TOPIC 5 CURRENCY MARKETS: ARBITRAGE, SPECULATION AND HEDGING INTERNATIONAL FINANCIAL MARKETS 2020-2021 PROFESSOR ALEXANDRA HOROBET, PHD 1 Spot markets AGENDA Definition of conventions exchange rates and quoting Bid and ask rates Inverting exchange rates in the presence of spreads The Law of One Price for spot quotes Triangular arbitrage Forward markets Forward market quotations Forward premium or discount Interest rate parity Long and short forward positions: speculation and hedging 2 DEFINITION OF EXCHANGE RATES Exchange rate amount of currency that one has to pay in order to buy one unit of another currency amount of currency that one receives when selling one unit of another currency Which money is being bought or sold? depends on home currency or reference currency (HC) 3 QUOTING CONVENTIONS Professional dealers and brokers quote currencies in either of two ways: direct basis → HC/FC when this quote involves the USD as HC : American terms indirect basis → FC/HC when this quote involves the USD as HC : European terms Most currencies are quoted on a direct basis the most important exceptions: British pound and the Euro 4 QUOTING CONVENTIONS Every exchange transaction involves two currencies 1.3245 CHF/USD terms/counter currency base/quoted currency numerator denominator A trader always buys or sells a fixed amount of the “base” currency How to interpret changes in exchange rates numerator increases → base currency is strengthening and becoming more expensive numerator decreases → base currency is weakening and becoming cheaper 5 MEASURING A CHANGE IN SPOT RATES ▪ Example: 1.5625 CHF/USD to 1.2800 CHF/USD ▪ % change in the value of the USD in terms of the CHF is: Ending rate - Beginning rate Beginning rate = 1.2800 - 1.5625 1.5625 = −18.08% USD depreciated by 18.08% against the CHF ▪ % change in the value of the CHF in terms of the USD is: Beginning rate - Ending rate Ending rate = 1.5625 - 1.2800 = + 22.09% 1.2800 CHF appreciated by 22.09% against the USD 6 SPOT BID AND ASK QUOTATIONS 7 www.fxstreet.com SPOT BID AND ASK QUOTATIONS www.bloomberg.com 8 SPOT BID AND ASK QUOTATIONS Market makers will quote the rate at which they are willing to buy the base currency (Bid) (in terms of the other currency) and the rate at which they are ready to sell the base currency (Ask) 1.5130 - 1.5145 CHF/USD Market maker buys USD Client sells USD Market maker sells USD Client buys USD Often the quotation will be shortened to 30/45. These numbers are points → a point is the fourth place to the right of the decimal point (0.0001) The difference between the bid and the ask price is the spread SPREAD = Sask,t – Sbid,t > 0 9 LAW OF THE WORST PRICE/ RIP-OFF RULE For any single transaction, the bank gives you (as a client) the worst rate from your point of view The rule works as follows: When you sell a currency: a bad rate is a low rate When you buy a currency: a bad rate is a high rate 10 SPREAD SIZE Spreads are variable one day to the other and within a trading day Factors that influence spread size: Traded currencies Exchange rate volatility Order nature and size 11 SPREAD SIZE 12 USD/EUR NOK/EUR INVERTING EXCHANGE RATES IN THE PRESENCE OF SPREADS Rule: the inverse of a bid quote is an ask quote, and vice versa S(CAD/USD)bid,t = 1 S(USD/CAD)ask,t S(CAD/USD)ask,t = 1 S(USD/CAD)bid,t Example: 1.3727 – 1.3730 CAD/USD 0.7283 - 0.7285 USD/CAD 13 THE LAW OF ONE PRICE FOR SPOT EXCHANGE QUOTES Law of one price (LOP) 2 mechanisms that enforce LOP In frictionless markets, two securities that