Question

In London, interest paid on pounds is 1.11%. In New york, interest paid on dollars is 3.27%. The Spot rate is $1.5512/ pound. The One year forward rate is $1.5529/ Pound. The spread on borrowing & lending rates is zero. The bid ask spread is Zero. The arbitrageur has no money of his own but can borrow up to 1,000,000 of any local currency. A. what is the covered yield on dollars( if the investor borrows pounds in London) and covered yield on pounds( if the investor borrows dollars in New york) B. Identity the steps and timing of this covered interest arbitrage, and compute the amounts involved at each state (including the gain at the end). C. The ROA is very low. How does an arbitrageur create acceptable ROE from covered interest arbitrage?

Answer 1

A. what is the covered yield on dollars( if the investor borrows pounds in London) and covered yield on pounds( if the investor borrows dollars in New york)

Please see the table below:

Parameter	Unit	Value	Linkage
Amount Borrowed	Pounds	1,000,000	A
spot rate	$ / Pound	1.5512	B
Amount in $	$	1,551,200	C = A x B
Interest rate on $	%	3.27%	D
Maturity amount after a year	$	1,601,924	E = C x (1 + D)
One year forward rate	$ / Pound	1.5529	F
Maturity amount in Pounds	Pounds	1,031,569	G = E / F
Interest rate on borrowed pounds	%	1.11%	H
Interest on borrowed pounds	Pounds	11,100	I = H x A
Borrowed pounds to be returned	Pounds	1,011,100	J = A + I
Resultant amount	Pounds	20,469	K = G - J
The covered yield on dollars	%	2.05%	L = K / A

Second sub part:

Parameter	Unit	Value	Linkage
Amount Borrowed	$	1,000,000	A
spot rate	$ / Pound	1.5512	B
Amount in Pounds	Pounds	644,662	C = A / B
Interest rate on Pounds	%	1.11%	D
Maturity amount after a year	Pounds	651,818	E = C x (1 + D)
One year forward rate	$ / Pound	1.5529	F
Maturity amount in Pounds	$	1,012,208	G = E x F
Interest rate on borrowed $	%	3.27%	H
Interest on borrowed $	$	32,700	I = H x A
Borrowed $ to be returned	$	1,032,700	J = A + I
Resultant amount	$	-20,492	K = G - J
The covered yield on pounds	%	-2.05%	L = K / A

B. Identity the steps and timing of this covered interest arbitrage, and compute the amounts involved at each state (including the gain at the end).

First part in part (A) illustrates the arbitrage. You end up making risk free money at the end of 1 year without investing any thing. Steps have been shown below. All the amounts that you see below had been calculated in the first table of part (A)

1. Borrow 1,000,000 pounds and convert them into $ = $  1,551,200
2. Lend in New York for 1 year to get the maturity amount as = $  1,601,924
3. Convert the maturity proceeds back to pounds = Pounds  1,031,569
4. Return the borrowed pounds along with interest = Pounds  1,011,100
5. Net gain =  1,031,569 - 1,011,100 = Pounds  20,469

C. The ROA is very low. How does an arbitrageur create acceptable ROE from covered interest arbitrage?

The ROA is 2.05%, which is indeed low, but one must understand that initial investment is zero. Hence, ROE is infinite.

ROE = ROA x A / E

So, the arbitrageur can create acceptable ROE by:

• Increasing the equity multiplier
• Increasing the leverage i.e. using the borrowed funds