# QM ( Reading 8, Lesson 2)

rename
lightenning's
version from
2017-04-02 17:33

## Section

Question | Answer |
---|---|

Cov (XY) Formula | Cov (XY) = E{[X-E(X)][Y-E(Y)]} |

Properties of Cov | 1. Measures how a randon variable varies with another random variable, 2. Cov(XY)=Cov(YX), 3. Ranges from positive infinity to negative infinity, 4. Cov(XX) = Var(X) 5. negative cov means inverse relationship but doesnt tell us about the strength, 6. Cov =0 if variables are unrelated. |

Probabilistic Cov | Cov(Ra, Rb) = Sigma i Sigma j P (Ra,i , Rb,j) x [(Ra,i - ERa ) (Rb,j - ERb )] |

Correlation Coefficient | Corr(Ra,Rb) = Rho (Ra, Rb) = [Cov (Ra,Rb)] / std (A) std(B) |

Properties of Corr | 1. measures the strength of a relationship between two variables, 2. No unit, 3. between -1 and 1, 4.+1 indicates perfect correlation and -1 perfect negative correlation and 0 indicates zero linear correlation |

Correlation definition | measures the strength and direction of the linear relationship between two random variables. |

Expected Value of returns on a portfolio (E(Rp) ) | E(Rp) = Sigma (wi x E(Ri) = w1 E(R1) + w2E(R2) + ... + Wn E(Rn) where w= Market value of investment/Total portfolio value |

Variance (Rp) | Var(Rp) = Sigma Sigma Wi Wj Cov (Ri, Rj) |

Variance of a 2-asset portfolio | Var(Rp) = Wa^2 σ^2(Ra) + Wb^2 σ^2(Rb) + 2 Wa Wb Cov(Ra,Rb) |

Variance of a 2-asset portfolio based on rho | Var(Rp) = Wa^2 σ^2(Ra) + Wb^2 σ^2(Rb) + 2 Wa Wb ρ (Ra, Rb) σ(Ra) σ(Rb) |

Var (Rp) for 3-asset portfolio | Var (Rp) = Wa^2 σ^2(Ra) + Wb^2 σ^2(Rb) + Wc^2 σ^2(Rc)+ 2 Wa Wb Cov(Ra,Rb)+ 2 Wa Wc Cov(Ra,Rc)+ 2 Wc Wb Cov(Rc,Rb) |

E(XY) when X and Y are uncorrelated | E(XY)= E(X)E(Y) |

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