IFM Slides
Descripción
Prof. Dr. Streitferdt
International Financial Management
Winter semester 2015/16
1. Prologue
1.
Prologue
2.
Foreign exchange markets
3.
Foreign exchange exposure management
4.
Financial management of multinational corporations
5.
Financial management of multinational corporations
6.
Corporate Governance
7.
Mergers & Acquisitions
8.
Risikomanagement
Prof. Dr. Streitferdt: International Financial Management
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1. Prologue
Discounting
Calculating present value t=0
0
t=1
t=2
t=3
2,000
4,500
3,000
t=4
t=5
3,500
6,000
How much would you be willing to pay for this stream of future cash flows, if the interest is at i = 5.65%?
Why is the result today’s value of the future cash flows? What are the assumptions of this calculation?
Prof. Dr. Streitferdt: International Financial Management
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1. Prologue
Discounting
Calculating present value 10/28
10/14
6,000
0
How much would you be willing to pay for this stream of future cash flows, if the two week Euribor is at i = 5.65%?
What makes this calculation different from the last slide’s calculation? How many days has a year?
Prof. Dr. Streitferdt: International Financial Management
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1. Prologue
Discounting
Interests for investments with less than one year maturity Interests are always quoted for one year: A company has in 2012 an overdraft credit of 100,000 € with interests of 6%. The credit is used for 75 days. 75 The company has to pay interests of 6% · · 100,000 €. days per year Different day-count conventions
act/360
75 100,000€ 6% 1,250 360
act/365
75 100,000 € 6% 1,232.88 365
act/act
75 100,000 € 0.06 1,229.50 366 2012 is a leap year
Prof. Dr. Streitferdt: International Financial Management
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1. Prologue
Discounting
Simplification We will only use the day-count convention act/360 within this course. Additionally, we will assume that one month has always 30 days.
Our year always has 360 days!!!! Attention!:
In real life you will have to calculate with the actual number of days.!!!!
Prof. Dr. Streitferdt: International Financial Management
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1. Prologue
Discounting
Calculating present value: Different approach
10/28
10/14
6,000
0
Instead of calculating the present value with a fraction of the interest rate, we can also work with a fraction of time! 14 0.038 360
PV
6,000
1.0565
0.038
5,987.19
But this yields a different result. Since the present value is a unique number it follows: If we use this method of calculation, we have to adjust the interest rate, in a way that we get the same result as before. The resulting interest is called the ZERO BOND INTEREST rate! Prof. Dr. Streitferdt: International Financial Management
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1. Prologue
Discounting
Calculating present value: Different approach
We must always be aware of what type of interest we have:
Euribor interest rate
V0
Zero bond interest rate
V0
CFt 1 i E t CFt
1 i
t
Be aware, that this is only for payments due within one year. Payments with more than one year maturity are always discounted with the zero bond method.
In this lecture we will assume that:
If nothing else is stated, the zero bond interest rate method applies. The interest rate is constant over time (flat interest rate curve)
Prof. Dr. Streitferdt: International Financial Management
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1. Prologue
Discounting
Calculating the value of a bond
The value of a bond is the present value of it‘s future payments: Issuer:
Federal Republic of Germany
Maturity:
01/04/18
Coupon:
5.25%
In Germany bonds have yearly coupon payments. For a face value of 50 € the bond above has the following payment structure: 01/04/13
0
01/04/14
2.625
01/04/15
2.625
01/04/16
01/04/17
01/04/18
2.625
2.625
52.625
Question: What is the bond price on the 4th of January 2013 if the risk adequate interest rate is 3.28%? Prof. Dr. Streitferdt: International Financial Management
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1. Prologue
Discounting
Calculating the value of a bond with payments in uneven years
05/27/13 01/04/14
1 year
0.6 0
01/04/15
2.625
01/04/16
01/04/17
01/04/18
1 year 1 year 1 year 2.625 2.625 52.625 2.625
1.6 years 2.6 years 3.6 years 4.6 years PV
2.625 2.625 2,625 2.625 52.625 5518 . 0.6 1.6 2.6 3.6 4.6 1.0328 1.0328 1.0328 1,0328 1.0328 Price 110.37
Prof. Dr. Streitferdt: International Financial Management
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1. Prologue
Discounting
Calculating the value of a bond with semi-annually coupon payments
Issuer:
British Government (Gilt)
Maturity:
01/04/15
Coupon:
5.25%
In Great Britain bonds have semi-annual coupon payments. For a face value of 50 € the bond above has the following payment structure: Semi-annual payment 50 € · 5.25%/2 = 1.3125 01/04/13
0
07/04/13
1.3125
01/04/14
1.3125
07/04/14
01/04/15
1.3125
51.3125
Question: What is the bond price on the 4th of January 2010 if the risk adequate interest rate is 3.28%? Prof. Dr. Streitferdt: International Financial Management
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1. Prologue
Discounting
Valuing risky cash flows PV0
162 157.28 1 is
Is the present value bigger or smaller?