have 1. Arbitrage identical cash flows 2. Least cost dealing must have the same price Works if: - the price difference exceeds the difference of the transaction costs - there are investors that want to make that particular transaction 14 LAW OF ONE PRICE - EXAMPLE USD/CHF quotes (USD is base currency) Citibank 1.65 Chemical Bank 1.6501 Arbitrage opportunity you can buy cheap USD from Citibank and immediately sell to chemical Bank, netting CHF 0.0001 per USD Opportunity for least cost dealing all buyers of USD will buy from Citibank, and all sellers will deal with Chemical Bank The only way to avoid such trading imbalances is if both banks quote the same rate 15 ARBITRAGE ACROSS MARKET MAKERS Quotes: Bank X 20.50 – 20.55 CZK/USD (USD as base) Bank Y 20.60 – 20.65 CZK/USD buy USD from bank X at 20.55 CZK immediately resell it to bank Y at 20.60 CZK profit = 0.05 CZK/USD no risk, no net investment A situation with arbitrage possibilities is not an equilibrium situation Graphically, the no arbitrage condition says that any two banks’ quotes should overlap by at least one point 16 BOUNDS IMPOSED ON SPOT RATES BY ARBITRAGE TRANSACTIONS 20.50 BID X 20.55 ASK 20.61 BID 20.60 BID X’ Y 20.66 ASK 20.65 ASK Quotes There is a strong arbitrage opportunity between banks X and Y: you can buy cheap from X at its ask rate, and resell at a higher bid price to Y. In contrast, if the first bank’s quote is X’, you cannot profitably buy from either X’ or Y and sell to the other 17 LEAST-COST DEALING ACROSS MARKET MAKERS Quotes: Bank X’ 20.61 – 20.66 CZK/USD Bank Y 20.60 – 20.65 CZK/USD All buyers buy from Y, at 20.65 All sellers sell to X’, at 20.61 This situation can be intended by the two banks If both banks want to be in the market for selling and buying, their quotes have to be equal 18 SPOT FX TRADING What happens in a static market? A market-maker for a currency would generate revenues equal to the spread times the volume of dollars bought and sold Given costs, the profit margin would be relatively predictable What happens in a dynamic market? Rates (prices) change constantly and the competition is fierce (thin spreads) The trader cannot live off the bid/ask spread and must take speculative positions Speculative or trading positions carry currency risk • If the trader buys more of a currency than he/she sells, the trader is long (overbought) • If the trader sells more of a currency than he/she buys, the trader is short (oversold) 19 SPOT FX TRADING Short position Long position Bought 30M USD Bought 20M USD Sold 20M USD Sold 30M USD “Square” position Bought 20M USD Sold 20M USD 20 CROSS EXCHANGE RATES Cross exchange rate = exchange rate between 2 currency pairs where neither currency is the USD ( S t (CHF/GBP) = S t (CHF/USD) S t USD/GBP ) Example: S(CHF/USD) = 0.8828 S(USD/GBP) = 1.6489 Cross exchange rate CHF/GBP is: S(CHF/GBP) = 0.8828 x 1.6489 = 1.4556 21 CROSS EXCHANGE RATES USING BID AND ASK Bid cross exchange rates - calculated from the bid USD exchange rates ( ) S t,bid (CHF/GBP) = S t,bid (CHF/USD) S t,bid USD/GBP Ask cross exchange rates - calculated from the ask USD exchange rates ( ) S t,ask (CHF/GBP) = S t,ask (CHF/USD) S t,ask USD/GBP 22 COMPUTING CROSS-RATES - EXAMPLE Find the cost of buying GBP against CHF when 1.2776 – 1.2782 CHF/USD 1.7905 – 1.7906 USD/GBP Divide or multiply? Look at the dimensions → CHF/GBP, so we multiply. S(CHF/GBP) = S(CHF/USD) x S(USD/GBP) Bid or ask? Sbid[CHF/GBP] = 1.2776 1.7905 = 2.2875 Sask[CHF/GBP] = 1.2782 1.7906 = 2.2887 23 TRIANGULAR