Fi8000Fi8000Exchange RatesExchange Rates

Forwards, FuturesForwards, Futures

Milind ShrikhandeMilind Shrikhande

Final ExamFinal Exam

☺ 30% of your grade30% of your grade

☺ The exam is comprehensive – covers everything The exam is comprehensive – covers everything on the syllabuson the syllabus

☺ 1.5-2 hours, 4-5 questions1.5-2 hours, 4-5 questions

☺ Bring your calculator and a formula sheet (Bring your calculator and a formula sheet (oneone page, letter, you may write on both sides)page, letter, you may write on both sides)

☺ StockTrak written assignment – StockTrak written assignment – typetype and bring and bring with you to the exam.with you to the exam.

Tonight and Next WeekTonight and Next Week

☺Currency exchange rateCurrency exchange rate☺ SpotSpot☺ ForwardForward

☺Debt instrumentsDebt instruments☺ TypesTypes☺ Ratings (default risk)Ratings (default risk)☺ Spot and forward interest rateSpot and forward interest rate☺ The yield curveThe yield curve☺ DurationDuration

Currency Exchange Rate (Spot)Currency Exchange Rate (Spot)

☺ A spot currency transaction is an exchange of A spot currency transaction is an exchange of one currency for another.one currency for another.

☺ The currency exchange rate is a simple The currency exchange rate is a simple conversion factor:conversion factor:

☺ The direct exchange rate is the number of $US to be The direct exchange rate is the number of $US to be paid for 1 unit of foreign currency (usually for the paid for 1 unit of foreign currency (usually for the £UK and the Euro);£UK and the Euro);

☺ The indirect exchange rate is the number of foreign The indirect exchange rate is the number of foreign currency units paid for 1 $US (usually for the Swiss currency units paid for 1 $US (usually for the Swiss franc and Japanese yen).franc and Japanese yen).

Currency Exchange RateCurrency Exchange Rate

Numeric ExampleNumeric Example::

The exchange rate between the $US and The exchange rate between the $US and £UK is 1.6757 $US/ £UK - i.e. one has to £UK is 1.6757 $US/ £UK - i.e. one has to pay $1.6757 for £1 (direct).pay $1.6757 for £1 (direct).

The same exchange rate can be presented The same exchange rate can be presented as 1/1.6757 = 0.5968 £UK /$US - i.e. one as 1/1.6757 = 0.5968 £UK /$US - i.e. one has to pay £0.5968 for $1 (indirect).has to pay £0.5968 for $1 (indirect).

Currency Exchange RateCurrency Exchange Rate

Example continuedExample continued::

The exchange rate between the $US and The exchange rate between the $US and £UK is 1.6757 $US/ £UK.£UK is 1.6757 $US/ £UK.

The exchange rate between the $US and J¥ The exchange rate between the $US and J¥ is 0.007331 $US/J¥.is 0.007331 $US/J¥.

What should be the exchange rate between What should be the exchange rate between the £UK and the J¥?the £UK and the J¥?

Currency ArbitrageCurrency Arbitrage

☺ There are at least two ways to convert pounds to There are at least two ways to convert pounds to yen:yen:

☺ Direct conversion of Direct conversion of £UK to£UK to J¥J¥☺ Conversion using an intermediary currency:Conversion using an intermediary currency:

☺Convert Convert £UK to£UK to $ $USUS

☺Convert $Convert $US toUS to J¥J¥

☺ If there is no opportunity to make arbitrage If there is no opportunity to make arbitrage profits, both conversion methods must imply the profits, both conversion methods must imply the same pound to yen exchange rate . same pound to yen exchange rate .

Currency Exchange RateCurrency Exchange Rate

Example (data)Example (data)::

1.6757 $US/£UK1.6757 $US/£UK oror 0.5968 £UK/$US.0.5968 £UK/$US.

0.007331 $US/J¥0.007331 $US/J¥ oror 136.40 J¥/$US.136.40 J¥/$US.

We will use the no-arbitrage argument to We will use the no-arbitrage argument to calculate the £UK/J¥ (or J¥/£UK) exchange calculate the £UK/J¥ (or J¥/£UK) exchange rate.rate.

