# Chapter 7 International Arbitrage and Interest Rate Parity Objectives

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```					Chapter 7
International Arbitrage and Interest Rate Parity

Objectives

• To explain the conditions that will result in various
forms of international arbitrage, along with the realignments that will occur in response; and

• To explain the concept of interest rate parity, and
how it prevents arbitrage opportunities.

B7 - 1

International Arbitrage
• Arbitrage can be loosely defined as
capitalizing on a discrepancy in quoted prices to make a riskless profit.

• The effect of arbitrage on demand and supply
is to cause prices to realign, such that no further risk-free profits can be made.

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International Arbitrage
• As applied to foreign exchange and
international money markets, arbitrage takes three common forms:
¤

locational arbitrage

¤
¤

triangular arbitrage
covered interest arbitrage

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Locational Arbitrage
• Locational arbitrage is possible when a
bank’s buying price (bid price) is higher than another bank’s selling price (ask price) for the same currency.

• Example:
Bank C Bid Ask NZ\$ \$.635 \$.640 Bank D Bid Ask NZ\$ \$.645 \$.650

Buy NZ\$ from Bank C @ \$.640, and sell it to Bank D @ \$.645. Profit = \$.005/NZ\$.
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Problem 7-14
• • • • •
Assume the following information:

Bank X Bank Y Bid price of New Zealand dollar \$.401 \$.398 Ask price of New Zealand dollar \$.404 \$.400 Given this information, is locational arbitrage possible? If so, explain the steps involved in locational arbitrage, and compute the profit from this arbitrage if you had \$1,000,000 to use. • Based on the information in the previous question, what market forces would occur to eliminate any further possibilities of locational arbitrage?
B7 - 5

Triangular Arbitrage
• Triangular arbitrage is possible when a
cross exchange rate quote differs from the rate calculated from spot rates.

• Example:

Bid Ask British pound (£) \$1.60 \$1.61 Malaysian ringgit (MYR) \$.200 \$.202 £ MYR8.1 MYR8.2 Buy £ @ \$1.61, convert @ MYR8.1/£, then sell MYR @ \$.200. Profit = \$.01/£. (8.1.2=1.62)
B7 - 6

Triangular Arbitrage
\$
Value of £ in \$ Value of MYR in \$ Value of £ in MYR

£

MYR

• When the exchange rates of the currencies
are not in equilibrium, triangular arbitrage will force them back into equilibrium.
B7 - 7

Self Test 7-1
• Assume that the following spot exchange
rates exist today:

• • • •

£1=\$1.50 C\$=\$0.75

£1=C\$2
Assume no transaction costs. Based on these exchange rates, can triangular arbitrage be used to earn a profit? Explain.
B7 - 8

Problem 7-25
• • • • •
Assume the following information for a particular bank:

Quoted Price Value of Canadian dollar in U.S. dollars \$.90 Value of New Zealand dollar in U.S. dollars \$.30 Value of Canadian dollar in New Zealand dollars NZ\$3.02 • Given this information, is triangular arbitrage possible? If so, explain the steps that would reflect triangular arbitrage, and compute the profit from this strategy if you had \$1,000,000 to use.
B7 - 9

Covered Interest Arbitrage
• Covered interest arbitrage is the process
of capitalizing on the interest rate differential between two countries, while covering for exchange rate risk.

• Covered interest arbitrage tends to force a
relationship between forward rate premiums and interest rate differentials.

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Covered Interest Arbitrage
• Example:
£ spot rate = 90-day forward rate = \$1.60 U.S. 90-day interest rate = 2% U.K. 90-day interest rate = 4%
Borrow \$ at 3%, or use existing funds which are earning interest at 2%. Convert \$ to £ at \$1.60/£ and engage in a 90-day forward contract to sell £ at \$1.60/£. Lend £ at 4%.

Note: Profits are not achieved instantaneously.
B7 - 11

Problem 7-16
• Assume the following information: • Spot rate of Mexican peso = \$.100 • 180-day forward rate of Mexican peso = \$.098 • 180-day Mexican interest rate = 6% • 180-day U.S. interest rate = 5% • Given this information, is covered interest
arbitrage worth-while for Mexican investors who have pesos to invest? Explain your answer.

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Comparing Arbitrage Strategies
Locational : Capitalizes on discrepancies in Arbitrage exchange rates across locations.
\$/£ quote by Bank X \$/£ quote by Bank Y

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Comparing Arbitrage Strategies
Triangular : Capitalizes on discrepancies in Arbitrage cross exchange rates.
€/£ quote by Bank A

\$/£ quote by Bank B

\$/€ quote by Bank C

B7 - 14

Comparing Arbitrage Strategies
Covered Capitalizes on discrepancies Interest : between the forward rate and the Arbitrage interest rate differential.
Forward rate of £ quoted in dollars

Differential between U.S. and British interest rates

B7 - 15

Summary of Three International Arbitrages

• Locational arbitrage ensures that quoted exchange
rates are similar across banks in different locations.

