ch7 最优资产组合

p = 22%
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Figure 7.3 The Opportunity Set with Differential Borrowing and Lending Rates
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7.1 无风险资产与风险资产 之间的资产配置
7.1.1 风险资产与无风险资产组合的资本 配置 7.1.2 一种风险资产与一种无风险资产的 资产组合（客观可能：可行集） 7.1.3 风险容忍度与资产配置（主观决定： 最优选择） 7.1.4 资本市场线
基本思路与步骤
投资过程：
证券与市场的分析：评估资产的预期收益和风险 最优资产组合的构建：决定最佳风险－收益机会
资产配置：风险与收益之间最优的权衡关系
无风险资产与风险资产之间的资产配置 风险资产之间的资产配置 完整的资产配置过程
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的具有最高收益的组合，2、给定收益水平下具有最小 风险的组合。 有效集（ Efficient set） ：有效组合的集合，又称为有 效边界（ Efficient frontier）。
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CAL (Capital Allocation Line，资本配置线)
E(r) CAL P
E(rp) = 15% E(rp) - rf = 8%
) S = 8/22 rf = 7% F
0
p = 22%

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基本概念
可行集与有效集
资产组合的机会集合（Portfolio opportunity set），又
称可行集，即在资金约束下，可构造出的所有组合的 期望收益和风险（方差或标准差）。
每一个组合在均方平面上就是一个点，因此，可行集是一个
区域。
有效组合（Efficient portfolio ）：1、给定风险水平下
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Example Using Chapter 7.3 Numbers
rf = 7% E(rp) = 15%
rf = 0% p = 22%
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7.1.1 风险资产与无风险资产组合的资本配置
资产配置决策，面向广泛的投资类型，而不是某 类资产中选择特定的证券。
最基本的资产配置选择：无风险资产、风险资产 组合之间投资比例的确定 风险资产组合：证券包，有固定的投资比例 当财富在风险资产与风险组合资产之间转移时， 风险资产组合作为一个整体的相对权重发生改变， 而各种不同风险资产在风险资产组合中的相对比 例则没有改变。
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主要内容
7.1 无风险资产与风险资产之间的资产配置 (资本配置选择：股票、债券、不动产、 海外资产等广泛的资产等级的投资分布） 7.2 最优风险资产组合 （证券选择决策：每一资产等级中特定证 券持有的选择） ——完整的资产组合 （股票、债券与国库券之间的配置）
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7.1.2 一种风险资产与一种无风险资产的资产组合
Examine risk/return tradeoff. Demonstrate how different degrees of risk aversion will affect allocations between risky and risk free assets.
y = % in p
(1-y) = % in rf
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Expected Returns for Combinations
E(rc) = yE(rp) + (1 - y)rf rc = complete or combined portfolio
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Combinations Without Leverage（杠杆）
If y = 0.75, then

c
= 0.75(0.22) = 0.165 or 16.5% = 1(0.22) = 0.22 or 22%
If y = 1

c
If y = 0 c = (0.22) = 0.00 or 0%
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CAL：equation formula
E(rc ) rf y(E(r p ) rf )
E(rc ) yE(rp ) (1 y)rf rf y(E(rp ) rf ) 0.07 y(0.15 0.07)
Figure 7.2The Investment Opportunity Set with a Risky Asset and a
Risk-free Asset in the Expected Return-Standard Deviation Plane
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For example, y = 0.75 E(rc) = 0.75(0.15) + 0.25(0.07) = 0.13 or 13%
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Variance For Possible Combined Portfolios
Since
r = 0, then
f
c = y p*
* Rule 4 in Chapter 6
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Capital Allocation Line with Leverage
Borrow at the Risk-Free Rate and invest in stock. Using 50% Leverage, rc = (-0.5) (0.07) + (1.5) (0.15) =0 .19 c = (1.5) (0.22) = 0.33 For exampe, buying on margin.
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Possible Combinations
E(r)
E(rp) = 15% E(rc) = 13% rf = 7%
P C
F
0
c
22%

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Utility Function
U = E ( r ) - 0.5 A 2 Where U = utility E ( r ) = expected return on the asset or portfolio A = coefficient of risk aversion（风险厌 恶系数） 2 = variance of returns
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资产组合理论基本假设
均方准则：投资者仅仅以期望收益率和方 差（标准差）来评价资产组合（Portfolio） 投资者理性：投资者是不知足的和风险厌 恶的。 瞬时投资：投资者的投资为单一投资期， 多期投资是单期投资的不断重复。 有效组合：在资金约束下，投资者希望持 有具有最高的均方标准的组合。
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CAL with Higher Borrowing .27 9% 7% ) S = .36
σc rf [E(rp ) rf ] σp 8 0.07 σ c 22 E(rp ) rf 8 S σp 22 (报酬与波动比率) (夏普比率）
σ c yσ p 0.22y
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7.1.3 风险容忍度与资产配置
CAL为所有的投资者提供了投资机会集，而最优 组合的最终选择则取决于个体对资产收益－风险 的权衡关系。 个人风险厌恶程度不同，意味着在给定一个相同 的投资机会集下，不同的投资者会选择不同的风 险资产头寸。
求解最优组合：
个体效用最大化 无差异曲线
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Risk Aversion and Allocation
Greater levels of risk aversion lead to larger proportions of the risk free rate. Lower levels of risk aversion lead to larger proportions of the portfolio of risky assets. Willingness to accept high levels of risk for high levels of returns would result in leveraged combinations.