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CFA LevelⅠ: Quantitative Methods(Part2)

作者:admin 文章来源:CFA培训 点击数: 更新时间:2012-12-27 16:03
PartⅡ:Probability Concepts
  1. Basic Concepts
·Random variable 随机变量
·Outcome 结果
·Event 事件(互斥、遍历、互补、独立事件)
  1. Two Defining Properties of Probability
·0≦P(E)≦1
·P(E1)+P(E2)+……+P(En)=1
  1. Four Kinds of Probabilities
·Empirical probability 经验概率
·A priori probability 先验概率
·Posterior probability 后验概率
·Subjective probability 主观概率
  1. Odds For or Against an Event
  2. Three Important Rules
·Conditional probability 条件概率P(A∣B)
·Joint probability 联合概率P(AB)
·Multiplication rule:P(AB)=P(A∣B)*P(B)=P(B∣A)*P(A)
·Addition rule:P(A or B)=P(A)+P(B)-P(AB)
·Total probability rule:
P(R)=P(R∣S1)*P(S1)+P(R∣S2)*P(S2)+…+P(R∣Sn)*P(Sn)
  1. Expected value:
·E(X)=∑Xi*P(Xi)=X1*P(X1)+X2*P(X2)+…+Xn*P(Xn)
·Portfolio expected value:
E(Rp)= ∑wiE(Ri)=w1E(R1)+w2E(R2)+…+wnE(Rn)
Wi=market value of investment in asset i/market value of the portfolio
  1. Covariance and Correlation
·Covariance:COV(X,Y)=E[((X-E(X)(Y-E(Y))]
·Correlation:Corr(Ri,Rj)=Cov(Ri,Rj)/ σ(Ri) σ(Rj)
  1. Variance
·Variance: σ2=∑Pi(Xi-E(X))2
·Standard deviation: σ
·Portfolio variance:Var(Rp)= ∑∑wiwjCov(Ri,Rj)
  1. Bayes’s Formula:
P(AB)=P(A∣B)*P(B)=P(B∣A)*P(A)
P(A∣B)-=[P(B∣A)/ P(B)]P(A)
  1. Counting Problems
·Multiplication rule;Factorial;Labeling;Combination;Permutation.
 
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