II-Theories-3

Question 1

Investor utility

function

Answer 1

Question 2

Capital Allocation Line CAL

1. 是什么
2. 性质2

Answer 2

1. a portfolio of a risk-free asset and risky asset
2. 一条直线，不同点代表组合中两种资产权重

标准差即risky asset的标准差*权重

Question 3

From a portfolio of 2 assets,

evolve to

Effective Frontier

Answer 3

Question 4

Effective Frontier Chart

1. 横轴/纵轴
2. Minimum-variance frontier
3. Global Minimum-Variance Portfolio
4. Effective Frontier

Answer 4

Question 5

1. From Effective Frontier to

Optimal Risky Portfolio (chart)

2. why it’s optimal?

Answer 5

1. 见图
2. 无风险资产与Effective Frontier上其余任何一点连接，组成的portfolio中都可以找到一点，CAL比其相同risk但return更高

Question 6

from Optimal risky portfolio

+ risk-free asset

evolve to

Optimal Investor Portfolio

Answer 6

Question 7

Capital Market Line CML

1. 由来
2. 横纵轴
3. 斜率
4. 原optimal risky portfolio=，包含
5. 描述方程

Answer 7

1. CAL由于每个投资者对不同组合收益的perseptive不同，会有多个。

CML假设所有投资者预期相同，客观存在一个最好的market portfolio.

CAL多个，CML只有一个

2. x：portfolio标准差，y: expected return
3. 见方程
4. market portfolio, 包含all risky assets, regardless tradable/investible or not
5. 图

Question 8

【risks】

1. risk分为
2. total variance=
3. 公式

Answer 8

1. systematic / nonsystematic risk
2. total variance=

systematic variance+

nonsystematice variance

【not 标准差】

3.图

Question 9

Return-Generating Models

4

最后一个加公式

Answer 9

1. multi-factor model- macroeconomic/ fundemental/ statistical
2. 3-factor, 4-factor
3. single-index
4. market model

α+βX+e

Question 10

1. single asset β
2. portfolio β二种

Answer 10

1. 见图
2. β=r_f+(w₁β₁+w₂β₂)[R_m-r_f]

β=σ_p/σ_m

Question 11

CAPM模型

6大假设

Answer 11

1. investors are risk-averse, u-maximizing, rational
2. investors have same expectations, valuation
3. investors are price takers
4. same single holding period
5. market is fractionless, no transaction costs
6. all investments are infinitety divisible

Question 12

security market line SML

1. 图形
2. 横轴
3. 斜率
4. 用途2

Answer 12

1. 图
2. β
3. Rm-Rf
4. CAPM：确定expected return

判断新的securities 高估还是低估

Question 13

比较SML&CML

1. measure of risk
2. applicaition
3. slope
4. 涵盖的资产

Answer 13

4. CML: 只有有效边界上的资产组合

SML：任一资产

Question 14

【evaluation】

1. sharpe ratio等式
2. 衡量哪种风险？
3. Treynor ration等式
4. 衡量哪种风险？

Answer 14

1. (R_p-r_f)/σ_p

总风险

2. (R_p-r_f)/β_p

系统性风险

Question 15

【evaluation】

1. M^₂ 公式

衡量哪种风险

2. Jensen’s α 两个公式

衡量哪种风险

Answer 15

1. =(R_p-r_f) α_m/α_p - (R_m-r_f)

total risk

2. α=(R_p-r_f) - β(R_m-r_f)

= R_p - CAPM

系统性风险

Question 16

4种evaluation方式

什么情况下用什么？

Answer 16

1. non-diversified portfolio: 用总体风险

Sharpe ratio, M²

2. fully-diversified: 用系统性风险

Treynor ratio, Jensen’s α

Question 17

security characteristick line

SCL

1. 用于什么
2. 横纵轴
3. 斜率
4. 公式
5. 纵截距

Answer 17

1. 用于单个资产超额收益与market portfolio超额收益之对比
2. 横轴：rm-rf

纵轴： ri-rf

3. slope: βi
4. Ri-rf = α-βi (Rm-rf)

即jensen’s α

5. α

Question 18

【CAPM】limitations

1. theoratical 2
2. practical 4

Answer 18

1. single factor/ single period
2. market portfolio:有的资产无法投资

homogeneity in investor expectations假设

beta could be 不准确

CAPM计算结果经常不准确