Currency Exchange RateCurrency Exchange Rate

Conversion using an intermediary currencyConversion using an intermediary currency::

Convert £UK to $US: Convert £UK to $US: the cost of 1 $US is 0.5968 £UKthe cost of 1 $US is 0.5968 £UK

Convert $US to Convert $US to J¥:J¥:the cost of 1 the cost of 1 J¥J¥ is is 0.007331 $US0.007331 $US

The £UK cost of 1 The £UK cost of 1 J¥:J¥:0.5968 £UK/$US * 0.5968 £UK/$US * 0.007331 0.007331 $US/$US/J¥ =J¥ = 0.004375 0.004375 £UK/£UK/J¥J¥

Currency Exchange RateCurrency Exchange Rate

The Pound-Yen no-arbitrage exchange rateThe Pound-Yen no-arbitrage exchange rate::

The The £UK/£UK/J¥J¥ exchange rate is 0.004375, exchange rate is 0.004375,

i.e. i.e. the cost of the cost of 1 J¥1 J¥ is 0.004375 is 0.004375 £UK.£UK.

The J¥/The J¥/£UK£UK exchange rate is exchange rate is

1/0.004375 = 228.5641,1/0.004375 = 228.5641,

i.e. i.e. the cost of the cost of 1 £UK1 £UK is is 228.5641228.5641 J¥J¥..

Currency Exchange ArbitrageCurrency Exchange Arbitrage

Example continuedExample continued::The $US/ £UK exchange rate is 1.6757.The $US/ £UK exchange rate is 1.6757.

The $US/J¥ exchange rate is 0.007331.The $US/J¥ exchange rate is 0.007331.

Is there an arbitrage opportunity if the £UK/J¥ exchange Is there an arbitrage opportunity if the £UK/J¥ exchange rate is 0.004494? rate is 0.004494?

Yes! The £UK/J¥ exchange rate in the market is different Yes! The £UK/J¥ exchange rate in the market is different from the no-arbitrage rate (two-stage currency exchange):from the no-arbitrage rate (two-stage currency exchange):

Market: 0.004494 £UK/J¥ > 0.004375 £UK/J¥ :No-arbitrageMarket: 0.004494 £UK/J¥ > 0.004375 £UK/J¥ :No-arbitrage

How can we make an arbitrage profit?How can we make an arbitrage profit?

Currency Exchange ArbitrageCurrency Exchange Arbitrage

Cross currency (triangle) arbitrage strategyCross currency (triangle) arbitrage strategy::

Sell the expensive J¥ – convert J¥ to £UK in one step:Sell the expensive J¥ – convert J¥ to £UK in one step:1. Sell J¥ for £UK 1. Sell J¥ for £UK (i.e., Buy £UK with J¥ or convert £UK to J¥)(i.e., Buy £UK with J¥ or convert £UK to J¥)

Buy the cheap J¥ - convert £UK to J¥ in two steps, using Buy the cheap J¥ - convert £UK to J¥ in two steps, using the $US as an intermediary:the $US as an intermediary:

2. Buy $US with £UK (convert £UK to $US)2. Buy $US with £UK (convert £UK to $US)3. Buy J¥ with $US (convert $US to J¥)3. Buy J¥ with $US (convert $US to J¥)

Note: this is a round trip transaction. You start with J¥ Note: this is a round trip transaction. You start with J¥ (before step 1) and you end up with J¥ (after step 3).(before step 1) and you end up with J¥ (after step 3).

Currency Exchange ArbitrageCurrency Exchange Arbitrage

Cross currency (triangle) arbitrage strategyCross currency (triangle) arbitrage strategy::

Sell the expensive J¥ - conversion using the direct £UK to Sell the expensive J¥ - conversion using the direct £UK to J¥ exchange rate:J¥ exchange rate:

1. Sell 1 J¥ for 0.004494 £UK 1. Sell 1 J¥ for 0.004494 £UK (i.e., Buy 0.004494 £UK for 1 J¥)(i.e., Buy 0.004494 £UK for 1 J¥)

Buy the cheap J¥ - conversion from £UK to J¥ in two Buy the cheap J¥ - conversion from £UK to J¥ in two stages, using the $US as an intermediary:stages, using the $US as an intermediary:

