III-Probabilities-5

Question 1

3 kinds of probabilities

Answer 1

empirical, priori (objective)

subjective

Question 2

interprete:

1. odds for E is 1 to 7
2. odds against E is 15 to 1

Answer 2

1. E发生的可能性是1， 不发生是7，概率是1/8
2. E不发生可能性是15，发生是1，概率是1/16

Question 3

标记法与读法：

1. unconditional probability
2. conditional probability
3. joint probability

Answer 3

1. P(A)
2. P(A丨B)”probability of A given B”
3. P (AB) “probability of A and B”

Question 4

unconditional probability

又叫什么

Answer 4

marginal probability

Question 5

Joint probability (A given B)

equation

multiplication rule

Answer 5

Question 6

addition rule for probabilities

equation

Answer 6

Question 7

define:

independent events

Answer 7

Question 8

relationship between

mutually exclusive event

independent event

Answer 8

如果互斥，则一定不独立

Question 9

Total Probability Rule

equation

Answer 9

前提：mutually exclusive + exhaustive events

Question 10

概率中的方差

如何计算？

Answer 10

每种可能结果同期望值之偏差

的平方

的概率加权和

Question 11

covariation equation

Answer 11

Cov (Ri, Rj) = E

Question 12

3properties of

covariance

Answer 12

1 理论数值范围为正负无穷大

2结果为负数：两投资回报相同情况下相反移动

结果为0：两投资回报互相无关

. 结果为正数：两投资回报相同情况下正向移动

4. 单位为平方** (percentage square)

Question 13

一个投资组合的variance （risk）

计算方式

Answer 13

variance = 每项投资自身方差*配置占比²之和

+2*每两项投资协方差*各自占比*（根据矩阵，上下对称）

σ = w₁²σ₁² + w₂²σ₂² + 2w₁w₂cov₁₂

Question 14

define:

diversification benefit

3点

Answer 14

σ = w₁²σ₁² + w₂²σ₂² + 2w₁w₂cov₁₂

1资产1，2的相关系数为1时，方差组合最大，为两项资产各自标准差的加权平均值

即 （w1σ1 + w2σ2）²

2相关系数-1时，方差组合最小，风险最小

即 (w1σ1 - w2σ2) ²

3a risk reduction when holding a portfolio of assets with less even negative covariance

Question 15

correlation

definition

Answer 15

相关系数

Question 16

correlation的性质4条

Answer 16

1. 没有单位，是一个纯数量
2. 表达两者间的线性关系
3. 一定大于等于-1且小于等于1，绝对值越大线性关系越强
4. 等于0时，两者互不相关

数值越正越大，越正相关

数值越负越小，越负相关

Question 17

correlation (X, Y) = 0

and

X, Y 相互独立

之辩析

Answer 17

• correlation = 0只能说明XY无线性关系（加减），但不能代表XY相互独立（完全没有关系）
• 相反，若XY相互独立，则correlation一定为0

Question 18

Bayes’ Formula

加理解

Answer 18

也可理解为P(AB)同时发生，在P(B)中所占的分量

Question 19

posterior probability

Answer 19

后验概率

Question 20

组合

排列

阶乘

多项式/二项式

英文

Answer 20

combination

permutation

factorial

multinominal / binominal

Question 21

公式

nCr

nPr

Answer 21

对n个数值中选出r个，进行无顺序组合

对n个数值中选出r个，进行排列