A) Suppose you have two stocks (A and B) in your portfolio, worth $400,000 and $600,000 respectively. The annual volatility is 0.30 and 0.35 respectively. The correlation between the two stocks is 0.42. Please calculate the 10-day, 95% VaR for the two positions separately and for the portfolio. How much is the VaR reduction in the portfolio? Re-calculate the portfolio VaR and VaR reduction assuming a correlation of 0.9. What can you conclude? (Hint: for accuracy and convenience, it is a good idea to set up the calculation in a spreadsheet. Also, assume 252 days in a year.)
B) Suppose you add Stock C to your portfolio. Stock C has an annual volatility of 0.25. The correlations are ρ_{AB}=0.42, ρ_{AC}=0.20, and ρ_{BC}=0.33. Keeping the total investment at $1,000,000, and assuming that achieving the lowest VaR is the only objective, what is optimal allocation among the three stocks? (Hint: please Solver in Excel.)