A risky payment in the future has a lower value than a safe payment of the same amount at the same date in the future
The present value must go down
The interest rate must rise. It contains a risk premium Risk adequate discount rate: Prof. Dr. Streitferdt: International Financial Management
i i s RP 11
1. Prologue
Discounting
The risk premium
RP (Spreads)
AAA
27 bp
AA
40 bp
A
65 bp
BBB
125 bp
BB
374 bp
B
493 bp
Junk Bonds
Rating
Investmentgrade
The risk premiuim of a company‘s debt depends on it‘s rating (example):
Important rating agencies: Standard & Poors, Moodys, Fitch Prof. Dr. Streitferdt: International Financial Management
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1. Prologue
Discounting
Summary of the chapter
Interests are always quoted for one year. Our year always has 360 days If money is invested for less than one year, the interest is calculated by using the year’s fraction times the interest Alternatively, we can calculate one plus the interest rate to the power of the time fraction Both ways lead to the same result, but the interest rates are different. If nothing else is stated, we will apply the second methodology For valuing risky cash flows we have to add a risk premium to the safe interest rate The risk premium for debt payments can be calculated by using the rating, if this is public available information
Prof. Dr. Streitferdt: International Financial Management
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Prof. Dr. Streitferdt
International Financial Management
Winter semester 2015/16
2. Foreign exchange markets
1.
Prologue
2.
Foreign exchange markets
3.
Foreign exchange exposure management
4.
Financial management of multinational corporations
5. 6.
Corporate Governance
7.
Mergers & Acquisitions
8.
Risikomanagement
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.
Foreign exchange markets 2.1 The spot market for foreign exchange 2.2 Foreign exchange derivatives
2.3
2.2.1
Foreign exchange forwards and futures
2.2.2
Currency swaps
2.2.3
Currency options
Exchange rate theory 2.3.1
Purchasing power parity
2.3.2
Interest rate parity
2.3.3
Forecasting exchange rates
3.4 Managing foreign currency exchange risk Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Definition of FX spot market Foreign exchange (FX) market: Market for conversion of one currency into another currency today On the spot market, currencies are exchanged immediately. The deals are directly executed! (+ 2 days settlement period) Shares of reported global foreign exchange turnover, 2013 Denmark; 2% Canada; 1% Russia; 1% Germany; 2% Luxembourg; 1% Netherlands; 2% Australia; 3% France; 3% Switzerland; 3% United Kingdom; 41%
Hong Kong SAR; 4% Japan; 6% Singapore; 6% United States; 19%
Source: Bank for International Settlements Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Function of the FX spot market Over the counter market (OTC): No central market place. It is a linkage of bank currency traders, nonbank dealers, and FX brokers that deal with each other via a network of telephones, computer terminals, and automated dealing. Quotes are available from information service broker like Bloomberg, Reuters or Thomson Financials. Major market participants are:
Prof. Dr. Streitferdt: International Financial Management
Central banks International banks Nonbank dealers (Hedge funds etc.) Bank customers Foreign exchange brokers 17
2. Foreign exchange markets
2.1 The spot market for foreign exchange
The FX spot market
Interbank market
Nonbank dealer
Nonbank dealer
FX Broker
Central Banks
International Banks
International Banks
Bank customers Prof. Dr. Streitferdt: International Financial Management
Bank customers
FX Broker
Bank customers
International Banks
Bank customers 18
2. Foreign exchange markets
2.1 The spot market for foreign exchange
The FX spot market Average daily trading volume within FX market participants (in bn.$)
6000
Bank customers International banks
5000
Nonbank dealers
4000 3000 2000 1000 0 2004
2007
2010
2013 Source: Bank for International Settlements (2013)
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
The FX spot market Currency involved on one side of the transaction as % of all transactions
77,37%
37,04%
86%
2007
76,08%
Others Euro US$
79,50%
39,07%
33,40%
85%
87%
2010
2010 Source: Bank for International Settlements (2013)
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Quotation of exchange rates Exchange rates are very, very confusing, because there are always two sides of the same deal. Buying US$ with € is the same as selling € for US$. Generally: If we buy a good the price tells us, how much Euros we have to pay for one unit of that good If we buy a foreign currency, the natural thing to do, would be to quote how much Euros we have to pay for one unit of that currency! 0.7005 €/US$ This is called a direct quote! Problem: For an US-American it would be exactly the other way round! He would quote: 1.4276 US$/€ This is a direct quote for US citizens, but it is an indirect quote for German citizens! We can express exchange rates as direct or indirect quotes, depending on the person we are talking about! Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Quotation of exchange rates
If a currency quote is a direct quote from a European point of view, it is also called a quote in European terms If a currency quote is a direct quote from an American point of view, it is also called a quote in American terms
The Euro quote is in American terms! For an European citizen it is an indirect quote in $/€!
Source: FAZ,
On the international FX market it is assumed that everybody knows the first two numbers of an exchange rate and only the last two numbers are the price. For the bid-ask price of the US$ the price quote would be 09-15. Also, amounts are traded in mn. A “5 at 15” order means: 5 mn. US$ at 1.4215 US$/€ (how many € are this?) Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Quotation of exchange rates Important points for the quotation of exchange rates
The mathematical rules for fractions are also applied to the units! To avoid confusion, we will use the variable S(j/k) to denote the exchange rate that tells us, how much units of j you have to pay for one unit of k. It is therefore a direct quote for the citizens of the country with currency j. If you get confused: Concentrate on the units!