• Triangular arbitrage ensures that cross exchange
rates are set properly.

• Covered interest arbitrage ensures that forward
exchange rates are set properly.

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Comparing Arbitrage Strategies
• Any discrepancy will trigger arbitrage, which
will then eliminate the discrepancy, thus making the foreign exchange market more orderly.

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Interest Rate Parity (IRP)
• As a result of market forces, the forward
rate differs from the spot rate by an amount that sufficiently offsets the interest rate differential between two currencies.

• Then, covered interest arbitrage is no
longer feasible, and the equilibrium state achieved is referred to as interest rate parity (IRP).
B7 - 18

Derivation of IRP
• When IRP exists, the rate of return
achieved from covered interest arbitrage should equal the rate of return available in the home country.

• End-value of a \$1 investment in covered
interest arbitrage = (1/S) (1+iF)  F = (1/S) (1+iF)  [S(1+p)] = (1+iF) (1+p) where p is the forward premium.
B7 - 19

Derivation of IRP
• End-value of a \$1 investment in the home
country = 1 + iH

• Equating the two and rearranging terms:
p = (1+iH) – 1 (1+iF)
i.e. forward = (1 + home interest rate) – 1 premium (1 + foreign interest rate)
B7 - 20

Example:

• Suppose 6-month ipeso = 6%, i\$ = 5%. • From the U.S. investor’s perspective,
forward premium = 1.05/1.06 – 1  - .0094

• If S = \$.10/peso, then
6-month forward rate = S  (1 + p) _  .10  (1 .0094)  \$.09906/peso
B7 - 21

• Note that the IRP relationship can be
rewritten as follows:
F – S = S(1+p) – S = p = (1+iH) – 1 = (iH–iF) S S (1+iF) (1+iF)

• The approximated form, p  iH–iF, provides
a reasonable estimate when the interest rate differential is small.

B7 - 22

Problem 7-18
• Assume that the existing U.S. one-year interest
rate is 10 percent and the Canadian one-year interest rate is 11 percent. Also assume that interest rate parity exists. Should the forward rate of the Canadian dollar exhibit a discount or a premium? If U.S. investors attempt covered interest arbitrage, what will be their return? If Canadian investors attempt covered interest arbitrage, what will be their return?

B7 - 23

Graphic Analysis of Interest Rate Parity
Interest Rate Differential (%) home interest rate – foreign interest rate 4 Z

IRP line
B X

2

Forward Discount (%)

-3 Y

-1

1

A
W

-2

-4
B7 - 24

Graphic Analysis of Interest Rate Parity
Interest Rate Differential (%) home interest rate – foreign interest rate 4 Zone of potential covered interest IRP line arbitrage by foreign investors 2

Forward Discount (%)

-3

-1

1

Zone of potential - 2 covered interest arbitrage by local investors -4
B7 - 25

Test for the Existence of IRP
• To test whether IRP exists, collect actual
interest rate differentials and forward premiums for various currencies, and plot them on a graph.

• IRP holds when covered interest arbitrage
is not possible or worthwhile.

B7 - 26

Interpretation of IRP
• When IRP exists, it does not mean that
both local and foreign investors will earn the same returns.

• What it means is that investors cannot use
covered interest arbitrage to achieve higher returns than those achievable in their respective home countries.

B7 - 27

Does IRP Hold?
Forward Rate Premiums and Interest Rate Differentials for Seven Currencies

7 - 28

Does IRP Hold?
• Various empirical studies indicate that IRP
generally holds.

• While there are deviations from IRP, they
are often not large enough to make covered interest arbitrage worthwhile.

• This is due to the characteristics of
foreign investments, such as transaction costs, political risk, and differential tax laws.
7 - 29

Considerations When Assessing IRP
Transaction Costs

iH – iF
Zone of potential covered interest arbitrage by foreign investors Zone where covered interest arbitrage is not feasible due to transaction costs

IRP line
Zone of potential covered interest arbitrage by local investors

p

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Considerations When Assessing IRP
Political Risk ¤ A crisis in a country could cause its government to restrict any exchange of the local currency for other currencies. ¤ Investors may also perceive a higher default risk on foreign investments. Differential Tax Laws ¤ If tax laws vary, after-tax returns should be considered instead of before-tax returns.
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Annualized interest rate

