1 answer

Consider the 2Y zero-rates in Poland and USA are 3% pa. and 1,5% pa, respectively. The...

Question:

Consider the 2Y zero-rates in Poland and USA are 3% pa. and 1,5% pa, respectively. The spot exchange currently quoted is 3 PL

Consider the 2Y zero-rates in Poland and USA are 3% pa. and 1,5% pa, respectively. The spot exchange currently quoted is 3 PLN/USD. The FX rate under 2Y forward contract for a delivery of 1.000 USD is 3,05 PLN/USD. Suppose you are a financial speculator. What loan should you take now in order to realize a profit on one forward contract under arbitrage strategy?

Answers

Step 1 :
Take loan in USD @ 1.50%
For instance, if you take US$ 1,000,000 loan for two years, the amount to be returned after two years is as follows:
Amount = Principal X (1 + Interest)^Period
Amount = 1,000,000 X (1+0.0150)^2
=USD 1,030,225
Step 2 :
Convert the US$ 1,000,000 into PLN (at 3 PLN/USD)
=1,000,000 * 3
=3,000,000
Invest this amount for 2 years @ 3%
After 2 years the amount to be received will be = 3,000,000 X (1+0.03)^2
=PLN 3,182,700
Also, at this point, the speculator will have to enter into a 2 years forward contract to convert USD at 3.05 PLN/USD

Step 3 :

Convert the amount of PLN 3,182,700 into USD at 3.05 PLN/ USD after two years
= USD 1,043,508 (3,182,700 / 3.05)
Step 4 :
Return back the USD loan
As per step 1, the amount to be returned is = USD 1,030,225
However, due to arbitrage, the speculator will have USD 1,043,508
Arbitrage gains will be USD 1,043,508 - USD 1,030,225
=USD 13283 per USD 1,000,000

Hence, to make arbitrage gains USD loan will have to be taken

.

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