S0 $ / € 1.4276
$ €
Direct quote for Americans/ Indirect quote for Europeans
1 1 1 € € 0.7005 S0 € / $ Indirect quote for Americans/ $ S0 $ / € 1.4276 $ 1.4276 $ Direct quote for Europeans/ € Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Quotation of exchange rates Appreciation: If a currency gets stronger, it is said to appreciate. This means the currency gets more expensive. This does no necessarily imply that the exchange rate increases! In direct terms for Europeans an appreciation of the US$ means that we have to pay more € for a $ and the direct quote €/$ increases
In indirect terms for Europeans an appreciation of the US$ means that we get less $ for a € and the indirect quote $/€ decreases
Depreciation: If a currency gets weaker, it is said to depreciate. This means the currency gets cheaper. This does no necessarily imply that the exchange rate decreases! In direct terms for Europeans a depreciation of the US$ means that we have to pay less € for a $ and the direct quote €/$ decreases
In indirect terms for Europeans an appreciation of the US$ means that we get more $ for a € and the indirect quote $/€ increases
What happens if the € appreciates/depreciates with the direct/indirect quote? Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Cross rates
Cross rate: Exchange rate that is determined by two other exchange rates. We have 100 £ and want to convert them into US$. We only observe the following rates in the newspaper: S0 US$ / € 1.4209 Sell the £ for €: (= Buy € with £)
100 £
S0 £/€ 0.8672
1 1 € 100 £ 115.31€ S0 £/€ 0.8672 £
US$ Sell € for US$: 115.31 € S0 US$/€ 115.31 € 1.4209 163.85US$ (= Buy US$ with €): € We have converted our £ into US$ via the €. The effective exchange rate is called the cross rate: US$ 1.6385 £ Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Cross rates
We could have done the cross rate calculation directly by dividing the two exchange rates: US$ 1.4209 S0 US$ / € € 1.4209 US$ € 1.6385 US$ S US$ / £ 0 £ 0.8672 £ £ S0 £ / € € 0.8672 € 1 £ £ S0 £/US$ 0.6103 1.6385 US$ US$
It is not necessary, that the exchange rates are divided by each other, sometimes they have to be multiplied, to get the cross rate. To know how to combine the rates, you have to concentrate on the units to see, how you can eliminate an unwanted unit. This is often the way, trades are executed in real life due to organizational reasons These cross rates are no mathematical construct but must prevail on the market due to triangular arbitrage!
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Cross rates
Cross rates are usually quoted in tables:
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Triangular arbitrage and cross rates Exchange rate S0(€/£)
1.1531
S0(US$/€)
1.4209
S0(£/US$)
0.6103
£ Convert at 1.1531 €/£
Convert at 0.6103 £/US$
Convert at 1.4209 US$/€ US$
€
With any exchange rate S0(£/US$) 0.6103 I would earn or lose money! Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Exercise 3.1 1. Calculate all possible cross rates out of the following data:
Prof. Dr. Streitferdt: International Financial Management
S0(£/US$)
0.6063
S0(€/SFR)
0.6559
S0(US$/SFR)
0.9341
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Exercise 3.2 You observe the following exchange rates in the market: S0(€/SFR)
0.6559
S0(¥/€)
135.41
S0(¥/SFR)
157.21
On a cocktail party you hear that with the prevailing exchange rates there is money lying on the street. Explain, how the above exchange rates could be exploited to realize an arbitrage profit and calculate the profit.
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
The bid-ask spread
S0(US$/€)
Bid
Ask
2.0000
2.0006
Bid price: The price at which a trader is willing to buy the currency Ask price: The price at which a trader is willing to sell the currency The difference between those two prices is the bid-ask spread!
The trader buys 1 € for 2.0000 US$ and sells 1 € for 2.0006 US$! The bid-ask spread is 2.0006-2.0000=0.0006 Question: Can we get the €/US$-quotes from this data? Precisely:
How much € do we get for 1 US$? How much € do we have to pay for 1 US$? Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
The bid-ask spread
If we have 1 € and we want to convert it into US$, there are two ways for doing this: 1. Sell the € at the traders bid price S US$ / € b
0
2. Buy US$ at the traders ask price S0a € / US$ 1. Sell the € at the bid price S US$ / € 2.0000 b
0
1€ Customer
S US$ / € 2.0000
Exchange trader
b
0
2. Buy US$ at the traders ask price S0a €/US$ 1€ International Banks
Customer 1/ S0a €/US$ ??? Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
The bid-ask spread
I have to get the same dollar amount on both ways because otherwise, all market participants would choose the way, where you get more US$! Therefore: 1 2.000 S0b US$ / € a S0 € / US$ S0a € / US$
1 € 0.5000 S0b US$ / € US$
We now have:
S0(US$/€) S0(€/US$)
Prof. Dr. Streitferdt: International Financial Management
Bid
Ask
2.0000
2.0006 0.5000
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
The bid-ask spread
If we have US$ and we want to convert it into €, there are two ways for doing this: 1. Sell the US$ at the traders bid price S €/US$ b
