40. CML Var(R P ) = σ p 2 = a 2 σ m 2 σ p = a*σ m a = σ p / σ m ( 代入 E(R P ) 中 ) E(R P ) = (1-a) R f + a*E(R m ) , a>0 E(R P ) = R f + ( σ p / σ m )*[E(R m )-R f ] = R f + { [E(R m )-R f ] / σ m } * σ p riskless asset market portfolio
41.
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43. CML Var(R P ) = σ p 2 = a 2 σ m 2 σ p = a*σ m a = σ p / σ m ( 代入 E(R P ) 中 ) E(R P ) = (1-a) R f + a*E(R m ) , a>0 E(R P ) = R f + ( σ p / σ m )*[E(R m )-R f ] = R f + { [E(R m )-R f ] / σ m } * σ p riskless asset market portfolio
44. β p = = = = + = + = W 1 β 1 + W 2 β 2 σ pm σ m 2 E{ [W 1 R 1 +W 2 R 2 –W 1 E(R 1 )–W 2 E(R 2 )]*[R m –E(R m )]} σ m 2 E{ [W 1 (R 1 –E(R 1 ) +W 2 (R 2 –E(R 2 )]*[R m –E(R m )]} σ m 2 E [W 1 (R 1 –E(R 1 )]*[R m –E(R m )] σ m 2 E [W 2 (R 2 –E(R 2 )]*[R m –E(R m )] σ m 2 σ m 2 W 1 σ 1m σ m 2 W 2 σ 2m
45. E(R A ) = 15.0% E(R Z ) = 8.6% E(R P ) = 0.5 *15.0% + 0.5 *8.6% = 11.8% Beta of Portfolio: = 0.5 *1.5 + 0.5 *0.7 = 1.1 Under the CAPM, the E(R P ) is E(R P ) = 3% + 1.1 *8.0% = 11.8%
46. σ p 2 = E [R P –E(R P )] 2 = E [(W 1 R 1 +W 2 R 2 ) – (W 1 E(R 1 ) + W 2 E(R 2 ))] 2 = E [(W 1 (R 1 – E(R 1 )) + W 2 (R 2 – E(R 2 )] 2 = = W 1 2 σ 1 2 + W 2 2 σ 2 2 + 2W 1 W 2 E [(R 1 – E(R 1 ))*(R 2 – E(R 2 )] W 1 2 σ 1 2 + W 2 2 σ 2 2 + 2W 1 W 2 σ 1 2 = W 1 2 σ 1 2 W 2 2 σ 2 2 W 1 W 2 σ 1 2 W 2 W 1 σ 21 設 Portfolio 中只有兩種資產 Σ W i 2 σ i 2 + Σ Σ W i W j σ ij i=1 2 i=1 2 j=1 2 i≠j
47. σ p 2 = = + + = + = = (when N->∞) (10.10) Σ X i 2 σ i 2 + Σ Σ X i X j σ ij i=1 N i=1 N j=1 i≠j N N N 2 1 Var N(N – 1) N 2 1 COV N 1 Var N(N – 1) N 2 COV N 1 Var COV (N – 1) N COV
48. Portfolio Risk and Number of Stocks Nondiversifiable risk; Systematic Risk; Market Risk Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk n In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not. Portfolio risk
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