An investor shorts a futures contract today to hedge the value of an asset over the next three days (day 1 thorough day 3). The maintenance margin of the investor's margin account is $1,500k, which is 75% of the initial margin. The balance in the margin account at the end of today is $1,600. If the investor receives a margin call, the investor tops up the margin account to the initial margin level at the end of the next day. The investor does not withdraw any balance in the margin account in excess of the initial margin.
A- What is the probability that the investor has a negative balance in the margin account on day 3 assuming that daily settlement price changes are normally distributed with mean zero and standard deviation $2000? Note that in this case the investor is tempted to walk away instead of closing our the position.
B- What is your answer to part a if the investor holds a long position?
C- Suppose the investor holds a short position, what is the minimum initial margin so the that there is a 5% chance that the investor has a negative balance on day 3? Assume that the balance today is $100 above the maintenance margin.
D- What is your answer to part c if the investor holds a long position?
E-Repeat parts a and c assuming that daily settlement price changes are normally distributed with mean $100 and standard deviation $200
F-What is your answer to part e if the investor holds a long position?