0
a 2. Buy € at the traders ask price S0 US$ / €
1. Sell the US$ at the bid price S0b €/US$ 1 US$ Customer S0b €/US$ ???
Exchange trader
2. Buy € at the traders ask price 1/ S0a US$ / € 0.4999 1 US$ International Banks
Customer 1/ S0a US$ / € 0.4999 Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
The bid-ask spread
I have to get the same dollar amount on both ways because otherwise, all market participants would choose the way, where you get more US$! Therefore: S0b € / US$
1 1 0.4999 S0a US$ / € 2.0006
We now have:
Prof. Dr. Streitferdt: International Financial Management
Bid
Ask
S0(US$/€)
2.0000
2.0006
S0(€/US$)
0.4999
0.5000
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
The bid-ask spread
We can use the indirect bid quote to get the direct ask quote We can use the indirect ask quote to get the direct bid quote This works in both directions!
Bid
S0b US$ / €
S0b € / US$
Prof. Dr. Streitferdt: International Financial Management
1 S0a US$ / €
Ask
S0a US$ / €
S0a € / US$
1 S0b US$ / €
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Exercise 3.3 Calculate the bid-ask spread for the exchange rates S0(SFR/€), S0(€/¥) and S0(US$/£) using the following data:
Bid
Ask
S0(£/US$)
0.6063
0.6068
S0(€/SFR)
0.6559
0.6562
S0(¥/€)
135.41
137.22
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Cross rates and the bid-ask spread
We can complicate things further by realizing, that the bid-ask spread influences the calculation of cross rates. General rule: Start with the bid side and then calculate the ask side
We have 1 £ and want to convert it into US$. We only observe the following rates in the newspaper: Bid Ask S0(£/€)
0.8617
0.8622
S0(US$/€)
1.4209
1.4215
We want to calculate the following table: Bid
Ask
S0(US$/£)
Sb(US$/£)
Sa(US$/£)
S0(£/US$)
Sb(£/US$)
Sa(£/US$)
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Cross rates and the bid-ask spread First we calculate all bid rates available from the data! Bid rates S0b £/€ 0.8617
S0b €/£
1 € € 1.1598 0.8622 £ £
S0b US$ / € 1.4209 S0b € / US$
1 € € 0.7035 1.4215 US$ US$
Now we can convert £ to US$ and US$ to £ by selling the corresponding currencies (see next slide)! Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Cross rates and the bid-ask spread To convert £ into US$ -We sell 1 £ for S € / £ 1.1598 b
0
-Then we sell the earned € for S0b US$ / € 1.4209 1£ 1.1598
€ US$ 1.6480US$ 1.4209 £ €
If we sell 1 £ we get 1.6480 US$ S US $ / £ b
0
To convert US$ into £
-We sell 1 US$ for S0b € / US$ 0.7035 -Then we sell the earned € for S0b £ / € 0.8617 1US$ 0.7035
€ £ 0.6062 £ 0.8617 US$ €
If we sell 1 US$ we get 0.6062 £ S0b £ / US$ Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Cross rates and the bid-ask spread Bid
With S0a US$ / £
S0(US$/£)
1.6480
S0(£/US$)
0.6062
Ask
1 1 a S £/US$ b and 0 the table is complete S0 US$ / £ S0b £/US$
Bid
Ask
S0(US$/£)
1.6480
1.6496
S0(£/US$)
0.6062
0.6068
These cross rates must prevail on the capital market because otherwise, market participants could earn riskless money by triangular arbitrage! Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Exercise 3.4 1. Calculate the cross rates for the British Pound and Euro on basis of the following data: Bid
Ask
S0(£/SFR)
0.6044
0.6049
S0(€/SFR)
0.5457
0.5463
2. Show that using triangular arbitrage transaction yields a loss and explain this loss.
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.1 The spot market for foreign exchange
Summary of the chapter
In the spot market, currencies are immediately exchanged It is an OTC market If a transaction is buying or selling a currency depends on the viewpoint of the actor. We have to define, what position we are taking We know direct quotes that are like prices and indirect quotes which are the inverted direct quotes. Direct quotes for Americans are called American quotes and direct quotes for Europeans are called European quotes From two exchange rights with three currencies we are able to calculate a cross rate, assuming markets that are free of arbitrage Bid and ask spread complicate the story because the bid price for one currency is the inverted ask price for the other currency and the other way round Still we are able to calculate cross rates from prices including a bid-ask spread
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.
