FBE459_Homework1_solutions

FBE459_Homework1_solutions - UNIVERSITY OF SOUTHERN...

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UNIVERSITY OF SOUTHERN CALIFORNIA MARSHALL SCHOOL OF BUSINESS FBE 459 Financial Derivatives (P. Matos – Spring 08) Homework 1 (Solutions): 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 $3,000, 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? This exercise is similar to the example in pages 27-28 of HULL except we consider here only one futures contract (instead of two) and initial price S=$500. There will be a margin call when $1,500 has been lost from the margin account. On a long position, this occurs if Dec futures price of gold decreases by $1,500/(100oz.) =$15. Therefore a margin call happens for long position if futures price falls to $485. On a short position, this occurs if Dec futures price of gold increases by $1,500/(100oz.) =$15. Therefore a margin call for short position happens if futures price rises to $515. 1.b. What happens if you do not meet a margin call? If a margin call is not met, your position is closed (with your broker or directly at CMX). 1.c. Suppose you buy a December gold futures at $500 per ounce, on July 1st. You hold the position until selling on July 16th at $485.50. The daily prices on the intervening days are as shown in the table below. Complete the table below on gains/losses and charges/credits to the margin account.
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Day Futures Price Daily Gain/Loss ($) Cumulative Gain/Loss ($) Margin Account Balance ($) Margin Call ($) 1-Jul 500.00 3000 2-Jul 501.50 150 150 3150 3-Jul 502.00 50 200 3200 4-Jul 493.60 -840 -640 2360 5-Jul 491.70 -190 -830 2170 6-Jul 492.90 120 -710 2290 7-Jul 488.90 -400 -1110 1890 8-Jul 494.20 530 -580 2420 9-Jul 488.40 -580 -1160 1840 10-Jul 482.30 -610 -1770 3000 1770 11-Jul 478.70 -360 -2130 2640 12-Jul 478.30 -40 -2170 2600 13-Jul 482.40 410 -1760 3010 14-Jul 475.50 -690 -2450 2320 15-Jul 480.30 480 -1970 2800 16-Jul 485.50 520 -1450 3320 1.d. Suppose that on July 1st you hold 10,000 ounces of gold. At present, the gold spot
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FBE459_Homework1_solutions - UNIVERSITY OF SOUTHERN...

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