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

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

XAXA Portfolio weight in stock B 1.00 Q U S L Y’ XBXB Portfolio weight in stock A 0 X XAXA Portfolio weight in stock B 1.00 Q U S L Y’ XBXB Portfolio weight in stock A 0 X T R

1.00 XBXB Portfolio weight in stock A 0 XAXA Portfolio weight in stock B Isoexpected return line 10% 12% 16% 18% 20%

B XBXB MVP XAXA 30% 28% 21% 26% 17% C W X Portfolio weight in stock A Portfolio weight in stock B

XBXB MVP XAXA 30% 28% 21% 26% 17% Q W N Z Y Critical Line -0.5 Isovariance ellipse Isoexpected return line 10% 12% 16% 18% 20% D E F -0.5

XAXA Portfolio weight in stock B 1.0 Q S Z XBXB Portfolio weight in stock A R T

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

XAXA Portfolio weight in stock B 1.0 Q S Z XBXB R T AA CC BB Standard deviation of return E(r) σ(r) 10% 20% 30% 40% 50% Expected return % MVP N CSCS Z Q W ATAT BRBR

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

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

10% =γ F γFγF E (γ) E (γ M ) M σ (γ) oo Capital market line Expected return 15% = E (γ M ) Security market line 17.5% β Standard deviation 11.5 Beta A M E (γ M ) ﹣ γ F FIGURE 8.8 CAPITAL MARKET LINEFIGURE 8.9 SECURITY MARKET LINE β M = 1.00

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

SML v.s. Characteristic line

C FIGURE 8.10 CHARACTERISTIC LINES UNDER THE CAPITAL ASSET PRICING MODEL E(γ A ) E(γ B ) γJγJ A B E(γ M )γFγF 10% =γ F = E(γ B ) -10% 5% γMγM Market return o

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

SML(CAPM) in (E (r), σ )

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

資本資產定價模式 (CAPM) Where is the price?

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

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

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

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

Jensen Index Based on CAPM(SML) 母體 樣本

FIGURE 11.4 E STIMATED SML (B ULL M ARKET ) o γPγP βPβP Portfolio beta Average portfolio return B A

Treynor Index Based on CAPM(SML) 母體 樣本

FIGURE 11.6 L EVERING A LPHA TO D OMINATE O MEGA γFγF Expected return E(γ)E(γ) β M o A’ A’’ O’ Beta

Sharpe Index Based on CAPM(CML) 母體 樣本

FIGURE 11.7 P ERFORMANCE OF A LPHA AND OM EGA A CCORDING TO THE S HARPE I NDEX γFγF Expected return Standard deviation E(γ)E(γ) σ (γ) M o A’ A O O’

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)