Foreign exchange markets 2.1 The spot market for foreign exchange 2.2 Foreign exchange derivatives
2.3
2.2.1
Foreign exchange forwards and futures
2.2.2
Currency swaps
2.2.3
Currency options
Exchange rate theory 2.3.1
Purchasing power parity
2.3.2
Interest rate parity
2.3.3
Forecasting exchange rates
3.4 Managing foreign currency exchange risk Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.2 Foreign exchange derivatives
The market for FX derivatives Global OTC derivatives market turnover daily average (in bn. US$) 3500 Spot transactions
3000 FX Forwards
2500
Currency Swaps
2000
FX Options
1500 1000 500 0 2004
Prof. Dr. Streitferdt: International Financial Management
2007
2010
2013
45
2. Foreign exchange markets
2.2.1 Forwards and futures
Definition of a FX forwards
A FX forward is the obligation to buy
a certain currency (Underlying) on a certain point of time in the future (Maturity) for a fixed exchange rate (Forward rate) Forwards are only OTC- traded (not public).
Long-Forward
Short-Forward
Buying a forward. A market participant with a long forward position has the obligation to buy the currency in the future.
Selling a forward. A market participant with a short forward position has the obligation to deliver the currency in the future.
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.2.1 Forwards and futures
Value of an FX forward at maturity
Forward on 1,000,000 US$ for F0.25(€/US$)=0.7000 €/US$, due in 3 months
3 scenarios for the exchange rate (spot rate in 3 months) 0.6000 €/US$
0.7000 €/US$
0.9000 €/$
1,000,000 · 0.6000 € 1,000,000 · 0.7000 € 1,000,000 · 0.9000 € -1,000,000 · 0.7000 € -1,000,000 · 0.7000 € -1,000,000 · 0.7000 € =
0€ =
-100,000 € =
Short Forward
ST
0
F
Prof. Dr. Streitferdt: International Financial Management
CF (Fw)
CF (Fw )
Long Forward
+200,000 €
ST
0
F
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2. Foreign exchange markets
2.2.1 Forwards and futures
Pricing a FX forward
- Spot rate for 1 US$ at: 0.7224 €/US$ - Safe interest rate in Europe i€=4%, - Safe interest rate in USA i$=2% Two ways to generate a safe cash flow after 0.5 years for a European investor: 1. Invest 1€ at the safe European rate to get
1€ (1.04)0.5=1.0198
2. Convert 1 € into 1/0.7224 $ = 1.3842$ and invest it at the safe American rate to get 1.3843$ (1.02)0,5 =1.3980$. This cash flow is still risky because we don’t ‘ know how many Euros we will get in half a year but we can enter today into a forward agreement with a forward rate of F0,5 (€/US$)and maturity of half a year in order to fix the future exchange rate today. The safe cash flow in € is then: Prof. Dr. Streitferdt: International Financial Management
1.3980$ F0,5(€/$) 48
2. Foreign exchange markets
2.2.1 Forwards and futures
Pricing a FX forward
In equilibrium both future cash flows must be the same, if we invest the same amount of 1 €. Therefore 1.0198 € 1.3980 $ F0.5 € / US $ F0.5 € / US $
1.0198 € 0.7295 1.3980 $
Reasoning: If the forward rate would be lower than 0.7295 the cash flow from a safe investment in Europe is higher than the safe cash flow from an American investment. Nobody would invest in America and everybody would invest his capital in Europe. There’s no demand for the Forward and the Forward price goes down.
Some investors would even pick up debt at the cheap American interest rate and invest the proceeds in Europe and earn a risk free profit if the forward price doesn’t change. For the same reason, the forward rate can not be higher than 0.7295.
Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.2.1 Forwards and futures
Pricing a FX forward
- Spot rate: S0(D/F) - Safe interest rate in D iD, - Safe interest rate in USA iF Two ways to generate a safe cash flow after T years for an investor from D: 1. Invest 1 unit at the safe rate in D to get
1 (1+iD)T
2. Convert 1 unit into 1/ S0(D/F) and invest it this amount at the safe rate in F to get 1/S0(D/F) (1+iF)T $. This cash flow is still risky . We can enter today into a forward agreement with a forward rate of FT (D/F) and maturity of T in order to fix the future exchange rate today. The safe cash flow in is then: Prof. Dr. Streitferdt: International Financial Management
1 1 i F 1 S0 D / F
T
FT D / F 50
2. Foreign exchange markets
2.2.1 Forwards and futures
Pricing a FX forward
1 1 i D
T
1
1 1 i F S0 D / F
FT D / F S0 D / F
T
FT D / F
1 i 1 i D F
T
T
The forward rate can be bigger or smaller than the spot rate, depending on the relationship of the two interest rates! This equation must hold, if there are no arbitrage opportunities. Of course, this is only true without any transaction costs! Forwards also usually have a bid-ask spread which we will ignore here Cross forward rates can be derived the same way as for spot rates Be aware that the interest in the nominator in the last fraction of the pricing formula is the interest rate in the currency that is in the nominator of the forward rate as well!
Prof. Dr. Streitferdt: International Financial Management
51
2. Foreign exchange markets
2.2.1 Forwards and futures
Exercise 3.5 You observe in Japan a safe interest rate of iJ = 3.2%. In the UK, the safe interest rate is iUK =5.10%. The spot rate for the Brit. Pound is S0(¥/£)=156.85. Calculate the fair forward rate for a maturity of 9 months.
