Question

6. Assume that annual interest rates are 5 percent in the United States and 4 percent in Turkey. An FI can borrow (by issuing CDs) or lend (by purchasing CDs) at these rates. The spot rate is $0.6624/Turkish lira (TL).

a. If the forward rate is $0.6735/TL, how could the bank arbitrage by using a sum of $5 million? What is the spread earned?

b. At what forward rate is this arbitrage eliminated?

Answer 1

Given:

annual interest rate US- 5 %, annual interest rate Turkey- 4 %, Spot rate : 1TL= $0.6624

Part a.

forward rate : 1 TL= $0.6735

Note: In the absence of information, Forward rate is assumed to be of 1 year.

By observation, it is clear that TL is at premium, so it will be more beneficial to deposit in Turkey.

Solution:-

Loss of interest in US due to deposit in Turkey = $5,000,000 * 5% = $2,50,000

Gain due to deposit in Turkey :

(i) Convert $5,000,000 to TL using spot rate= $5,000,000 / $0.6624 = TL 7,548,309.17874

(ii) Deposit it into Turkey and earn Interest @ 4%: Amount received in Turkey after 1 year = TL 7,548,309.17874 * 4% = TL 301932.367149

(iii) Tota amount after 1 year = TL 7,548,309.17874 + TL 301932.367149 = TL 7,850,241.54588

(iv) Convert this amount into US $ after 1 year using forward rate: Amount in US $ = TL 7,850,241.54588 * $0.6735 = $ 5,287,137.68115

(v) Gain due to deposit in Turkey = $ 5,287,137.68115 - $5,000,000 = $2,87,137.68115

Net Gain due to Arbitrage = Gain due to deposit in turkey - Loss of interest in US

= $2,87,137.68115 - $ 2,50,000

= $ 37,137.68115

Part b.

This arbitrage will be eliminated at the Forward rate at which TL 7,850,241.54588 earned in Turkey will be converted to US $ 5,250,000.00

Forward rate = US $ 5,250,000 / TL 7,850,241.54588

   = US $ 0.6688/TL

arbitrage will be eliminated at the Forward rate of 1TL=US$0.6688.