Question

Show all work to support your final numerical answers, and carefully label all numbers with the appropriate units to receive full credit. Quote all ex-rates with both currency units ($/£) to 4 decimal places. Please do not copy payoff diagrams directly from the lecture notes. Full essays of a paragraph or more are required.

Current one-year interest rate for USD LIBOR: 5.20%

Current one-year interest rate for Sterling (UK) LIBOR: 4.25%

Current spot ex-rate (S): = $1.5200/£

Current one-year forward rate (F) = $1.5428/£

1. (3 points) a. Given the information above, is the British pound selling at a premium or discount? How much (round to two decimal places, e.g. 1.35%)?

b. Is Interest Rate Parity (IRP) holding? Why or why not? Explain in an essay, and show a calculation to support your answer using this IRP formula: i_us = i_uk +/- %£

c. Given the information above, how could you make arbitrage profits, starting with either $5 million or £5 million? Calculate and report your profits, and explain each calculation in words.   

Answer 1

1(a)	Given F is higher then s -
	That is we have to pay more $ for 1 pound.
	Therefore $ is at discount and Pound is at a premium.
	Premium =		(F-S)/S x 100 x 12/n
			(1.5428-1.52)/1.52 x 100 x 12/12
			1.5%
(b)	IRP says That -		F/S =	(1+ia)/(1+ib)
	F = Forward Rate
	S = Spot Rate
	ia =	Interest rate of Dollor
	ib =	Interest rate on Pound
	If this equation holds good then the exchange rate across the globe will be the same.
	ia =	5.20%
	ib =	4.25%
	s =	$/Pound	1.52
	F =	$/Pound	1.5428
	Calculate the F as per IRP =
	F/1.5428 =	1.052/1.0425			(Assuming compounded annually)
	F =	1.009113	x 1.5428
	F =	1.5569
	Here the Should be Fwd rate is not equal to the actual fwd rate, that imply that the IRP does not hold.
(c )	Here the Should be Fwd rate is not equal to the actual fwd rate, there is a opportunity for arbitrage.
	As we can see the actual F is lower then the F that should have prevaled, that menas the pound can be purchsed at a lower rate and $ can be sold at a higher rate.
	Therefore we should sell $ forward and buy Pound instead. That means we invest in $ and borrow Pound to make profit(Riskless).
	Stepts in Arbitrage -
	Step 1 =	Borrow Pound 5000000 today at 4.25% for 1 year
		Pound payable at the end of Year =	5000000 x 1.0425 =	£          52,12,500.00
	Step 2 =	Convert Pound to $ today using exchange rate 1.52
		5000000 x 1.52 =		$          76,00,000.00
	Step 3 =	Invest these $ for 1 year at 5.2%
		$ inflow at the end of year		7600000 x 1.052
				€          79,95,200.00
	Step 4 =	Cover this amount using forward rate-
		Sell $ 1 year forward at 1.5428/pound
		Pound receivable at the end of year =
		3460526.32/1.5428 =		£          52,43,441.76
	Profit =	$ Receivable		£          52,43,441.76
		- $ payable		£          52,12,500.00
		Profit -		£                30,941.76