Suppose you are a trader at a bank with a portfolio of 100 long call options on the S&P 500 with a delta of 0.8 ( = 0.8). Assume the current price of the S&P 500 is $1266, and its returns are normally distributed with mean of 5% and standard deviation of 15%, and the risk-free rate is 2% (all annualized). (19 points) (a) What is the one month 99% VaR for an investor who holds one share long in the S&P 500 given the assumptions above and interpret what this means?

Given the information above, describe the transactions you would need to complete to delta hedge your portfolio of options?

Suppose you entered the hedge described above and the next day the value of a single option in the portfolio increases by $1.56 following a $2 increase in the S&P. What is your profit/loss on the delta-hedged portfolio and why was it not a perfect hedge?