Question

1. Consider the futures contract to buy/sell December gold for $500 per ounce on the New York Commodity Exchange (CMX). The contract size is 100 ounces. The initial margin is S3,000, and the maintenance margin is $1,500. 1.a. Suppose that you enter into a long futures contract to buy December for $500 per ounce on the CMX What change in the futures price will lead to a margin call? If you enter a short futures contract, what futures price will lead to a margin call? 1.b. What happens if you do not meet a margin call? 1.c. Suppose you buy a December gold futures at $500, on July 1st. You hold the position until selling on July 16th at $485.50. The daily prices on the intervening days are as shown in the table below. Complete the table below on gains/losses and charges/credits to the margin account. Daily Gain/Loss (S) Gain/Loss () Balance (S) Cumulative Margin Acco unt Margin Call (S) Day Futures Price 1-Jul 2-Jul 3-Jul 4-Jul 5-Jul 6-Jul 7-Jul 8-Jul 9-Jul 10-Jul 11-Jul 12-Jul 13-Jul 500.00 501.50 502.00 493.60 491.70 492.90 488.90 494.20 488.40 482.30 478.70 478.30 482.40

Answer 1

1) a) In case of a long position a fall in futures price by more than 1500 from 50000 to 48499 will lead to a margin call as the futures position will drop below the maintainence margin. In case of sale a rise in futures price from 50000 to 51501 will drop margins from 3000 to 1499 leading to margin call.

b) If margin call is not honoured the brokerage firm close the open position.

c) Solution:

d) i) A short hedge should be taken as we afre concerned with the price falling.

ii)A long basis position is beneficial with a spot at 480 and Futures at 500 a convergence will lead to a gain of 20 per ounce i,e, 20*100000=2000000

2) a) the farmer should short his position as he will be affected with a fall in price.

b)Pros of hedging- Price Certainty, Cons- Carrying cost

c)the real risk being the weather if the farmer takes a derivative position on the crop going wiped out which means in that case demand will exceed supply and the prices will rise thus by buying a call option he can hedge himself to a certain extent.

3)a)Futures Price= Spot Price*e^(rt)

r=risk free rate, t=time

F=20*E^.05=21.03

Initial value= 21.03/1.05=20.02

b)The trader can use a cash and carry arbitrage where he buys the asset at a lower value till maturity and then makes a riskless profit by selling futures against them, on maturity he hands over the asset he held at a lower value.

4) Reverse cash and carry arbitrage as the value of 200 comes to 203.77 i.e. 200((1.1)^4/12)/((1.04)^4/12) whereas the future value is 202 buying futures on maturity and short selling the asset will create an arbitrage opportunity.