Prof. Dr. Streitferdt: International Financial Management
52
2. Foreign exchange markets
2.2.1 Forwards and futures
Premium and discount of FX forwards
FT(j/k) > S(j/k)
Trades at a premium
FT(j/k) < S(j/k)
Trades at a discount
The premium and discount (fT) can be expressed as annual % of the spot price:
fT j / k
FT j / k S0 j / k 1 S0 j / k T
Example:
S0(€/US$) = 0.8245 f0.5 € / US $
F0.5(€/US$) = 0.8144
0.8144 0.8245 360 0.0245 2.45% discount 0.8245 180
Prof. Dr. Streitferdt: International Financial Management
53
2. Foreign exchange markets
2.2.1 Forwards and futures
Exercise 3.6 The spot rate for the SFR exchange rate is at the moment at S0(€/SFR) = 0.9123. Calculate all discounts and premiums of the €/SFR forward rate and the US$/SFR forward rate, using the following data: Rate
Prof. Dr. Streitferdt: International Financial Management
F0.25(€/SFR)
1.1137
F0.5(€/SFR)
1.1344
F0.75(US$/SFR)
0.8579
S0(€/US$)
0.8244
54
2. Foreign exchange markets
2.2.1 Forwards and futures
The problem with forwards
Forwards always include a promised future payment. But the parties of a forward contract must make sure, that the other party will be able to fulfill it’s duty
How can that be done?
Prof. Dr. Streitferdt: International Financial Management
55
2. Foreign exchange markets
2.2.1 Forwards and futures
Definition of a FX future
A FX future is the obligation to buy
a certain currency (Underlying) on a certain point of time in the future (Maturity) for a fixed exchange rate (Forward rate) Futures are only traded on exchanges (XT).
Important trading places are:
Chicago Board of Trade (CBOT) Chicago Mercantile Exchange (CME) Eurex London International Financial Futures and Options Prof. Dr. Streitferdt: International Financial Management
56
2. Foreign exchange markets
2.2.1 Forwards and futures
Structure of future trading Client
Client
Broker (Bank)
Client
Broker (Bank)
Clearinghouse
Client
Broker (Bank)
Clearinghouse Can be the same institution
Exchange (e.g., Eurex) Prof. Dr. Streitferdt: International Financial Management
57
2. Foreign exchange markets
2.2.1 Forwards and futures
Advantages of future trading
The exchange guarantees that the future contract will be fulfilled There is always a price for each future Easier to understand due to standardization Standardized by the exchange
Contract size
Maturity
Margins
Limits
Prof. Dr. Streitferdt: International Financial Management
58
2. Foreign exchange markets
2.2.1 Forwards and futures
Comparing forwards und futures
Forward
Only OTC traded Not standardized Special delivery date Payments made at the end Often physical settlement
Future
Only XT traded Standardized Same maturities for a lot of futures Margins Futures are often unwinded before maturity
Forwards and futures both have to be valued at the end of each year. Increases and decreases of future and forward values are reported as earnings/losses and influence the result of the P&L (IFRS) Prof. Dr. Streitferdt: International Financial Management
59
2. Foreign exchange markets
2.2.1 Forwards and futures
Summary of the chapter Forwards are exchanges of currencies that will take place in the future and are only OTC traded
On arbitrage free markets, the forward rate (in direct quotation) equals the spot rate compounded with the domestic interest rate and discounted with the foreign interest rate Forwards are also quoted with their percentage premium or discount to the spot price We can calculate cross rates from forwards, assuming that there is no bidask spread for the forwards We distinguish outright forward transactions and foreign exchange swaps. The first is an unhedged transaction, the latter is a forward deal where the risk is eliminated with an appropriate investment on the capital market Futures are like forwards but they are traded on an exchange. That is why they are standardized in size and maturity For futures and forward we must be sure that the counterparty will fulfill it’s duty
Prof. Dr. Streitferdt: International Financial Management
60
2. Foreign exchange markets
2.
Foreign exchange markets 2.1 The spot market for foreign exchange 2.2 Foreign exchange derivatives
2.3
2.2.1
Foreign exchange forwards and futures
2.2.2
Currency swaps
2.2.3
Currency options
Exchange rate theory 2.3.1
Purchasing power parity
2.3.2
Interest rate parity
2.3.3
Forecasting exchange rates
3.4 Managing foreign currency exchange risk Prof. Dr. Streitferdt: International Financial Management
61
2. Foreign exchange markets
2.2.2 Currency swaps
Definition of a currency swap
To swap means to exchange. In a swap agreement we exchange future payments in one currency for payments in another currency. Usually, the payments are determined as interest on a fixed amount (= notional) E.g.: Paying 3% in $
S(US$/€)=1.3423
Receiving: 5% in €
Notional: 2 mn. €.