2. Buy $US for 0.004494 £UK (you can buy2. Buy $US for 0.004494 £UK (you can buy 0.004494 £UK * 1.6757 $US/£UK = 0.00753 $US)0.004494 £UK * 1.6757 $US/£UK = 0.00753 $US)3. Buy J¥ for 0.00753 $US (you can buy3. Buy J¥ for 0.00753 $US (you can buy 0.00753 $US * 136.40 J¥/$US = 1.02717 J¥)0.00753 $US * 136.40 J¥/$US = 1.02717 J¥)

Arbitrage profit: you start with 1 J¥ and end up with 1.02717 J¥. Arbitrage profit: you start with 1 J¥ and end up with 1.02717 J¥.

Currency Exchange ArbitrageCurrency Exchange Arbitrage

Cross currency arbitrage strategy (end up with $US)Cross currency arbitrage strategy (end up with $US)::

2. Sell 136.40 J¥ for £UK (you can buy 2. Sell 136.40 J¥ for £UK (you can buy 136.40 J¥ * 0.004494 £UK/J¥ = 0.6130 £UK)136.40 J¥ * 0.004494 £UK/J¥ = 0.6130 £UK)

3. Buy $US for 0.6130 £UK (you can buy3. Buy $US for 0.6130 £UK (you can buy 0.6130 £UK * 1.6757 $US/£UK = 1.02717 $US)0.6130 £UK * 1.6757 $US/£UK = 1.02717 $US)

1. Buy J¥ for 1 $US (you can buy1. Buy J¥ for 1 $US (you can buy 1 $US * 136.40 J¥/$US = 136.40 J¥)1 $US * 136.40 J¥/$US = 136.40 J¥)

Arbitrage profit: you start with 1 $US and end up with Arbitrage profit: you start with 1 $US and end up with 1.02717 $US. An arbitrage profit of 0.02717 $US.1.02717 $US. An arbitrage profit of 0.02717 $US.

Currency Exchange Rate (Forward)Currency Exchange Rate (Forward)

☺ Forward or Futures ContractsForward or Futures Contracts☺ An agreement between a buyer and a seller, to An agreement between a buyer and a seller, to

trade at a specific date in the future, a specific trade at a specific date in the future, a specific quantity of a specific quantity of a specific currencycurrency for an agreed for an agreed exchange rateexchange rate..

☺ Forward – tailored OTC market contracts for Forward – tailored OTC market contracts for creditworthy traders and large trades.creditworthy traders and large trades.

☺ Futures – formal markets of standardized Futures – formal markets of standardized contracts (International Monetary Market in contracts (International Monetary Market in Chicago, London International Financial Futures Chicago, London International Financial Futures Exchange).Exchange).

Covered Interest ArbitrageCovered Interest Arbitrage

☺ There are at least two ways to invest money There are at least two ways to invest money without risk for one year:without risk for one year:

☺ Domestic risk-free investment Domestic risk-free investment ☺Buy US Treasury BillsBuy US Treasury Bills

☺ Foreign risk-free investmentForeign risk-free investment☺Convert $US for foreign currencyConvert $US for foreign currency☺Buy foreign risk-free bonds for 1 yearBuy foreign risk-free bonds for 1 year☺Convert the foreign currency back to $US (forward contract)Convert the foreign currency back to $US (forward contract)

☺ If there is no opportunity to make arbitrage If there is no opportunity to make arbitrage profits, both investment strategies should have profits, both investment strategies should have the same dollar denominated percentage return.the same dollar denominated percentage return.

Covered Interest ArbitrageCovered Interest Arbitrage

Numeric ExampleNumeric Example::

Suppose you would like to invest $100,000 in a Suppose you would like to invest $100,000 in a risk-free instrument.risk-free instrument.

In the US the annual risk free rate is 5.00%, while In the US the annual risk free rate is 5.00%, while in the UK the annual risk free rate is 5.20%.in the UK the annual risk free rate is 5.20%.

Is there an arbitrage opportunity? – Compare the Is there an arbitrage opportunity? – Compare the domestic and foreign investment strategies.domestic and foreign investment strategies.

