QM ( Reading 8, Lesson 2)

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


Question Answer
Cov (XY) FormulaCov (XY) = E{[X-E(X)][Y-E(Y)]}
Properties of Cov1. 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 CoefficientCorr(Ra,Rb) = Rho (Ra, Rb) = [Cov (Ra,Rb)] / std (A) std(B)
Properties of Corr1. 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 definitionmeasures 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 portfolioVar(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 rhoVar(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 portfolioVar (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 uncorrelatedE(XY)= E(X)E(Y)