Payments: annually
Maturity: 3 years
Paying
Receiving
t=0 t=1
- 80,538 $
100,000 €
t=2
- 80,538 $
100,000 €
t=3
- 2,765,138 $
2,100,000 €
The sign of payments always depends on your position. The notional amounts in t = 0 are usually not exchanged! They are just needed for calculating the cash flows. Prof. Dr. Streitferdt: International Financial Management
62
2. Foreign exchange markets
2.2.2 Currency swaps
Valuation of a currency swap
The valuation is straight forward. The Swap consists out of two cash flows. The value of those cash flows is their present value. Paying
Receiving
t=0 t=1
- 80,538 $
100,000 €
t=2
- 80,538 $
100,000 €
t=3
- 2,765,138 $
2,100,000 €
We can calculate the value of the Swap by calculating the present value of the two future payment streams and convert the present value of the foreign currency cash flow into domestic currency by using the spot rate. Then, we subtract the present value of the “paying” cash flow from the present value of the “receiving” cash flow! Prof. Dr. Streitferdt: International Financial Management
63
2. Foreign exchange markets
2.2.2 Currency swaps
Valuation of a currency swap
VS€t / $ VB€t VB$t S0 € / $
Value of currency swap: Pay in foreign currency, get domestic currency in t
Value of the payments in domestic currency
Value of the payments in foreign currency
For this valuation the discount rates for the domestic and for foreign currency are needed
The discount rates must also include a (currency specific) risk premium for the payer and the receiver!
How would the formula look like, if we pay domestic and buy foreign currency?
Prof. Dr. Streitferdt: International Financial Management
64
2. Foreign exchange markets
2.2.2 Currency swaps
Valuation of a currency swap
Paying 4.5% in $
Receiving: 5% in €
Notional: 4 mn. €., 5 mn. $
S0(US$/€)=1.3423
Payments: annually
Maturity: 3 years
Paying
Receiving
t=1
- 225,000 $
200,000 €
t=2
- 225,000 $
200,000 €
t=3
- 5,225,000 $
4,200,000 €
The risk adequate discount rate in € for the swap partner is 4.5%, our risk adequate discount rate in $ is 3.5%:
V €
0
V0$
200,000 € 200,000 € 4,200,000 € 1.045 1.045 1.045 2
3
225,000 $ 225,000 $ 5,225,000 $ 2 3 1.035 1.035 1.035
Prof. Dr. Streitferdt: International Financial Management
V
$/ €
0
4,054,979.28 € 5,140,081.85 US $
1 € 1.3423 US $
225,670.01 € 65
2. Foreign exchange markets
2.2.2 Currency swaps
Exercise 3.7 You take a look at a €/US$ swap with maturity of 3 years and annual payments. The notional amount of the swap is 10 mn. € and 11 mn. US$. The swap rate for the € payments is 4%, the swap rate for the US$ payments is 7%. The risk adequate discount rate for the € paying swap partner is 4,2% and for the US$ paying swap partner 6%. Calculate the swap‘s value with a spot exchange rate of S0(US$/€) = 1.2827!
Microsoft Excel-Arbeitsblatt
Prof. Dr. Streitferdt: International Financial Management
66
2. Foreign exchange markets
2.2.2 Currency swaps
Some remarks on currency swaps
For the valuation of currency swaps we need the risk adequate discount rate for each party in the currency they are paying If we have no other data, we use the interest rates those companies have to pay on loans in the same currency If the value of a swap is not zero in the beginning, one party will have to make an upfront payment to the other as compensation It is also possible to combine currency swaps with variable interest rate payments or an exchange of e.g. fixed interests in US$ vs. variable interests in €, but we wont do this here The value of the swap must be calculated at the end of each year. In- or decreases in swap value are earnings/losses and influence the P&L result (IFRS)
Prof. Dr. Streitferdt: International Financial Management
67
2. Foreign exchange markets
2.2.2 Currency swaps
Summary of the chapter
Currency swaps are future exchanges of payments in two different currencies The valuation of swaps is simply the difference between two bond prices, where one bond price is in a foreign currency and must be converted by using the spot rate In the valuation of swaps we have to be aware of the credit risk of the contract partner and must include a risk premium into the discount rate The risk premium in the discount rate usually depends on the currency of the payment stream
Prof. Dr. Streitferdt: International Financial Management
68
2. Foreign exchange markets
2.
Foreign exchange markets 2.1 The spot market for foreign exchange 2.2 Foreign exchange derivatives
2.3
2.2.1
Foreign exchange forwards and futures
2.2.2
Currency swaps
2.2.3
Currency options
Exchange rate theory 2.3.1
Purchasing power parity
2.3.2
Interest rate parity
2.3.3
Forecasting exchange rates
3.4 Managing foreign currency exchange risk Prof. Dr. Streitferdt: International Financial Management
69
2. Foreign exchange markets
2.2.3 Currency options
Definition of a currency option Definition: A currency option is the right, to buy or sell a currency (underlying):
at a specified exchange rate (exercise rate, E) on or before a specified exercise date (maturity, T).
Buyer (long position)
The buyer of an option can choose, if he buys the currency at the exercise rate The buyer will always have positive earnings if he exercises the option
Seller (short position)
Has to buy or sell the currency if the option buyer exercises the option He will always lose money at maturity if the option is exercised
The buyer of an option has guaranteed a minimum selling price or a maximum price how much he has to pay for the underlying currency
The option buyer purchases a right, the option seller has an obligation. That is why the option buyer has to pay a price to the option seller. Prof. Dr. Streitferdt: International Financial Management
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2. Foreign exchange markets
2.2.3 Currency options
Different types of options Options
European
Call
American
Put
Call
Put
European Option:
The option can only be exercised at maturity
American Option:
The option can be exercised at any time until maturity.
