Tutorial 6

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Question 1 a) Define interest rate parity. What is the relationship between interest rate parity and forward rates?

b) Define the terms covered interest arbitrage and uncovered interest arbitrage . What is the differences between these two transaction?

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a) Interest rate parity (IRP)

Is the differences in the national interest rates for securities of similar risk and maturity should be equal. So when IRP is hold , there is no covered interest and arbitrage profit.(profit=Costs )

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The relationship between IRP and forward rates If the HC have high interest than FC .When HC is at forward discount

that is F>S. HC is expected to depreciate against the FC . If so ,HC interest rate should be higher than the FC to compensate for the expected depreciation of the HC. If not nobody will hold HC securities

If HC low interest than FC , when HC is at forward premium that is F<S , This has indicate that the forward exchange rate will deviate from the spot rate as long as of the 2 countries are not same

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When IRP hold , we able to in different between our investing money in HC and FC with forward hedging.

If IPR violated, we will better off by investing in HC (FC) if (1+i$)is greater (LESS) than (F/S)(1+i£). When need borrow , we will choose to borrow the currency interest rate is lower.

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b) Coverage interest arbitrage (CIA) is an arbitrage trading strategy whereby an investor capitalize on the interest rate differential between two countries by using two a forward contract to cover exchange rate risk.

Uncovered interest arbitrage (UIA) wherein investors borrow in currency exhibiting relatively low interest rates and convert the proceeds into the currency which offer higher interest rates

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The differences CIA – have the similar way like IRP even the spot and forward

exchange market not always state in equilibrium but it have the opportunity for low riskless arbitrage exist and have a higher return on a cover forward basis by entering the contract to hedging the risk.

UIA-it has high risk high return because they buy in lower price and sell in high price at the future spot rate without entering any forward contract.

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Question 2 Peter Solskjaer is a foreign exchange dealer for a bank in Manchester. He has £2,000,000 (or its Singapore dollar equivalent) for a short-term money market investment. He wonders if he should invest in pounds sterling or make a covered interest arbitrage investment in the Singapore dollar. He faces the following rates.

Spot exchange rate S$ 2.9880/£3-month forward rate S$ 3.0000/£3-month UK interest rate 3% p.a.3-month Singapore interest rate 5% p.a.

Which country’s money market do you recommend Solskjaer to invest? Why? Calculate the arbitrage profit or loss in £?

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90 days

Pound money market

Singapore dollar money market

£2,000,000 £2,015,000£2,016,900

S = S$ 2.9880/£

S$ 5,976,000 S$ 6,050,700

F90 = S$ 3.0000/£

x 1.0125

x 1.0075Start End

i £ = 3% per annum(0.0075 % per 90 days)

1 + (0.03 x 90/360)

i S$ = 5% per annum(1.25% per 90 days)1 + (0.05 x 90/360)

Profit of £ 1900

Arbitrage potential

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Question 3Mary Smith is a foreign exchange dealer for a bank in New York City. She has $1,000,000 (or its Swiss franc equivalent) for a short-term money market investment and wonder if she should invest in U.S. dollars or make a covered interest arbitrage investment in the Swiss franc. She faces the following rates.

Spot exchange rate SF 1.6000/$3-month forward rate SF 1.5800/$3-month US interest rate 8% p.a.3-month Swiss interest rate 6% p.a.

(a) Where do you recommend Ms Smith to invest? Why? Calculate the arbitrage profit/loss?

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US interest rate 8% p.a.Start $1,000,000 x1.02 $1,020,000 Arbitrage

1+(0.08x90/360) $1,164,556.96 Potential

Dollar money market S= SF 1.6000/$ F= SF1.5800/$

Swiss franc marketSF 1,600,000 X1.15 SF 1,840,000 1 + (0.06x90/360) Swiss interest rate 6% p.a.

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90 Days

CIA profit $1,164,556.96 - $1,020,000 = $144,556.96

CIA annualised rate of return = (1+($144,556/$1,000,000)360/90 -1 =0.716 =71.6%

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Question 4

Walcott Ltd, a Belgian company with subsidiaries all over Southeast Asia, has been funding its Kuala Lumpur subsidiary primarily with euros debt because of the cost and availability of euros capital as opposed to Ringgit Malaysia (RM) funds. The Finance Director of Walcott (Malaysia) Sdn. Bhd. is considering a one-year bank loan for €1,800,000. The current spot exchange rate is RM 4.1000/€, and the euro-based interest is 6.80% for the one year period.

