deviation C’’

  21. CAPM之應用 • 投資風險評估－系統風險(貝他係數) • 投資績效評估－風險調整績效評估 • Jensen Index • Treynor Index • Sharpe Index • 資本預算評估－估計權益資金成本

  22. 風險控管 • 個別風險；非系統風險－ 分散多種證券(cross-sectional diversification) 例如，共同基金；ETF。 • 市場風險；非系統風險－分散不同時間點(time-series diversification) 。 例如，定時定額投資；期貨避險。 • What risk take , what return make

  23. 投資績效評估－風險調整績效評估 • Jensen Index (Based on CAPM) • Treynor Index • Sharpe Index

  24. Jensen Index • Based on CAPM(SML) • 母體 • 樣本

  25. FIGURE 11.4 ESTIMATED SML (BULL MARKET) γP B Average portfolio return A o βP Portfolio beta

  26. Treynor Index • Based on CAPM(SML) • 母體 • 樣本

  27. FIGURE 11.6 LEVERING ALPHA TO DOMINATE OMEGA A’’ E(γ) O’ A’ M Expected return γF β o 1.00 1.50 Beta

  28. Sharpe Index • Based on CAPM(CML) • 母體 • 樣本

  29. FIGURE 11.7 PERFORMANCE OF ALPHAAND OMEGA ACCORDING TOTHE SHARPE INDEX E(γ) O’ O M A’ Expected return A γF σ (γ) o Standard deviation

  30. 資本預算－估計權益資金成本 • 估計β ，依CAPM決定權益資金成本E(r) • 預測投資方案現金流量，估計淨現值(NPV)

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