Sample Test

Financial Maths (Prof. Mahendra Mehta)

Question 1 – Sitting on a Forex desk in the bank, John is of the view that USD would appreciate against CHF in near future. Thus, John wants to buy USD using USD / CHF forward contract. John thus asks a market maker (MM) for a price for a price of 1 year USD / CHF forward contract. MM quotes the price of the forward contract as 0.9050/0.9052 (bid and offer prices). At this time, the spot was quoting as 0.8903/0.8905 and 1 year USD interest rate is 1% and the 1 year CHF interest rate is 2.1%. With these variables, when John did some rough calculations, he concluded that forward has been mispriced by the MM. Thus, John wanted to take advantage of this mispricing. Thus, John goes to his boss and explains the mispricing of the forward contract by the MM and potential opportunity to make money. Boss agrees to give a position limit of 5MM Dollar to John for 1 year. With this in mind, please answer the following questions –

1. Is there a mispricing in the forward contract? If Yes, please explain.

2. If John wants to exploit the mispricing and make some money, what transactions would he undertake to make money? (Assume that bank is not providing the funds for the transactions but he can borrow money freely from the market at the above rates)

3. If John took position of 5 million USD, how much money he will make in CHF?

(Total: 6 Marks)

Answer –

Forward calculated	0.9000	0.9002
Spot (USD / CHF)	0.8903	0.8905
CHF Rate	2.10%	2.10%
USD Rate	1%	1%
Days	260	260
Total Days	260	260
Time	1	1

Forward price quoted by MM

0.9050

0.9052

For a USD / CHF transaction, forward rate is Spot*(1+ CHF*Time)/(1+USD*Time)

Answer 1 – Yes, there is a mis-pricing. The price quoted by MM is higher than the calculated forward price based on the parameters given.

Difference

0.005004

0.005001

Answer 2 – Any person can make money if there is an opportunity for arbitrage (free lunch). An arbitrage happens when any of the ask rate quoted is less than any of the bid rates available in the market.

Here, the arbitrage is shown in color.

Forward calculated (in CHF per USD)	0.9000	0.9002
Forward Price quoted by MM (in CHF per USD)	0.9050	0.9052

Combining the above two, we get,

· Sell the forward contract to MM @ 0.9050 (MM will bid / buy the contract)

· Buy the forward contract from open market @ 0.9002 (Open Market will sell @ 0.9002)

Profit in CHF (per USD)

0.0048

Please note that the above profit is after 1 year, the day when forward contract expires. To find profit for today, find the spot price using the 0.9050 and 0.9002 prices and then calculate the difference OR find the spot price of 0.0048 CHF.

Answer 3 – A position is taken today. Let’s calculate for 1 USD.

Today, I sell 1 USD and buy CHF (meaning market sells CHF @ ask-spot rate) = 0.8905 …………. (1)

Execute the above 2 transactions done in question 2, but @ its spot / today’s price (position is as of today),

Sell the contract = 0.89525 (Spot price of 0.9050 forward price) ……………….. (2)

Buy back the contract = - 0.8905 (Spot price of 0.9002 forward price; negative sign indicates outflow of CHF to buy the contract) ………………………….. (3)

Adding (1), (2) and (3) we get, 0.895249 CHF

Hence, for 1 USD = 0.895249 CHF

For 5 Million USD, it will be 4,476,245 CHF.