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Fi8000 Exchange Rates Forwards, Futures

Fi8000 Exchange Rates Forwards, Futures. Milind Shrikhande. 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)

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Fi8000 Exchange Rates Forwards, Futures

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  1. Fi8000Exchange RatesForwards, Futures Milind Shrikhande

  2. 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.

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

  4. 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).

  5. 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).

  6. 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¥?

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

  8. 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.

  9. 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¥

  10. 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 228.5641J¥.

  11. 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?

  12. 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).

  13. 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¥.

  14. 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.

  15. 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).

  16. 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.

  17. 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.

  18. 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?

  19. Comparing the Two Strategies Domestic risk-free investment: 1. Buy US Treasury Bills

  20. 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)

  21. 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

  22. Covered Interest Arbitrage

  23. Covered Interest Arbitrage What is the no-arbitrage UK risk free rate? (r = 6.5909%)

  24. 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:

  25. 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:

  26. 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

  27. 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.

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

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