Fi8000 Exchange Rates Forwards, Futures

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Fi8000Exchange RatesForwards, Futures

• Milind Shrikhande

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Final Exam

• 30 of your grade
• The exam is comprehensive covers everything on
  the syllabus
• 1.5-2 hours, 4-5 questions
• Bring your calculator and a formula sheet (one
  page, letter, you may write on both sides)
• StockTrak written assignment type and bring
  with you to the exam.

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Tonight and Next Week

• Currency exchange rate
• Spot
• Forward
• Debt instruments
• Types
• Ratings (default risk)
• Spot and forward interest rate
• The yield curve
• Duration

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Currency Exchange Rate (Spot)

• A spot currency transaction is an exchange of one
  currency for another.
• The currency exchange rate is a simple conversion
  factor
• The direct exchange rate is the number of US to
  be paid for 1 unit of foreign currency (usually
  for the UK and the Euro)
• The indirect exchange rate is the number of
  foreign currency units paid for 1 US (usually
  for the Swiss franc and Japanese yen).

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Currency Exchange Rate

• Numeric Example
• The exchange rate between the US and UK is
  1.6757 US/ UK - i.e. one has to pay 1.6757 for
  1 (direct).
• The same exchange rate can be presented as
  1/1.6757 0.5968 UK /US - i.e. one has to pay
  0.5968 for 1 (indirect).

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Currency Exchange Rate

• Example continued
• The exchange rate between the US and UK is
  1.6757 US/ UK.
• The exchange rate between the US and J is
  0.007331 US/J.
• What should be the exchange rate between the UK
  and the J?

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Currency Arbitrage

• There are at least two ways to convert pounds to
  yen
• Direct conversion of UK to J
• Conversion using an intermediary currency
• Convert UK to US
• Convert US to J
• If there is no opportunity to make arbitrage
  profits, both conversion methods must imply the
  same pound to yen exchange rate .

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Currency Exchange Rate

• Example (data)
• 1.6757 US/UK or 0.5968 UK/US.
• 0.007331 US/J or 136.40 J/US.
• We will use the no-arbitrage argument to
  calculate the UK/J (or J/UK) exchange rate.

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Currency Exchange Rate

• Conversion using an intermediary currency
• Convert UK to US
• the cost of 1 US is 0.5968 UK
• Convert US to J
• the cost of 1 J is 0.007331 US
• The UK cost of 1 J
• 0.5968 UK/US 0.007331 US/J
• 
  0.004375 UK/J

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Currency Exchange Rate

• The Pound-Yen no-arbitrage exchange rate
• The UK/J exchange rate is 0.004375,
• i.e. the cost of 1 J is 0.004375 UK.
• The J/UK exchange rate is
• 1/0.004375 228.5641,
• i.e. the cost of 1 UK is 228.5641 J.

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Currency Exchange Arbitrage

• Example continued
• The US/ UK exchange rate is 1.6757.
• The US/J exchange rate is 0.007331.
• Is there an arbitrage opportunity if the UK/J
  exchange rate is 0.004494?
• Yes! The UK/J exchange rate in the market is
  different from the no-arbitrage rate (two-stage
  currency exchange)
• Market 0.004494 UK/J 0.004375 UK/J
  No-arbitrage
• How can we make an arbitrage profit?

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Currency Exchange Arbitrage

• Cross currency (triangle) arbitrage strategy
• Sell the expensive J convert J to UK in one
  step
• 1. Sell J for UK
• (i.e., Buy UK with J or convert UK to J)
• Buy the cheap J - convert UK to J in two
  steps, using the US as an intermediary
• 2. Buy US with UK (convert UK to US)
• 3. Buy J with US (convert US to J)
• Note this is a round trip transaction. You start
  with J (before step 1) and you end up with J
  (after step 3).

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Currency Exchange Arbitrage

• Cross currency (triangle) arbitrage strategy
• Sell the expensive J - conversion using the
  direct UK to J exchange rate
• 1. Sell 1 J for 0.004494 UK
• (i.e., Buy 0.004494 UK for 1 J)
• Buy the cheap J - conversion from UK to J in
  two stages, using the US as an intermediary
• 2. Buy US for 0.004494 UK (you can buy
• 0.004494 UK 1.6757 US/UK 0.00753 US)
• 3. Buy J for 0.00753 US (you can buy
• 0.00753 US 136.40 J/US 1.02717 J)
• Arbitrage profit you start with 1 J and end up
  with 1.02717 J.

