（2）债券1和债券2
Cov(1,2) = 0.10(0.25 – 0.1750)0(.25 – 0.1750) + 0.40(0.20 – 0.1750)(0.15 – 0.1750)
+ 0.40(0.15 – 0.1750)(0.20 – 0.1750) + 0.10(0.10 – 0.1750)(0.10 – 0.1750)
= 0.000625
ρ1,2 = Cov(1,2) / σ1σ2= .000625 / (0.0403)(0.0403)= 0.3846 债券1 和债券3
Cov(1,3) = 0.10(0.25 – 0.1750)(0.10 – 0.1750) + 0.40(0.20 – 0.1750)(0.15 – 0.1750)
+ 0.40(0.15 – 0.1750)(0.20 – 0.1750) + 0.10(0.10 – 0.1750)(0.25 – 0.1750)
= –0.001625
ρ1,3 = Cov(1,3) /σ1σ3= –0.001625 / (0.0403)(0.0403)= –1 债券2和债券3
Cov(2,3) = 0.10(0.25 – 0.1750)(0.10 – 0.1750) + 0.40(0.15 – 0.1750)(0.15 – 0.1750)
+ 0.40(0.20 – 0.1750)(0.20 – 0.1750) + 0.10(0.10 – 0.1750)(0.25 – .1750) = –0.000625
ρ2,3 = Cov(2,3) / σ2σ3–0.00625 / (0.0403)(0.0403)–0.3846 （3）E(RP) = w1E(R1) + w2E(R2)
= 0.50(0.1750) + 0.50(0.1750) = 17.50%
σP2 = w12σ12 + w22σ22 + 2w1w2σ1σ2ρ1,2
= 0.502(0.04032) + 0.502(0.04032) + 2(0.50)(0.50)(0.0403)(0.0403)(0.3846) ", = 0.001125", σP = (.001125)1/2 = 3.35%
（4）E(RP) = w1E(R1) + w3E(R3)= 0.50(0.1750) + 0.50(0.1750) = 17.50% σP2 = w12σ12 + w32σ32 + 2w1w3σ1σ3ρ1,3
= 0.502(0.04032) + 0.502(0.04032) + 2(0.50)(0.50)(0.0403)(0.0403)(-1) ", = 0", σP = 0
（5）E(RP) = w2E(R2) + w3E(R3)= 0.50(0.1750) + 0.50(0.1750) = 17.50% σP2 = w12σ12 + w32σ32 + 2w1w3σ1σ3ρ2,3
= 0.502(0.04032) + 0.502(0.04032) + 2(0.50)(0.50)(0.0403)(0.0403)(-0.3846) ", = 0.0005",
σP = (0.0005)1/2=2.24%
5.保持每只股票的预期收益不变，负相关的股票组合比正相关的股票组合分散的风险更多。 47.
（1）E(RA) = 0.25(–0.10) + 0.50(0.10) + 0.25(0.20) = 7.50% E(RB) = 0.25(–0.30) + 0.50(0.05) + 0.25(0.40) = 5.00% 24.SlopeCML=(0.075-0.05)/0.25=10% 预期的市场风险溢价是10%。 48. 21.股票A
不景气 RRecession = ($40 – 50) / $50 =-20% 正常 RNormal = ($55 – 50) / $50 = 10% 持续发展 RExpanding =($60 –50) /$50 =20%
E(RA) = 0.10(–0.20) + 0.80(0.10) + 0.10(0.20) = 8.00%
σA2 = 0.10(–0.20 – 0.08)2 + 0.80(0.10 – 0.08)2 + 0.10(0.20 – 0.08)2 = 0.0096 σA = (0.0096)1/2 = 9.8%
βA = (ρA,M)(σA) /σM= (0.80)(0.098) /0 .10=0 .784 股票B
βB = (ρB,M)(σB) / σM= (0.20)(0.12) / 0.10= 0.240
股票B的预期收益高于股票A的预期收益，股票B的贝塔系数小于股票A，即股票B的风险更小。因此我更喜欢股票B。 （2）E(RP) = wAE(RA) + wBE(RB) E(RP) = 0.70(0.08) + 0.30(0.09) E(RP) = 8.30%
σP2= wA2σA2+ wB2σB2 + 2wAwBσAσBρA,B
= (0.70)2(0.098)2 + (0.30)2(0.12)2 + 2(0.70)(0.30)(0.098)(0.12)(0.60) = .00896
σP = (0.00896)1/2= 9.47%