ARBITRAGE IN FOREX Same 2 mechanisms for spot rates quoted in various currencies: Triangular arbitrage (try) to make money by sequentially buying and selling three currencies, ending with the original currency Triangular least cost dealing search for the cheapest way to achieve a desired conversion 24 TRIANGULAR ARBITRAGE - EXAMPLE Cross-rate quoted by a trader deviates from the quotes against the dollar → possibility for arbitrage Example (using mid-point rates): Spot 0.5000 USD/DEM Spot 8.0200 FIM/USD Quoted cross-rate 4.0000 FIM/DEM Calculated cross-rate 4.0100 FIM/DEM 25 TRIANGULAR ARBITRAGE – EXAMPLE 3. Resell USD for FIM @ 8.02 FIM/USD Finish FIM 4,010,000 Start FIM 4,000,000 Divided by 4 FIM/DEM Multiplied by 8.02 FIM/USD USD 500,000 1. Buy DEM 1m for FIM 4m @ 4 FIM/DEM Multiplied by $0.5/DEM DEM 1,000,000 2. Sell DEM for USD @ 0.5 USD/DEM 26 TRIANGULAR ARBITRAGE – TO NOTE! To be effective, arbitrage transactions must all be conducted simultaneously As traders place orders to conduct the arbitrage, market forces are created that bring the quoted direct cross-rate back into alignment with the indirect cross-rate The triangular arbitrage would be profitable starting from any of the currencies, as long as we trade in the same direction and go completely around the triangle 27 FORWARD MARKET QUOTATIONS Buying and selling currencies for delivery on a stipulated future date, at a rate agreed upon now Practice: forward price spot Premium versus discount When quoted currency is more expensive in the future than it is now in terms of the other currency, the former is said to be at a premium (assuming direct quotes) When quoted currency is less expensive, it is said to stand at a discount (assuming direct quotes) 28 FORWARD MARKET QUOTATIONS Mid-market rates in Toronto at noon, Sept.13, 2000 $1 U.S. in Cdn.$ $1 Cdn. In U.S.$ 1.4835 0.6741 1 month forward 1.4824 0.6746 2 months forward 1.4814 0.6750 3 months forward 1.4804 0.6755 6 months forward 1.4769 0.6771 12 months forward 1.4709 0.6799 3 years forward 1.4510 0.6892 5 years forward 1.4323 0.6882 7 year forward 1.4085 0.7100 10 years forward 1.3785 0.7254 U.S./Canada spot Here, the CAD trades at forward premium, the USD at a forward discount 29 FORWARD MARKET QUOTATIONS https://www.netdania.com/quotes/forex-usdforwards 30 FORWARD MARKET QUOTATIONS Outright rate Spot 1.5130 - 1.5145 CHF/USD 3-month forward 1.5053 - 1.5078 Forward/Swap points(pips) (1 pip = 0.0001) Spot 3-month forward 1.5130 - 1.5145 CHF/USD 77 - 67 31 FORWARD MARKET QUOTATIONS Recovering the outright forward price from the forward points: 1. If the points are decreasing, subtract from the spot price (F<S) 2. If the points are increasing, add to the spot price (F>S) Spread on spot + 15 Spread on forward points 10 = Spread on outright forward 25 32 FORWARD MARKET QUOTATIONS Suppose you read the following quotations: Spot 3-month forward Spot 6-month forward 1.4815 – 29 CAD/USD 40 – 38 0.6556 – 70 CHF/USD 51 – 64 The 3-month CAD/USD outright forward rate is: F(USD/CAD) = 1.4775 - 1.4791 The 6-month CHF/USD outright forward rate is: F(USD/CAD) = 0.6607 – 0.6634 33 FORWARD QUOTATIONS IN PERCENTAGE TERMS F - S 360 Premium/Discount = 100 S n F - forward price S - spot price n - number of days in the contract Discount on base currency is different from the premium on terms currency 34 FORWARD QUOTATIONS IN PERCENTAGE TERMS Suppose the following: Spot rate 1.5437 CHF/USD 3-month forward rate 1.5398 CHF/USD The discount on the USD is: 1.5398 - 1.5437 360 × × 100 = -1.01%p.a. 1.5437 90 The premium on CHF is: 1.5437 - 1.5398 360 × ×100 = +1.013% p . a . 