# Fi8000 Exchange Rates Forwards, Futures Milind Shrikhande.

## Presentation on theme: "Fi8000 Exchange Rates Forwards, Futures Milind Shrikhande."— Presentation transcript:

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

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

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).

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).

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¥?

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.

Currency Exchange Rate Example (data): 1.6757 \$US/£UKor0.5968 £UK/\$US. 0.007331 \$US/J¥or136.40 J¥/\$US. We will use the no-arbitrage argument to calculate the £UK/J¥ (or J¥/£UK) exchange rate.

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¥ 0.004375 £UK/ J¥

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¥.

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?

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).

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¥) (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) 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¥) 0.00753 \$US * 136.40 J¥/\$US = 1.02717 J¥) Arbitrage profit: you start with 1 J¥ and end up with 1.02717 J¥.

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) 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) 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¥) 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.

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).

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.

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.

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?

Comparing the Two Strategies Domestic risk-free investment: 1. Buy US Treasury Bills Strategy t = 0 t = 1 CF (\$US) CF (£UK) CF (\$US) CF (£UK) Buy T-Bills (5.00%)-100,000+105,000 Total-100,0000+105,0000

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) Strategy t = 0 t = 1 CF (\$US) CF (£UK) CF (\$US) CF (£UK) Convert \$US to £UK (spot rate 1.6750) - 100,000 +59,701 Buy UK risk-free bonds (5.20%) - 59,701 +62,806 Convert £UK to \$US (forward rate 1.6500) +103,630 - 62,806 Total-100,0000+103,6300

Arbitrage Strategy Buy Cheap: Domestic risk-free investment Buy US Treasury Bills 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

Covered Interest Arbitrage Strategy t = 0 t = 1 CF (\$US) CF (£UK) CF (\$US) CF (£UK) Buy US T-Bills (5.00%)-100,000+105,000 Convert £UK to \$US (spot rate 1.6750) +100,000-59,701 Sell UK risk-free bonds (5.20%)+59,701-62,806 Convert \$US to £UK (forward rate 1.6500) -105,000+63,636 Total000+803

Covered Interest Arbitrage What is the no-arbitrage UK risk free rate? (r = 6.5909%) Strategy t = 0 t = 1 CF (\$US) CF (£UK) CF (\$US) CF (£UK) Buy US T-Bills (5.00%)-100,000+105,000 Convert £UK to \$US (spot rate 1.6750) +100,000-59,701 Sell UK risk-free bonds (5.20%)+59,701-59,701(1+r) Convert \$US to £UK (forward rate 1.6500) -105,000+63,636 Total000 =0 +803

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:

Interest Rate Parity (Covered Interest Arbitrage) Notation: E 0 = spot exchange rate (\$US/£UK) or (£UK/\$US) F 0 = 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:

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: E 0 ( J¥/ \$US) = 109.7565

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.

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