Suppose your investment portfolio consists of 200 call options on stock X, 100 put options on stock Y, 50 forward contracts to purchase stock Z in 6 months, and also 100 shares of stock Y. The options have 6 months maturity and are at-the-money. Current stock prices are $10 for X, $20 for Y, and $5 for Z. Constant risk-free interest over the next 6 months is effectively 1%. The stocks do not issue dividends over the next 6 months. Annualized return volatility of the stock returns of X, Y, Z are respectively 10%, 45%, 20%. The correlation between each pair of the stock returns of X, Y, Z is the same at 0.5. The statistical measures above were measured for daily returns and a factor of 260 is used to scale the daily volatility into annualized volatility. What is the volatility of your investment portfolio dollar across one day? What is the probability of losing 20% of your portfolio value over 1 day if the portfolio return is assumed to be normally distributed? Assume the Black-Scholes model. Assume daily mean returns are zeros. You may assume gamma and other second order effects are too small.