1.5398 90 35 INTEREST RATE PARITY Interest rate parity (IRP) is an arbitrage condition It states that the forward premium or discount for the quoted currency reflects the difference in interest rates for banking deposits in the two currencies Eurocurrency market interest rates are used The currency with the higher interest rate is at a discount, the one with the lower interest rate is at a premium If IRP did not hold, then it would be possible for an arbitrageur to make money exploiting the arbitrage opportunity 36 INTEREST RATE PARITY At equilibrium: FHC/FC S HC/FC 1 + i HC = 1 + i FC Forward premium/discount = Interest differential F−S i HC - i FC S 37 INTEREST RATE PARITY 38 INTEREST RATE PARITY – EXAMPLE 90-day CHF interest rate 4% 90-day USD interest rate 8% Spot rate 1.4800 CHF/USD 90-day forward rate 1.4655 CHF/USD Is 1.4655 the correct forward price? Note that because we do not use bid and ask rates, buying and selling, as well as borrowing and lending, are done at the same rates 39 INTEREST RATE PARITY – EXAMPLE Start $1,000,000 S=CHF1.4800/$ i$ = 8.00% p.a. (2.00% per 90 days) x 1.02 Dollar money market 90 days End $1,020,000 F90=CHF1.4655/$ Swiss franc money market CHF1,480,000 x 1.01 CHF1,494,000 ICHF = 4.00% p.a. (1.00% per 90 days) 40 IRP AND COVERED INTEREST ARBITRAGE If IRP failed to hold, an arbitrage opportunity would exist Example: Consider the following set of foreign and domestic interest rates and spot and forward exchange rates Spot exchange rate S($/£) = 1.25 360-day forward rate F360($/£) = 1.20 US interest rate i$ = 7.10% p.a. UK interest rate i£ = 11.56% p.a. 41 IRP AND COVERED INTEREST ARBITRAGE According to IRP only one 360-day forward rate, F360($/£), can exist → this is F ($/£) = 1.25 1 + 0.0710 = 1.20 $/£ 360 1 + 0.1156 Why? If F360($/£) $1.20/£, an arbitrageur could engage in covered interest arbitrage (CIA) and make money with one of the following strategies: 42 ARBITRAGE STRATEGY 1 If F360($/£) > $1.20/£ 1. Borrow $1,000 at t = 0 at i$ = 7.10%. 2. Exchange $1,000 for £800 at the prevailing spot rate, (note that £800 = $1,000÷$1.25/£) 3. Invest £800 at 11.56% (i£) for one year to achieve £892.48 4. Translate £892.48 back into dollars → if F360($/£) > $1.20/£, £892.48 will be more than enough to repay your dollar obligation of $1,071 43 ARBITRAGE STRATEGY 2 If F360($/£) < $1.20/£ 1. Borrow £800 at t = 0 at i£= 11.56% . 2. Exchange £800 for $1,000 at the prevailing spot rate, 3. Invest $1,000 at 7.1% for one year to achieve $1,071. 4. Translate $1,071 back into pounds → if F360($/£) < 1.20/£, $1,071 will be more than enough to repay your £ obligation of £892.48 44 FORWARD CONTRACT AS A DERIVATIVE In mathematics, a derivative is a variable that derives from another variable A “derivative” is an asset that derives its value from something else The underlying asset can be share prices, prices of commodity, interest rates, exchange rates, indices, etc. For example, a derivative on Lufthansa share will derive its value from the share price of Lufthansa Similarly, as long as the forward price of currencies is obtained starting with the spot price, the forward contract is a derivative! 