《投资学 Investments》课程教学资源（PPT课件，中英文）第8章 最优风险资产组合 Optimal Risky Portfolios

第8罩 最优风险资产组合 Optimal risky portfolios

8-1 第8章 最优风险资产组合 Optimal Risky Portfolios

最优风险资产组合 Optimal risky portfolios 81分散化与资产组合风险 82两种风险资产的资产组合 83在股票、债券与国库券之间的资产配置 8.4马科维茨的资产组合选择模型 8.5电子表格模型 8.6具有无风险资产限制的最优资产组合

8-2 最优风险资产组合 Optimal Risky Portfolios 8.1 分散化与资产组合风险 8.2 两种风险资产的资产组合 8.3 在股票、债券与国库券之间的资产配置 8.4 马科维茨的资产组合选择模型 8.5 电子表格模型 8.6 具有无风险资产限制的最优资产组合

最优风险资产组合 Optimal risky portfolios 从分散化如何降低资产组合投资回报的风险开始。在建立这 基点之后,我们将从资产配置和证券选择的两方面考察有效分 散化策略。我们将首先考察一个不包含无风险资产的资产配置 ,我们将运用两个有风险的共同基金:一个是长期债券基金, 个是股票基金。然后我们将加上一个无风险资产来决定一个 最优资产组合 The efficient diversification strategies at the asset allocation and security selection levels. We start with a simple example of asset allocation that excludes the risk-free asset. To that effect we use two risky mutual funds: a long-term bond fund and a stock fund. With this example we investigate the relationship between investment proportions and the resulting portfolio expected return and standard deviation We then add a risk free asset to the menu and determine the optimal asset allocation

8-3 最优风险资产组合 Optimal Risky Portfolios 从分散化如何降低资产组合投资回报的风险开始。在建立这一 基点之后，我们将从资产配置和证券选择的两方面考察有效分 散化策略。我们将首先考察一个不包含无风险资产的资产配置 ，我们将运用两个有风险的共同基金：一个是长期债券基金， 一个是股票基金。然后我 们将加上一个无风险资产来决定一个 最优资产组合。 The efficient diversification strategies at the asset allocation and security selection levels. We start with a simple example of asset allocation that excludes the risk-free asset. To that effect we use two risky mutual funds: a long-term bond fund and a stock fund. With this example we investigate the relationship between investment proportions and the resulting portfolio expected return and standard deviation. We then add a risk￾free asset to the menu and determine the optimal asset allocation

分散化与风险 Risk Reduction with diversification 标准方差 St deviation 独特风险(非系统风险 Unique Risk 市场风险(系统风险) Market risk 股票数量 umber of Securities

8-4 分散化与风险 Risk Reduction with Diversification 股票数量 Number of Securities 标准方差 St. Deviation 市场风险(系统风险) Market Risk 独特风险(非系统风险) Unique Risk

多样化与组合风险 Diversification and portfolio risk 种股票:One- security: 风险来自宏观经济 Risks come from macro econ 风险来自企业自己 Risks come from company self 两种股票:Two- security 股票组合降低风险 Portfolio will reduce risk 8-5

8-5 多样化与组合风险 Diversification and Portfolio risk 一种股票： One-security ： 风险来自宏观经济 Risks come from macro econ. 风险来自企业自己 Risks come from company self 两种股票：Two - security 股票组合降低风险 Portfolio will reduce risk

单个股票收益 Single Security return R=[D++(Pt-Po]Po E(R)=∑RP;(=1ton R;预期收益率 expected return P:预期收益的概率 probabilit! 7 of expected return For example E (R) 15%*0.25+10%0.5+8%*25=10.75% R=(1/M)*∑R1(=1ton)如果假设未来各年的收益都 相等 when all expected returns are same (R)3R=(15%+10%+8%)/3=11% 8-6

8-6 R=[Dt+(Pt -P0 )]/P0 E( R ) = ∑ RiPi (I=1 to n) Ri : 预期收益率 expected return Pi :预期收益的概率 probability of expected return For example: E( R ) = 15%* 0.25 +10%* 0.5 +8% *0.25 =10.75% R =(1/M)*∑ Ri (I=1 to n) 如果假设未来各年的收益都 相等 when all expected returns are same E( R ) =R =（15%+10%+8%）/3=11% 单个股票收益 Single Security Return

单个股票风险 Single Security Risk R ∑P1(R1-E(R)2(=1ton) =(14)(15-11)2+(1/2)(10-1)2+(1/4)(8-11)2=675 (675)(112)=26 σ(R2均方差 (R) 标准方差

8-7 σR 2 = ∑ Pi（Ri - E( R )）2 (I=1 to n) = (1/4)(15-11)2 +(1/2)(10-11)2 +(1/4)(8-11)2 =6.75 σR= （6.75）（1/2）=2.6 σ（R） 2 均方差 σ（R） 标准方差 单个股票风险 Single Security Risk

两种股票组合:收益 TWO-Security Portfolio: Return 我们将考察一个包括两个共同基金的资产组合,一个是专门投资于长期债券的债 券资产组合D,一个是专门投资于股权证券的股票基金E,表8-1列出了影响这些 基金收益率的参数,这些参数可以从真实的基金中估计得出。 We will consider a portfolio comprised of two mutual funds, a bond fund that specializes in equity securities, E. Table 8.1 lists the parame. cK portfolio specializing in long-term debt securities, denoted D, and a ste describing the rate-of-return distribution of these funds. These parameters are representative of those that can be estimated from actual funds 表8-1两种共同基金的数据 项目 债券 股权 期望收益E()(%) 8 标准差o(%) 协方差Cov(rp,r) 相关系数pDE 0.3

8-8 我们将考察一个包括两个共同基金的资产组合，一个是专门投资于长期债券的债 券资产组合D，一个是专门投资于股权证券的股票基金E，表 8-1列出了影响这些 基金收益率的参数，这些参数可以从真实的基金中估计得出。 We will consider a portfolio comprised of two mutual funds, a bond portfolio specializing in long-term debt securities, denoted D, and a stock fund that specializes in equity securities, E. Table 8.1 lists the parameters describing the rate-of-return distribution of these funds. These parameters are representative of those that can be estimated from actual funds. 两种股票组合：收益 Two-Security Portfolio: Return

两种股票组合:收益 Two-Security Portfolio: Return 组合收益率r Wr t wr WD=投资与债券中的部分基金 D=投资债券的收益 WE= Proportion of funds in Security(股票) rE= Expected return on Security(股票) ∑W 8-9

8-9 组合收益率rp = WDrD + WErE WD =投资与债券中的部分基金 rD =投资债券的收益 WＥ = Proportion of funds in Security（股票） rＥ = Expected return on Security （股票） 两种股票组合：收益 Two-Security Portfolio: Return S Wi i=1 n = 1

两种股票组合:收益 Two-Security Portfolio: Return 资产组合的期望收益是资产组合中各种证券的 期望收益的加权平均值 The expected return on the portfolio is a weighted average of expected returns on the component securities with portfolio proportions as weights: E(rpEWDE(rD+WEE rE 8-10

8-10 资产组合的期望收益是资产组合中各种证券的 期望收益的加权平均值 The expected return on the portfolio is a weighted average of expected returns on the component securities with portfolio proportions as weights: E(rp)=WDE(rD)+WEE(rE) 两种股票组合：收益 Two-Security Portfolio: Return