Covered Interest ArbitrageCovered Interest Arbitrage

Numeric Example ContinuedNumeric Example Continued::We need the spot and forward (one year) We need the spot and forward (one year) $US/£UK exchange rates to answer that question.$US/£UK exchange rates to answer that question.

Note that if we do not use a forward contract to Note that if we do not use a forward contract to “lock in” the exchange rate, the foreign alternative “lock in” the exchange rate, the foreign alternative becomes a risky (exchange rate risk) rather than a becomes a risky (exchange rate risk) rather than a risk-free investment strategy.risk-free investment strategy.

Is there an opportunity to make arbitrage profits, if Is there an opportunity to make arbitrage profits, if the spot rate is 1.6750 $US/£UK and the (one the spot rate is 1.6750 $US/£UK and the (one year) forward exchange rate is 1.6500 $US/£UK?year) forward exchange rate is 1.6500 $US/£UK?

Comparing the Two StrategiesComparing the Two Strategies

Domestic risk-free investmentDomestic risk-free investment::

1. Buy US Treasury Bills1. Buy US Treasury Bills

StrategyStrategy t = 0t = 0 t = 1t = 1

CF ($US)CF ($US) CF (£UK)CF (£UK) CF ($US)CF ($US) CF (£UK)CF (£UK)

Buy T-BillsBuy T-Bills

(5.00%)(5.00%)

-100,000-100,000 +105,000+105,000

TotalTotal -100,000-100,000 00 +105,000+105,000 00

Comparing the Two StrategiesComparing the Two Strategies

Foreign risk-free investmentForeign risk-free investment::

1. Convert $US for foreign currency1. Convert $US for foreign currency

2. Buy foreign risk-free bonds for 1 year2. Buy foreign risk-free bonds for 1 year

3. Convert the foreign currency back to $US (forward contract)3. Convert the foreign currency back to $US (forward contract)

StrategyStrategy t = 0t = 0 t = 1t = 1CF ($US)CF ($US) CF (£UK)CF (£UK) CF ($US)CF ($US) CF (£UK)CF (£UK)

Convert $US to £UK Convert $US to £UK (spot rate 1.6750)(spot rate 1.6750)

--100,000100,000 +59,701+59,701

Buy UK risk-free bondsBuy UK risk-free bonds

(5.20%)(5.20%)--59,70159,701 +62,806+62,806

Convert £UK to $USConvert £UK to $US

(forward rate 1.6500)(forward rate 1.6500)+103,630+103,630 --62,80662,806

TotalTotal -100,000-100,000 00 +103,630+103,630 00

Arbitrage StrategyArbitrage Strategy

Buy Cheap: Domestic risk-free investmentBuy Cheap: Domestic risk-free investment Buy US Treasury BillsBuy US Treasury Bills get 5% dollar denominated risk free rateget 5% dollar denominated risk free rate

Sell Expensive: Foreign risk-free investmentSell Expensive: Foreign risk-free investmentConvert £UK to $USConvert £UK to $USShort sellShort sell UK risk-free bonds for 1 year UK risk-free bonds for 1 yearConvert $US back to £UK (forward contract)Convert $US back to £UK (forward contract) pay 3.63% dollar denominated risk free ratepay 3.63% dollar denominated risk free rate

Covered Interest ArbitrageCovered Interest Arbitrage

StrategyStrategy t = 0t = 0 t = 1t = 1

CF ($US)CF ($US) CF (£UK)CF (£UK) CF ($US)CF ($US) CF (£UK)CF (£UK)

Buy US T-Bills Buy US T-Bills

(5.00%)(5.00%)-100,000-100,000 +105,000+105,000

Convert £UK to $US Convert £UK to $US (spot rate 1.6750)(spot rate 1.6750)

+100,000+100,000 -59,701-59,701

Sell UK risk-free bondsSell UK risk-free bonds

(5.20%)(5.20%)+59,701+59,701 -62,806-62,806

Convert $US to £UKConvert $US to £UK

(forward rate 1.6500)(forward rate 1.6500)-105,000-105,000 +63,636+63,636

TotalTotal 00 00 00 +803+803

Covered Interest ArbitrageCovered Interest Arbitrage

What is the no-arbitrage UK risk free rate? (r = 6.5909%)What is the no-arbitrage UK risk free rate? (r = 6.5909%)

