Pierre is considering a portfolio with 50% invested in Stock A and 50% invested in Stock B. These are the expected returns.

Economic State Probability of State Return on Stock A Return on Stock B Return on Portfolio

Poor 0.30 -15% 25%

Fair 0.50 10% 5%

Boom 0.20 30% -5%

Questions:

1. What is the return on the total portfolio?
2. What is the variance and standard deviation of the portfolio?
3. Are the two stocks positively or negatively correlated? Why?

NB: Please show step-by-step calculations and give a detailed explanation for question 3.