Finance 411

Homework 1

Solutions

N2.28

There is a margin call if the margin account falls by $3,000 - $2,000 = $1,000.  This will happen if the new price increases to:

(X – $4.50) × 5,000 = $1,000

X – $4.50= $0.2

X = $4.70

Therefore, the price has to increase by 20 cents.

Similarly, to withdraw $1,500 from the account the price has to fall by 30 cents to $4.20.

N2.29

Futures prices:

Jun                80

Dec                86

To make money, you could long one June futures contract and short one December contract.  In June, Jun futures contract matures and you take delivery of crude oil. To pay for it you can borrow $80 per bbl. at 5% for 6 months. There are no storage costs for keeping oil for 6 months. In December, Dec contract matures and you sell crude oil for $86 per bbl. plus you need to pay back the loan with interest.  Interest is equal to:

$80 × 0.05 × 6/12 = $2 per bbl.

So, the gain is $86 - $80 - $2 = $4 per bbl.

Part 2

Futures rates on JPY:

01/21                0.009593

01/22                0.009581

01/23                0.009695

01/24                0.009777

Spot rate:

01/24                0.0097632

Contract size: 12,500,000 yen

1. Long

1. March 2014 7 contracts (90,000,000/12,500,000 = 7.2 –round down).

1. 01/21        long 7 futures contracts at 0.009593 (cost is zero)

01/22        pay                (0.009581 – 0.009593)×12,500,000×7 = -$1,050

01/23        receive                (0.009695 – 0.009581)×12,500,000×7 = $9,975

01/24        receive                (0.009777 – 0.009695)×12,500,000×7 = $7,175

01/24        short 7 futures contracts at 0.009777 (cost is zero)

1. Gain from futures:        $16,100

Final payment:        90,000,000×0.0097632 = $878,688

Total payment:        $862,588

1. If not hedged:                $878,688

Benefitted from hedging.

Futures rates on GBP:

01/21                1.6472

01/22                1.6570

01/23                1.6624

01/24                1.6500

Spot rate:

01/24                1.6491

Contract size: 62,500 pounds

1. Short

1. March 2014, 14 contracts (900,000/62,500 = 14.4 –round down).

1. 01/21        short 14 futures contracts at 1.6472 (cost is zero)

01/22        pay                (1.6472 – 1.6570)×62,500×14 = -$8,575

01/23        pay                (1.6570 – 1.6624)×62,500×14 = -$4,725