**Correlation & Covariance**

Correlation = Corr(R

_{i}, R

_{j}) = Cov(R

_{i}, R

_{j}) / σ(R

_{i})*σ(R

_{j})

Expected return, Variance of 2-stock portfolio:

E(R

_{p}) = w

_{A}E(R

_{A}) + w

_{B}E(R

_{B})

VaR(R

_{p}) =w

_{A}

^{2}σ

^{2}(R

_{A})+ w

_{B}

^{2}σ

^{2}(R

_{B}) +2w

_{A}w

_{B}σ(R

_{A}) σ(R

_{B})ρ(R

_{A}, R

_{B})

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%

Return = 9.4%, Std Deviation = 7.8%

Return = 9.4%, Std Deviation = 24%

Return = 9.4%, Std Deviation = 28%

**Answer:**

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