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Currency Exchange Arbitrage

• Cross currency arbitrage strategy (end up with
  US)
• 2. Sell 136.40 J for UK (you can buy
• 136.40 J 0.004494 UK/J 0.6130 UK)
• 3. Buy US for 0.6130 UK (you can buy
• 0.6130 UK 1.6757 US/UK 1.02717 US)
• 1. Buy J for 1 US (you can buy
• 1 US 136.40 J/US 136.40 J)
• Arbitrage profit you start with 1 US and end up
  with 1.02717 US. An arbitrage profit of 0.02717
  US.

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Currency Exchange Rate (Forward)

• Forward or Futures Contracts
• An agreement between a buyer and a seller, to
  trade at a specific date in the future, a
  specific quantity of a specific currency for an
  agreed exchange rate.
• Forward tailored OTC market contracts for
  creditworthy traders and large trades.
• Futures formal markets of standardized
  contracts (International Monetary Market in
  Chicago, London International Financial Futures
  Exchange).

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Covered Interest Arbitrage

• There are at least two ways to invest money
  without risk for one year
• Domestic risk-free investment
• Buy US Treasury Bills
• Foreign risk-free investment
• Convert US for foreign currency
• Buy foreign risk-free bonds for 1 year
• Convert the foreign currency back to US (forward
  contract)
• If there is no opportunity to make arbitrage
  profits, both investment strategies should have
  the same dollar denominated percentage return.

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Covered Interest Arbitrage

• Numeric Example
• Suppose you would like to invest 100,000 in a
  risk-free instrument.
• In the US the annual risk free rate is 5.00,
  while in the UK the annual risk free rate is
  5.20.
• Is there an arbitrage opportunity? Compare the
  domestic and foreign investment strategies.

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Covered Interest Arbitrage

• Numeric Example Continued
• We need the spot and forward (one year) US/UK
  exchange rates to answer that question.
• Note that if we do not use a forward contract to
  lock in the exchange rate, the foreign
  alternative becomes a risky (exchange rate risk)
  rather than a risk-free investment strategy.
• Is there an opportunity to make arbitrage
  profits, if the spot rate is 1.6750 US/UK and
  the (one year) forward exchange rate is 1.6500
  US/UK?

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Comparing the Two Strategies

• Domestic risk-free investment
• 1. Buy US Treasury Bills

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Comparing the Two Strategies

• Foreign risk-free investment
• 1. Convert US for foreign currency
• 2. Buy foreign risk-free bonds for 1 year
• 3. Convert the foreign currency back to US
  (forward contract)

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Arbitrage Strategy

• Buy Cheap Domestic risk-free investment
• Buy US Treasury Bills
• ? get 5 dollar denominated risk free rate
• Sell Expensive Foreign risk-free investment
• Convert UK to US
• Short sell UK risk-free bonds for 1 year
• Convert US back to UK (forward contract)
• ? pay 3.63 dollar denominated risk free rate

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Covered Interest Arbitrage
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Covered Interest Arbitrage

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

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Interest Rate Parity(Covered Interest Arbitrage)

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

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Interest Rate Parity(Covered Interest Arbitrage)

• Notation
• E0 spot exchange rate (US/UK) or (UK/US)
• F0 forward exchange rate (US/UK) or (UK/US)
  
• Note that if you use the UK/US (indirect)
  exchange rate you will also have to reverse the
  ratio of interest rates.
• Formula

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Practice Problems

• Practice Problem 1
• The annual risk-free rate in the US is 5.00
  while in Japan it is 3.20.
• What should be the spot J/US exchange rate, if
  the (one year) forward J/US exchange rate is
  107.875?
• Answer E0(J/US) 109.7565

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Practice Problems

• Practice Problem 2
• The annual risk-free rate in the US is 4.60
  while in Japan it is 3.50.
• The spot J/UK exchange rate is 205.00, the spot
  US/UK exchange rate is 1.8825, the (one year)
  forward J/UK exchange rate is 204.00 and the
  forward US/UK exchange rate is 1.8900.
• Describe an arbitrage transaction. Write down the
  same stages and use the table format presented in
  the lecture notes.

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Practice Problems

• BKM Ch. 23 10, 12-14.
• Practice problems
• Forward and futures contracts 1-5
• Currency exchange rates 6-9.