8% 8% 6% 6%
4% 2% 0%

i€ Euro’s interest rate i\$
U.S. interest rate
Q1

4% 2% 0% Q3 Q1 Q3 i€ Q1 2000i\$ >2001 2%
0%

Q3

Q3

Q1 2002
Q1

Q3

Q3

Q1

Q1 Q3 2003

Q1

Q3

i\$ – i€

i\$ = i€

i\$ < i€
-2% Q3 Q1 premium 2000 2001 2%
0%

Q3

Q1 2002

Q3

Q1 2003

Q3

discount
-2% Q3 Q1 Q3 Q1 Q3 Q1 Q3
7 - 32

2000

2001

2002

2003

Interest Rates iA iU.S.

t0
Spot and Forward Rates

t1

t2 time SA FA

Because of IRP, a forward rate will normally move in tandem with the spot rate.

t0

t1

t2 time

This correlation depends on interest rate movements, i.e. p  iH–iF
B7 - 33

• During the 1997-98 Asian crisis, the
forward rates offered to U.S. firms on some Asian currencies were substantially reduced for two reasons.
 The spot rates of these currencies declined substantially during the crisis.  Their interest rates had increased as their governments attempted to discourage investors from pulling out their funds.
B7 - 34

Impact of Arbitrage on an MNC’s Value
Forces of Arbitrage

m  E CFj , t  E ER j , t  n   j 1  Value =    t 1  k  t =1      
E (CFj,t ) = expected cash flows in currency j to be received by the U.S. parent at the end of period t E (ERj,t ) = expected exchange rate at which currency j can be converted to dollars at the end of period t k = weighted average cost of capital of the parent
B7 - 35

Problem 7-21
• The one-year interest rate in New Zealand is 6
percent. The one-year U.S. interest rate is 10 percent. The spot rate of the New Zealand dollar (NZ\$) is \$.50. The forward rate of the New Zealand dollar is \$.54. Is covered interest arbitrage feasible for U.S. investors? Is it feasible for New Zealand investors? In each case, explain why covered interest arbitrage is or is not feasible. • To determine the yield from covered interest arbitrage by U.S. investors, start with an assumed initial investment, such as \$1,000,000.

B7 - 36

Problem 7-22
• Assume that the one-year U.S. interest rate is 11
percent, while the one-year interest rate in Malaysia is 40 percent. Assume that a U.S. bank is willing to purchase the currency of that country from you one year from now at a discount of 13 percent. Would covered interest arbitrage be worth considering? Is there any reason why you should not attempt covered interest arbitrage in this situation? (Ignore tax effects.)

B7 - 37

Problem 7-19
• Assume that the annual U.S. interest rate is currently 8
percent and Germany’s annual interest rate is currently 9 percent. The euro’s one-year forward rate currently exhibits a discount of 2 percent.

• a) Does interest rate parity exist? • b) Can a U.S. firm benefit from investing funds in
Germany using covered interest arbitrage?

• c) Can a German subsidiary of a U.S. firm benefit by
investing funds in the United States through covered interest arbitrage?
B7 - 38

【聯合晚報╱編譯彭淮棟/綜合報導】 【2007/08/17 】@ http://udn.com/

• 美國次貸危機擴大，投資人一窩蜂脫手以低利率日圓炒作的美元
、歐元高收益投資。獲利了結風不可收拾，利差交易平倉潮連日 推高日圓，使日圓本周不但對美元飆漲，兌歐元還走向2000年3 月以來最大漲幅。

【聯合晚報╱編譯彭淮棟/綜合報導】 【2007/08/17 】@ http://udn.com/

• 日圓利差交易的這股平倉壓力，促成日圓本周對16種強勢貨

B7 - 40

【聯合報╱記者羅兩莎／台北報導】 【2007/08/17 】@ http://udn.com

• 美股重挫，信貸市場風暴延燒，日圓利差交易平倉單子大舉出

B7 - 41

【聯合報╱記者羅兩莎／台北報導】 【2007/08/17 】@ http://udn.com

• 外幣投資專家說，日圓短線漲幅已大，之前低逢介入日圓的

• 外匯銀行主管說，這一波新台幣匯率跌勢主要是來自外資大

• 但專家強調，因信貸風暴似有擴大之勢，預計短期內紐幣、

B7 - 42

日圓震撼教育重演？
【經濟日報╱編譯 廖玉玲】【2007/11/13 】@ http://udn.com/

• 信用風暴危機近來又有捲土重來之勢，而日圓似乎

B7 - 43

【經濟日報╱編譯 廖玉玲】【2007/11/13 】@ http://udn.com/

• 這幾年來低利率的環境，讓市場資金氾濫，但主要還是有三個

•

•
• • •

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