Question
Stock ABC has a mean daily return of .001 and standard deviation of daily returns of 0.03. Stock XYZ has mean daily return 0.005 and
Stock ABC has a mean daily return of .001 and standard deviation of daily returns of 0.03. Stock XYZ has mean daily return 0.005 and standard deviation of daily returns of .04. The correlation coefficient between daily returns on XYZ and ABC is 0.5. My portfolio worth $2,000 allocates $500 to ABC and $1,500 to XYZ. What are the weights of ABC and XYZ in my portfolio? What is the variance of my portfolios daily returns? What is the daily VaR for my portfolio at the 99% confidence level, assuming that returns have a normal distribution (assume the mean daily return on the portfolio is close enough to 0 that a 0 mean can be used)? What is the 10-day VaR, assuming that daily returns are independent and identically distributed (assume the mean daily return on the portfolio is close enough to 0 that a 0 mean can be used)? Go back to 1-day VaR. Calculate the 1-day VaR separately for ABC and for XYZ (use a 0 mean daily return for each stock). What can you say about the sum (VaR(ABC) + VaR(XYZ)) as compared to VaR(Portfolio)? What is the difference? What is the reason for the difference?
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