Question

II. (6) Questions below are based on the lecture notes (CH4).

a. Suppose that the value of E£ in yen is now in slide #12, which is :

Cross exchange rates and triangular arbitrage

An example with U.S. dollars ($), Japanese yen (¥), and Egyptian pounds (E£):

SE£/$ = E£5.000/$ Û S$/E£ = $0.2000/E£

S$/¥ = $0.01000/¥ Û S¥/$ = ¥100.0/$

S¥/E£ = ¥20.20/E£ Û SE£/¥ » E£0.04950/¥

SE£/$ S$/¥ S¥/E£

= (E£5/$)($0.01/¥)(¥20.20/E£)

= 1.01 > 1

,but all other exchange rates are the same. Describe the triangular arbitrage strategy and find its profit in $. Write down the strategy and show calculation of obtaining the amount of the profit. Refer to your text p.62–68 and lecture notes.

b. Suppose that the forward rate is now in slide #21 which is,

Interest rate parity is enforced

through “covered interest arbitrage”

An Example:

Given: i$ = 7% S0$/£ = $1.20/£

i£ = 3% F1$/£ = $1.25/£

F1$/£ / S0$/£ > (1+i$) / (1+i£)

1.041667 > 1.038835

The currency and Eurocurrency markets are not in equilibrium.

but all other values are the same. Describe the covered interest arbitrage strategy. Write down the arbitrage strategy and show how you obtain profits. Refer to your text p.67-69 and lecture notes.

Answer 1

6) a)

Given 1$ = 5E£ ;

1 ¥ = 0.01$

1E£ = 20.20¥

Triangular Arbitrage strategy :

Let us assume we have 10,000$

Step 1 : Buy Egyptian pounds (E£) and Sell  U.S. dollars ($)

1 $ = 5 E£

For 10,000 $ = ? E£

Therefore for 10,000 $ we get 50,000 E£ ( 5 * 10,000)

Step 2 : Buy Japanese yen (¥) and Sell Egyptian pounds (E£)

   1 E£ = 20.20 ¥

50,000 E£ = ?   ¥

Therefore for 50,000  E£ we get 10,10,000 Yens ( 50,000*20.20)

Step 3 : Buy U.S. dollars ($) and Sell Japanese yen (¥)

  1 ¥ = 0.01 $

10,10,000 ¥ = ? $

Therefore for 10,10,000 Yens We get 10,100$

First We assumed 10,000 $ at that end of the traingular strategy we have 10,100$

therefore Profit = 10,100$ -10,000$

=100 $ .

6) b) Given i$ = 7%

i£ = 3%

Spot rate = $1.20/£

Forward rate = $1.25/£

Interest rate Parity

Fair forward Price = Spot rate [ (1+i$) / (1+i£)]

= 1.2 [(1+0.07)/(1+0.03)]

1£ = 1.2466 $

Actual forward price is 1£ = 1.25 $ ; Fair forward Price is   1£ = 1.2466 $

Pound is Overpriced in the market ;

i)Sell '£' in the forward market

ii) To sell first we need to a) borrow $ in domestic market at interest rate 7%

Let us assume We borrow $ 10,000 in local market

interest = $ 700 [10,000*7%]

b) Convert '$ ' into '£' Spot market ( $1.20/£)

After Conversion we get 8333.33 £ [ 10,000$ /1.2 ]

iii) Deposit  '£' at Interest rate 3%  

NOw deposit 8333.33 at interest rate 3%

After one year we get 8583.33 [ 8333.33+250 ] which is along with interest

iv) Now covert 8583.33 £ into $ at Forward rate  1£ = 1.25 $

So, we get 10729.16 $ [ 8583.33*1.25 ]

Total outflow = Borrowed amount + interest

= 10,000$ +700 $

= 10,700$

Total inflow = 10729.16$

Profit = 10729.16$ -10,700 $

Profit = 29.16 $