You have a $6,000,000 portfolio that has a beta of 1.9 to the S&P 500. You have decided you want to hedge this portfolio over the next 12 months. The 13-month S&P 500 futures price is $2300, and the current S&P 500 index value is $2250. The 12-month continuously compounded risk-free rate is 1% and the annual dividend yield on the S&P 500 is 2%. As a reminder, futures contracts are based on $250 multiplied by the index value.
a) What position in futures contracts will you need to hedge your portfolio?
b) Now check to see if your answer to part a) hedges your position effectively or not. Find the value of your portfolio in one year (including the futures position) if the S&P drops to $1200, if it drops to $2100, and if it increases to $3200. Assume that at this time (i.e. in one year), the S&P 1- month futures price is $1205, $2107, and $3215, respectively. (Hint: table 3.4 in the textbook should help with this question.)