Correlation & Covariance

Correlation = Corr(Ri, Rj) = Cov(Ri, Rj) / σ(Ri)*σ(Rj)

Expected return, Variance of 2-stock portfolio:

E(Rp) = wAE(RA) + wBE(RB)

VaR(Rp) =wA2σ2(RA)+ wB2σ2(RB) +2wA wBσ(RA) σ(RB)ρ(RA, RB)

Q: Amit has invested $300 in Security A, which has a mean return of 15% and standard deviation of 0.4. He has also invested$700 in security B, which has a mean return of 7% and variance of 9%. If the correlation between A and B is 0.4, What is his overall expectation and Standard deviation of portfolio?

Return = 9.4%, Std Deviation = 7.8%
Return = 9.4%, Std Deviation = 24%
Return = 9.4%, Std Deviation = 28%

The correct answer is Return = 9.4%, Std Deviation = 24%

Practice Question:

Calculate the correlation between the following data set:

Data Set A: 10,20,30,40,50

Data Set B: 10,20,70,120,130