45 LONG AND SHORT FORWARD POSITIONS Buy a currency = taking a long position St+1 > Ft,t+1 → buyer gains St+1 < Ft,t+1 → buyer looses Sell a currency = taking a short position St+1 > Ft,t+1 → seller looses St+1 < Ft,t+1 → seller gains Example: F180 days= 105 ¥/$ 46 PAYOFF PROFILES FOR FORWARD CONTRACTS 47 PAYOFF PROFILES FOR FORWARD CONTRACTS 48 PAYOFF PROFILES FOR FORWARD CONTRACTS 49 EXCHANGE RATES AND CURRENCY RISK Nestlé, a Swiss multinational company, makes a sale and ships goods to a retailer in the US The price is $1 million and Nestlé allows the American customer to pay in 90 days The spot rate today is 1.5 CHF/USD Nestlé plans to receive $1 mill × 1.5 CHF/USD = 1.5 mill. CHF in 90 days 50 EXCHANGE RATES AND CURRENCY RISK Nestlé has currency risk exposure it may receive less than 1.5m CHF in 90 days Suppose the USD depreciates such that in 90 days the exchange rate is 1.4 CHF/USD Nestlé will receive $1 mill., but now this amount will be worth only 1.4m CHF ($1 mill × 1.4 CHF/USD) Nestlé receives 100.o00 CHF less than the expected amount (1.5m – 1.4m CHF) due to exchange rate fluctuations 51 WHEN SHOULD A COMPANY CONSIDER FX HEDGING? Selling abroad Buying from foreign suppliers Setting up manufacturing facilities abroad Outsourcing business functions (R&D, customer support, accounting, etc.) Acquisitions of foreign firms Competition with overseas competitors 52 HEDGING USING FORWARD CONTRACTS If you are going to owe foreign currency in the future • Buy the foreign currency now by entering into long position in a forward contract If you are going to receive foreign currency in the future • Sell the foreign currency now by entering into short position in a forward contract 53 HEDGING USING FORWARD CONTRACTS – NESTLÉ Today Nestlé signs the contract to sell goods for $1 mill. In 90 days Nestlé receives the money from the customer +$1m Nestlé gives the $1 mill. into the forward contract and receives the 1.496m CHF -$1m +1.496m CHF HEDGING NET RESULT +1.496m CHF Nestlé has a A/R of $1 mill. with 90 days maturity Nestlé is exposed to FX risk Nestlé sells forward $1 mill. to hedge against FX risk at F90=1.4960 CHF/USD Regardless of the future spot rate! 54 HEDGING USING FORWARD CONTRACTS 1.51 Nestlé A/R $1 million 3 months maturity S0 1.5000 CHF/$ F90 1.4960 CHF/$ A/R value (CHF, millions) 1.508 Unhedged 1.506 1.504 1.502 Losses 1.5 1.498 1.496 1.494 Gains Forward hedge 1.492 1.49 1.490 1.492 1.494 1.496 1.498 1.500 1.502 1.504 Spot rate in 3 m onths 1.506 1.508 1.510 55 HEDGING USING FORWARD CONTRACTS 1.51 A/R value (CHF, millions) 1.508 Unhedged 1.506 1.504 50% forward hedge 1.502 1.5 1.498 1.496 1.494 100% forward hedge 1.492 1.49 1.490 1.492 1.494 1.496 1.498 1.500 1.502 1.504 1.506 Spot rate in 3 m onths 1.508 1.510 56 HEDGING USING FORWARD CONTRACTS Forward contracts eliminate FX risk certainty over future revenues and payments in FC, when translated in HC Which is the cost of using forwards for hedging? Real cost compare forward rate with the future spot Real cost = F0,1 − S1 S1 It can be known only at contract maturity Expected cost = 0 (if forward rate is unbiased) Possibility of bias in forward rate SELECTIVE HEDGING: Long FC hedge when FC is at a forward discount Short FC hedge when FC is at a forward premium 57 WHY USING FORWARD CONTRACTS FOR HEDGING? Advantages of forward contracts Disadvantages of forward contracts • Private contracts between two parties for delivery sometime in the future (usually up to one year) • Flexible and customizable to the needs of the parties • Fixes the value of a contract in the future • There is no secondary market to get rid of the contract • Default/counterparty risk • Requires actual delivery to complete the contract • It offers “protects” in bad times, but also in good times ☺ 58