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(a) assume expected inflation rates of 5% and 2% in malaysia and europe for the coming year respectively. according to purchasing power parity, what would the effective cost of funds be in rm terms?

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• Malaysia Inflation Rate is 5%• Europe Inflation Rate is 2%• Spot Exchange Rate is RM 4.10/€

Answer (4a) =RM 4.10/€ X

= RM 4.22/€

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(b) if walcott (malaysia) sdn. bhd. could borrow from public bank berhad at 8.30% per annum, is this option more cost effective than part (i) above? 

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• Euro-based Interest 6.80%• Borrow from Public Bank Berhad at 8.30% per annum

Answer (5b)Step 1 €1,800,000 X 1.068 = € 1922400

Step 2 €1,800,000 X RM 4.10/€ = RM7,380,000

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Step 3RM 7,380,000 X 1.083 = RM 7,992,540

Step 4 RM 7,992,540 ÷ RM 4.10/€ = € 1,949,400

Conclusion (b) Is more cost effective than (a) because it generates higher return.

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Question 5. (a) When will an opportunity for locational arbitrage profits arise?

Locational arbitrage arise when a bank’s buying price (bid price) is higher than another bank’s selling price (ask price) for the same currency

Eg: Bid Ask

Bank A $.635/NZ$ $.640Bank B $.645 $.650

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Question 5(b) Podolski Swiensteiger holds MZ$ 500,000. Given the following quotes, what is the amount of locational arbitrage profits in NZ$ terms that he could earn?

Bid AskKiwi Bank NZ$1.3530/$ NZ$1.3580/$Auckland Bank NZ$1.3400/$ NZ$1.3450/$

1st: NZ$ 500,000 invest in $ @ NZ$1.3450/$ from Auckland Bankso, NZ$ 500,000 / NZ$1.3450 = $371747.212

2nd: sell $371747.212 @ NZ$1.3530/$ to Kiwi Bankso, $371747.212 x NZ$1.3530 = NZ$502973.978

3th: NZ$502973.978 – NZ$ 500,000 = NZ$2973.978 (locational arbitrage profit)

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Question 6

Suppose that the current spot exchange rate is €1.06/$ and the three-month forward exchange rate is €1.02/$. The three-month interest rate is 5.6 percent per annum in the United States and 5.40 percent per annum in France. Assume that you can borrow up to $1,000,000 or €1,060,000.

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Current Spot Rate, € 1.06 / $ 3 months Forward exchange rate , € 1.02/$ Interest rate in US = 5.6 p.a. ( = 1.4%) Interest rate in France = 5.4 p.a. = 1.35%) Money $ 1,000,000 or €1,060,000

(a)Show how to realize a certain profit via covered interest arbitrage, assuming that you want to realize profit in terms of U.S. dollars. Also determine the size of your arbitrage profit.

Answer 6(a) Step1 A : Numerator : France : FC : € B : Denominator : US : HC : $

Step2 Interest Differential = = 5.4% - 5.6% = -0.2%Step 3 €/ $ (Indirect Quote) FC/HC = = 15.69% (forward premium for euro(Currency A), forward

discount for dollar(Currency B) )

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Step 4

Interest Differential < Forward Discount on US dollar

-0.2 < -15.69%(Invest in France €) (Borrow from US $)

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Borrow US dollar rate = 5.6 % per annum

90 days

Dollar money market

Euro money market

$1,000,000 $1,014,000$1,053,245$ 39,245

S= €1.06/$

€1,060,000 €1,074,310

F90 = €1.02/$

x 1.0135

x 1.014

Start End

Invest Euro currency rate = 5.4% per annum

Borrow EarnProfit

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(b) Assume that you want to realize profit in terms of euros. Show the covered arbitrage process and determine the arbitrage profit in euros.

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Step1 A : Denominator : US : FC : $ B : Numerator : France : HC : €

Step2 Interest Differential = = 5.4% - 5.6% = -0.2%Step 3 €/ $ (direct Quote) HC/FC

=

= -15.09% (forward discount for dollar (Currency B) )27

Step 4 Interest Differential < Forward Discount on Currency France -0.2 < -15.09%(Invest in France €) (Borrow from US $)

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Borrow US dollar rate = 5.6 % per annum

90 days

Dollar money market

Euro money market

$1,000,000 $1,014,000$1,053,245$ 39,245

S= €1.06/$

€1,060,000 €1,074,310

F90 = €1.02/$

x 1.0135

x 1.014

Start End

Invest Euro currency rate = 5.4% per annum

Borrow EarnProfit

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