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