第五章CAPM的应用
第五章 CAPM的应用
■利用 Markowitz模型进行积极证券组合管 理 ■市场模型在消极证券组合管理中的应用 利用Beta去得到好的协方差估计 ■利用Beta去得到好的期望回报率佔计 CAPM在消极证券组合管理中的应用 Black-Litterman方法 例子: Global portfo| lo Optimization
◼ 利用Markowitz 模型进行积极证券组合管 理 ◼ 市场模型在消极证券组合管理中的应用 ◼ 利用Beta去得到好的协方差估计 ◼ 利用Beta去得到好的期望回报率估计 ◼ CAPM在消极证券组合管理中的应用 ◼ Black-Litterman 方法 ◼ 例子：Global Portfolio Optimization
1.利用 Markowitz模型进行积极证券 组合管理 ■经典 Markowitz模型的缺点 ■待估计的期望值、协方差参数数量大 利用历史数据得到的最优证券组合权重不合理 When investors impose no constraints the models almost always ordain large short positions in many assets When constraints rule out short positions the models often prescribe corner solutions with zero weights in many assets as well as unreasonably large weights in the assets of markets with small capitalizations These unreasonable results stem from two well recognized problems 由历史数据得到的期望值估计对将来回报率预测能力很差 最优证券组合权重对于期望回报率假设非常敏感
1. 利用Markowitz 模型进行积极证券 组合管理 ◼ 经典Markowitz 模型的缺点 ◼ 待估计的期望值、协方差参数数量大 ◼ 利用历史数据得到的最优证券组合权重不合理 ◼ When investors impose no constraints, the models almost always ordain large short positions in many assets. ◼ When constraints rule out short positions, the models often prescribe corner solutions with zero weights in many assets, as well as unreasonably large weights in the assets of markets with small capitalizations. ◼ These unreasonable results stem from two well recognized problems: ◼ 由历史数据得到的期望值估计对将来回报率预测能力很差 ◼ 最优证券组合权重对于期望回报率假设非常敏感
例:100种证券形成的证券组合 E(ri's ovIrir )sN(N=1)4950 Total 5N(N+3)5150
◼ 例：100种证券形成的证券组合
F: let us look at the sort of portfolio allocation we get if we use historical returns and volatilities as inputs. Historical Excess Returns (anuary 1975 through August 1991) Total Historical Excees Retrn9 Germany France Japan US. CAnada Australia Currenct 20,8 3.4 B。cscH 153 232 214 228 13.1 Equities CH 122s 291.3 2301 Annualized Eistorloal Excess Returns Grermaury France Japan 忑忘 Canda Aust1血 Currencies ,4 02 3 0.S c2 Bonde ch 0.s 03 0.8 Equities CH 4.T 4.8 s.6 52 09 Annualized volatility of Eistorical Excess Returns Grermany France Japan U:G Canada Australia Currencies 12.3 11.9 47 10.8 4 6.5 6.8 Equities CH 188 222 3.8 24T 16.1 18s 219 N:Bdd如am和可.4B,am0n可 heios are in et and eefuitieeaww in exams of the london interbank offered rate the onemmonth forward rate. Volatilities are epprewd n tnmmaitced atandard deviatio
例： let us look at the sort of portfolio allocation we get if we use historical returns and volatilities as inputs:
Historical correlations Exhibit 2 正 storical C。e1a心丑sf卫 xcess Returns (anuary I976 trough Azzszst z997) Germany Bonds Curreney Equities Bonds Currency Equities Bonds Currens C 1.00 france 0.o3 ds CH a 1.0 Bandier 0_87 .5 2.DP Currency o.。1 0.21 0.8 Equities CH 0.42 0.20 0.D Bonds CH Currency Bonds cH Equities CH 0.33 .16 0.0 083 0.04 0.yT 0s9.o curency ooo 2了
Historical correlations:
Lnited Kingdom E/noted Stater Canada austraia Equites Curency quities Bonds Equities Bonds Curency Equities Bond LK Equities 100 047 Currency 0.0 0.2 Equit 08023 .m2 100 Bncs 12028 018032 canada 5 quities05502701074018100 bonds 0.18 025 31 82023100 Currency 0.14 0.13 009 024 015032 124 .00 australia Equities 0.50 0.20 015 048 00061 002 0.18 100 017 0.17 02002101801303710 Currency 0.06 0.05 027 07 000019 028 027020
If you use our procedures and calculate and optimal portfolio, with o=10.7%/, you will get portfolio weights of: Optimal Portfolios Based on Historical Average Approach percent of portfolio value) Unconstrained Germany France Japan UK US. Cane dis Australia Currency exp5 78,7 46,5 15.5 286 60 52 Bonds 97 525 4,4 4圣 15 133 440 9.0 with constraints against shorting assets Gerrmany France dapan U五忘 Cannae Australia Currency exposure -160.0 I152 180 28.7 77. 8 13.8 B。ds .6 0.0 888 0.0 0.0 0.0 0.0 0 00 00 00 00 0. Q 00
If you use our procedures and calculate and optimal portfolio, with , you will get portfolio weights of: P =10.7%
We can make a number of points about these optimal portfolios They illustrate what we mean when we claim that standard mean-variance optimization models often generate unreasonable portfolios The use of past excess returns to represent a neutral set of views is equivalent to assuming that the constant portfolio weights that would have performed best historically are in some sense neutral. in reality of course, they are not neutral at all, but rather are a very special set of weights that go short assets that have done poorly and go long assets that have done well in the particular historical period
◼ We can make a number of points about these optimal portfolios. ◼ They illustrate what we mean when we claim that standard mean-variance optimization models often generate unreasonable portfolios. ◼ The use of past excess returns to represent a neutral set of views is equivalent to assuming that the constant portfolio weights that would have performed best historically are in some sense neutral. In reality, of course, they are not neutral at all, but rather are a very special set of weights that go short assets that have done poorly and go long assets that have done well in the particular historical period
a remedy for both of these problems is to use (1)market model to calculate asset covariance, (2)and use the CaPm to determine what market expectation must be, and then combine your "view with the CaPm derived estimates to get portfolio weights. The key input we will need for both of these is the set of asset betas so first we must consider the problem of estimating betas
◼ A remedy for both of these problems is to use ◼ (1) market model to calculate asset covariance, ◼ (2) and use the CAPM to determine what market expectation must be, and then combine your “view” with the CAPM derived estimates to get portfolio weights. ◼ The key input we will need for both of these is the set of asset betas, so, first, we must consider the problem of estimating betas