Call:
Right to buy the underlying asset at the strike price
Put:
Right to sell the underlying asset at the strike price
Prof. Dr. Streitferdt: International Financial Management
71
2. Foreign exchange markets
2.2.3 Currency options
Payment of a currency call option on US$ (paid in €)
Long Call on 1 mn. US$ with an exercise rate of 0.8744 €/US$, maturity 3 months
3 possible values for the €/US$ spot rate in 3 months 0.8500 €/US$ 0.8744 €/US$ 0.9000 €/US$ 0€ -0€ =
0€
1,000,000 · 0.8744 € -1,000,000 · 0.8744 €
1,000,000 · 0.9000 € -1,000,000 · 0.8744 €
=
=
0€
+ 25,600 €
Payment of a currency put option on US$ (paid in €)
Long put on 1 mn. US$ with an exercise rate of 0.8744 €/US$, maturity 3 months
3 possible values for the US$/€ spot rate in 3 months 0.8500 €/US$ 0.8744 €/US$ 0.9000 €/US$ 1,000,000 · 0.8744 € - 1,000,000 · 0.8500 €
1,000,000 · 0.8744 € -1,000,000 · 0.8744 €
=
=
24.400 €
Prof. Dr. Streitferdt: International Financial Management
0€
0€ 0€ =
0€ 72
2. Foreign exchange markets
2.2.3 Currency options
Option positions
Options can be settled in cash or by physical delivery of the underlying currency. The exact payment of an option depends on the option type (call or put) and the position (short/long):
Prof. Dr. Streitferdt: International Financial Management
long call
long put
short-call
short put
73
2. Foreign exchange markets
2.2.3 Currency options
Cash flows from options at maturity Long Put Zahlung Cash flow
Zahlung Cash flow
Long Call
ST 0
ST
E
0
Short Call
Prof. Dr. Streitferdt: International Financial Management
Short Put 0
ST
E
ST Zahlung Cash flow
E
Zahlung Cash flow
0
E
74
2. Foreign exchange markets
2.2.3 Currency options
Including the (compounded) option premium Long Put
ST 0
Zahlung Cash flow
Zahlung Cash flow
Long Call
E
0
ST 0
E
Prof. Dr. Streitferdt: International Financial Management
E
Short Put
Zahlung Cash flow
Zahlung Cash flow
Short Call
ST
ST 0
E
75
2. Foreign exchange markets
3.2.3 Currency options
Summary of the chapter A currency option is the right to buy or sell a currency in the future at a specified price
European options can only be exercised at maturity, American options can be exercised at any point of time until maturity If we buy an option we have a long position and if we sell an option we have a short position. The right to buy a currency is called a call, the right to sell a currency is called put The option will only be exercised at maturity if the long position gets a positive cash flow The short position can only lose at maturity. In the best case, the option is not exercised and the cash flow from the option is zero That is why we have to pay a price for the option if we enter into a long position - the option premium. The underlying good of the option is the foreign currency. What is foreign depends on the market we are trading in. E.g.: On US option markets the Euro is the foreign currency.
Prof. Dr. Streitferdt: International Financial Management
76
2. Foreign exchange markets
2.
Foreign exchange markets 2.1 The spot market for foreign exchange 2.2 Foreign exchange derivatives
2.3
2.2.1
Foreign exchange forwards and futures
2.2.2
Currency swaps
2.2.3
Currency options
Exchange rate theory 2.3.1
Purchasing power parity
2.3.2
Interest rate parity
2.3.3
Forecasting exchange rates
3.4 Managing foreign currency exchange risk Prof. Dr. Streitferdt: International Financial Management
77
2. Foreign exchange markets
3.3.1 Purchasing power parity
Why exchange rate theory is important
If we deal on the foreign exchange market, we must have an idea, how the exchange rate might behave in the future. We need to know, which forces drive exchange rate movements That is why we have to understand the determinants of exchange rates. There are two important general theories
Prof. Dr. Streitferdt: International Financial Management
Interest rate parity Purchase power parity
78
2. Foreign exchange markets
3.3.1 Purchasing power parity
Absolute purchasing power parity
Assume, you are living in a town somewhere near the Swiss border. You can buy your food in a German or in a Swiss Supermarket. Which one will you prefer, if both Supermarkets have the same distance to your house? At the end of the day, goods (or a representative basket of goods) should cost the same in all countries if the prices are measured in the same currency. Therefore, the following equation should hold:
P0D S0 D / F P0F P0D S0 D / F F P0
The exchange rate between the currencies of two countries should be equal to the ratio of the country’s price levels. This is called the absolute purchasing power parity! Prof. Dr. Streitferdt: International Financial Management
79
2. Foreign exchange markets
3.3.1 Purchasing power parity
Absolute purchasing power parity P0D S0 D / F F P0
Whenever this equation is not fulfilled, the spot rate is expected to change. For example, if S P / P (
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