StrategyStrategy t = 0t = 0 t = 1t = 1CF ($US)CF ($US) CF (£UK)CF (£UK) CF ($US)CF ($US) CF (£UK)CF (£UK)

Buy US T-Bills Buy US T-Bills

(5.00%)(5.00%)-100,000-100,000 +105,000+105,000

Convert £UK to $US Convert £UK to $US (spot rate 1.6750)(spot rate 1.6750)

+100,000+100,000 -59,701-59,701

Sell UK risk-free bondsSell UK risk-free bonds

(5.20%)(5.20%)+59,701+59,701 -59,701(1+r)-59,701(1+r)

Convert $US to £UKConvert $US to £UK

(forward rate 1.6500)(forward rate 1.6500)-105,000-105,000 +63,636+63,636

TotalTotal 00 00 00 =0 =0 +803+803

Interest Rate ParityInterest Rate Parity(Covered Interest Arbitrage)(Covered Interest Arbitrage)

IntuitionIntuition: : If two investments are risk-free they must have the same If two investments are risk-free they must have the same rate of return. Therefore, any difference in the domestic rate of return. Therefore, any difference in the domestic and foreign risk-free rates must be offset by a difference in and foreign risk-free rates must be offset by a difference in the spot and forward exchange rates.the spot and forward exchange rates.

FormulaFormula::

0 0

1$ $

£ £ 1

T

US

UK

rUS USF E

UK UK r

Interest Rate ParityInterest Rate Parity(Covered Interest Arbitrage)(Covered Interest Arbitrage)

NotationNotation: : EE00 = spot exchange rate ($US/£UK) or (£UK/$US) = spot exchange rate ($US/£UK) or (£UK/$US)

FF00 = forward exchange rate ($US/£UK) or (£UK/$US) = forward exchange rate ($US/£UK) or (£UK/$US)

* Note that if you use the £UK/$US (indirect) exchange rate * Note that if you use the £UK/$US (indirect) exchange rate you will also have to reverse the ratio of interest rates.you will also have to reverse the ratio of interest rates.

FormulaFormula::

0 0

0 0

1$ $

£ £ 1

1£ £

$ $ 1

T

US

UK

T

UK

US

rUS USF E

UK UK r

or

rUK UKF E

US US r

Practice ProblemsPractice Problems

Practice Problem #1Practice Problem #1The annual risk-free rate in the US is 5.00% The annual risk-free rate in the US is 5.00% while in Japan it is 3.20%.while in Japan it is 3.20%.

What should be the spot J¥/What should be the spot J¥/$US exchange $US exchange rate, if the (one year) forward rate, if the (one year) forward J¥/J¥/$US $US exchange rate is 107.875?exchange rate is 107.875?

Answer: EAnswer: E00((J¥/J¥/$US) = 109.7565$US) = 109.7565

Practice ProblemsPractice Problems

Practice Problem #2Practice Problem #2The annual risk-free rate in the US is 4.60% while The annual risk-free rate in the US is 4.60% while in Japan it is 3.50%.in Japan it is 3.50%.

The spot J¥/£UK exchange rate is 205.00, the spot The spot J¥/£UK exchange rate is 205.00, the spot $US/£UK exchange rate is 1.8825, the (one year) $US/£UK exchange rate is 1.8825, the (one year) forward J¥/£UK exchange rate is 204.00 and the forward J¥/£UK exchange rate is 204.00 and the forward $US/£UK exchange rate is 1.8900.forward $US/£UK exchange rate is 1.8900.

Describe an arbitrage transaction. Write down the Describe an arbitrage transaction. Write down the same stages and use the table format presented in same stages and use the table format presented in the lecture notes.the lecture notes.

Practice ProblemsPractice Problems

BKM Ch. 23: 10, 12-14.BKM Ch. 23: 10, 12-14.

Practice problems:Practice problems:

Forward and futures contracts 1-5;Forward and futures contracts 1-5;

Currency exchange rates 6-9.Currency exchange rates 6-9.