Question

Map a three month currency (GBP/EUR) forward with the following features: GBP/EUR spot 3.15; 3 months GBP rate=4.25%; 3 month EUR rate=2.50%; GBP/EUR rate forward=3.1521

Answer 1

Given ! Spot Raße ? 1GBP(K) = EUR(€) 3. 15 3 months £ intrest rate= 4.25%. 3 months € intrest rate=2 50% And 3 monthy forword rate :- 1 t= €3.1521 According to intrest rate parity theory fair forword Ratee (FFR) FFR = Spot rate x cit Periodic interest rale of Home - Currency ) (+ periodic intrest rate of Forigu Currency) In the given case 3 montus FFR = € 3.15*(1+0.0250* 3 ) (1+0.0425X2) 1:- 3 months FF R=> 1 3 = € 3.15 X1.006250 IFR =) 1 Z = €3.1364 Note :- we assumed that the given intrest rates are annualized intrest rates I actual i montus forword rate=) 1 # = €3.1521 and faire forword rate » 2z = €3. 1364. 2.7" was over valuad in forward market. 1.010625

: Arbitage is posible, I Arbitrage strategy :- Here the ² is over valued in forword market Hence we should buy at spot and sell it in future for earning risk free profits. By assuming an exposure of €10,000 the steff in arbitrage strategy are as followes. step-0 :- Borrow €10,000 and convert the same in to 7 using spot rale. j.e € 10,000 X K 3.15 = 3 3,174.60 And take a forword sell contract Invelt Step -o: the recived in step- at a "*" intrest rate of 4.2 Sy. Per three months Step- : At the end of 3-mouths collect Z along with sutrest. ie Ł3, 74.60Xto 0425 × 3 2 ) = £ 3,208.33 Step-@ -convert the ²" Proceeds using the forword rate contract career in to "t": je = £3,208. 334 7 3.1521 - €10,112.99. Step- & Re-day the "E" borrowings along with intret. pe=€10,000 (1+0.025 X 3 ) =€ 10,062.50 Arbitrag Gain = €50.49/-
give problem was solved on the basis of intrest rate parity theory.

The fair forword rate calculated using intrest rate parity theory was lower than the actual available forward rate in the market,

This situation leads to possibility of an arbitrage

Accordingly an exposure of €10000 was taken and the arbitrage strategy was explained in the above posted images

Which stating an earning of €50.49 without any risk at the end of 3rd month