两种股票组合:风险 TWo-Security portfolio: Risk o2=WD20D2+WE20E2+ 2WDWE coV(g!债券的方差 Variance of Security D σE2=股票的方差 Variance of Security E Cov(r,r)=债券和股票收益的协方差 Cov(rp, re)=Covariance of returns for Security d and Security E 8-11
8-11 sp 2 = wＤ 2sＤ 2 + wＥ 2sE 2 + 2wDwE Cov(rD,rE ) sD 2 = 债券的方差Variance of Security Ｄ sE 2 =股票的方差Variance of SecurityＥ Cov(rＤ，rＥ) =债券和股票收益的协方差 Cov(rＤ，rＥ) =Covariance of returns for Security Ｄ and Security Ｅ 两种股票组合：风险 Two-Security Portfolio: Risk
协方差 Covariance Cov(rp, rE=P DEODOE cov(rb,rp)=σ2 peE=收益的相关系数 Correlation coefficient of returns Op=WdOD+ WEOE+ 2WDWE PDE OD OE σ=证券D收益的标准方差 Standard deviation of returns for Security D e= Standard deviation of returns for Security E 8-12
8-12 协方差 Covariance ρDE = 收益的相关系数Correlation coefficient of returns Cov(rＤ，rE) = ρDE sDsE Cov(rＤ，rD) = σD 2 sD = 证券D收益的标准方差 Standard deviation of returns for Security D sE = Standard deviation of returns for Security E sp 2 = wＤ 2sＤ 2 + wＥ 2sE 2 + 2wDwE ρDE σD σ E
相关系数:取值范围 Correlation coefficients: Possible values ρDε取值范围 Range of values for p D, E -1.0≤p≤1.0 如果p=10,证券组合将是正相关 If p=1.0, the securities would be perfectly positively correlated 如果p=-1.0,证券组合将是负相关 If p=-1.0, the securities would be perfectly negatively correlated 8-13
8-13 相关系数：取值范围 Correlation Coefficients: Possible Values 如果 r = 1.0, 证券组合将是正相关 If r = 1.0, the securities would be perfectly positively correlated 如果 r = -1.0, 证券组合将是负相关 If r = - 1.0, the securities would be perfectly negatively correlated r D,E 取值范围 Range of values for r D,E -1.0 < r < 1.0
相关系数:取值范围 Correlation coefficients: Possible values 如果p=1.0p=10 o 2=W,22+WEOE D 20-2+ 2WDWE DUE Opl=(WDOD+ WEOE) p WDOd +WEOE 8-14
8-14 相关系数：取值范围 Correlation Coefficients: Possible Values 如果 r = 1.0 If r = 1.0 sp 2 = wＤ 2sＤ 2 + wＥ 2sE 2 + 2wDwE σD σ E sp = wＤsＤ + wＥsE sp 2 = (wＤsＤ + wＥsE) 2
相关系数:取值范围 Correlation coefficients: Possible values 如果p=-10p=-1.0 p W D 2+WEOE D 2WnW=σno D E p DOD WEO-2 Op-WDOD-WECEI W DOD WEO E E 0 WD=O/OD OE WE=OD/op+O:=1-WD 8-15
8-15 相关系数：取值范围 Correlation Coefficients: Possible Values 如果 r = -1.0 If r = -1.0 sp 2 = wＤ 2sＤ 2 + wＥ 2sE 2 - 2wDwE σD σ E sp = ︳wＤsＤ - wＥsE ︳ sp 2 = (wＤsＤ - wＥsE) 2 wＤsＤ - wＥsE = 0 wＤ=σE/(σD + σE) w E=σ D / (σD+σE) =1-WD