Law of One Price

1
Law of One Price

• A single asset/commodity can have only one price
  otherwise, markets cant clear.
• Therefore interest rate parity (IRP) ensures that
  the future values of money should be equal after
  accounting for exchange and interest rates.
• IRP is an arbitrage condition.
• If IRP didnt hold, arbitrage opportunities would
  allow an astute trader to make a killing.
• Since we rarely see arbitrage opportunities, we
  know IRP holds.

2
IRP Defined

• Formally,
• (F/S)(1 i) (1 ius)
• or

IRP is sometimes approximated as
3
Example of IRP

• Suppose you have 100,000 to invest for one year.
• You can either
• invest in the U.S. at i. Future value
  100,000(1 i)
• trade your USD for JPY at the spot rate, invest
  in Japan at i and hedge your exchange rate risk
  by selling the future value of the Japanese
  investment forward. The future value
  100,000(F/S)(1 i).
• ?Since both of these investments have the same
  risk, they must have the same future
  valueotherwise an arbitrage opportunity would
  exist.
• (F/S)(1 i) (1 ius)

4
IRP and Covered Interest Arbitrage (CIA)

• If IRP failed to hold, an arbitrage would exist.
• Example

5
IRP and CIA

• A trader with 1,000 to invest could invest in
  the U.S. In 1 year her investment will be worth
  1,071 1,000?(1 i) 1,000?(1.071)
• Alternatively, this trader could exchange 1,000
  for 800 at the prevailing spot rate 800
  1,0001.25/.
• She could then invest 800 at i 11.56 for 1
  year to earn 892.48.
• Translate 892.48 back into USD at F360(/)
  1.20/, the 892.48 will be exactly 1,071.

6
Interest Rate Parity Exchange Rate
Determination

• According to IRP only one 360-day forward rate,
• F360(/), can exist. It must be the case that
• F360(/) 1.20/
• Why?
• If F360(/) ? 1.20/, an astute trader could
  make money with an arbitrage strategy.

7
Arbitrage Strategy I(read on your own)

• If F360(/) 1.20/
• Borrow 1,000 at t 0 at i 7.1.
• Exchange 1,000 for 800 at the prevailing spot
  rate, (note that 800 1,0001.25/) invest
  800 at 11.56 (i) for 1 year to yield 892.48
• Translate 892.48 back into USD, if F360(/)
  1.20/ , 892.48 will be more than enough to
  repay your dollar obligation of 1,071.

8
Arbitrage Strategy II(read on your own)

• If F360(/)
• Borrow 800 at t 0 at i 11.56 .
• Exchange 800 for 1,000 at the prevailing spot
  rate, invest 1,000 at 7.1 for 1 year to
  achieve 1,071.
• Translate 1,071 back into GBP, if F360(/) 1.20/ , 1,071 will be more than enough to
  repay your obligation of 892.48.

9
IRP and Hedging Currency Risk

• You are a U.S. importer of British woolens and
  have just ordered next years inventory. Payment
  of 100M is due in 1 year.
• IRP implies that there are 2 ways that you fix
  the cash outflow
• a) Put yourself in a position that delivers 100M
  in 1 yeara long forward contract on the pound.
  You will pay (100M)(1.2/) 120M
• b) Form a forward market hedge as shown below.

10
IRP and a Forward Market Hedge
To form a forward market hedge 1. Borrow
112.05 million in the U.S. (in one year you will
owe 120 million). 2. Translate 112.05 million
into GBP at the spot rate S(/) 1.25/ to
receive 89.64 million. 3. Invest 89.64 million
in the UK at i 11.56 for one year. 4. In 1
year your investment will have grown to 100
millionexactly enough to pay your supplier.
11
Forward Market Hedge
Where do the numbers come from? We owe our
supplier 100 million in 1 yearso we know that
we need to have an investment with a future value
of 100 million. Since i 11.56 we need to
invest 89.64 million at the start of the year.
How many USD will it take to acquire 89.64
million at the start of the year if S(/)
1.25/?
12
IRP Exchange Rate Determination

• On 2 (F/S)(1 i) (1 ius)
• What we really care about is F. F is the
  expected value of the future spot rate given all
  the info we know now.
• F E(St1It) where It represents our current
  information set.
• Put these two equations together

13
Uncovered Interest Rate Parity

• Further rearrange the terms from the last
  equation and youll see that the difference
  between the 2 countries interest rates is the
  expected change in the exchange rate over the
  period.
• (i - ius) E(St1)-St/St E(e)

14
Reasons for Deviations from IRP

• Transactions Costs
• The interest rate available to an arbitrageur for
  borrowing, ib,may exceed the rate he can lend at,
  il.
• There may be bid-ask spreads to overcome, Fb/Sa F/S
• Thus
• (Fb/Sa)(1 il) ? (1 i b) ? 0
• Capital Controls
• Governments sometimes restrict import and export
  of money through taxes or outright bans.

15
Purchasing Power Parity

• PPP says that the exchange rate between 2
  currencies should equal the ratio of the
  countries price levels.
• S Pa/Pb where S is the spot rate S(a/b).
• Absolute PPP means this holds precisely.

16
Relative PPP Implications

• Relative PPP states that the rate of change in an
  exchange rate (e) equals the differences in the
  rates of inflation (p).
• e ? - ?
• Note relative PPP uses more generality than
  absolute PPP.
• If U.S. inflation is 5 and U.K. inflation is 8,
  the pound should depreciate by 3.
• ? Application In 1998 Indonesias inflation rate
  reached 77.54 while the US recorded 1.6 this
  implied that the rupiah should depreciate 75.94
  vs. the actual 72.5 depreciation.

17
Source Vincenzo Quadrini
18
Real Exchange Rate (RER)

• Nominal exchange rate what you see in the
  newspaper (e.g. JPY/USD 118).
• Real exchange rate a theoretical construct that
  has real-world implications for the relative
  values of two currencies.
• RER is widely used as a benchmark.
• Traded goods explained by RER.
• Non-tradable goods not explained by RER.

19
PPP Deviations and the Real Exchange Rate

• The real exchange rate is

• If PPP holds, (1 e) (1 ?)/(1 ?), then
  q 1.
• If q country improves with currency depreciations.
• If q 1, the competitiveness of the domestic
  country deteriorates with currency appreciations.

Source McGraw/Hill
20
Example of PPP RER

• Use q formula from previous page.
• (1pUS) 1.016
• (1pIndo) 1.7754
• (1e) 1.725
• q (1.016)/(1.77541.725)
• 0.3317
• Note this is an extreme example of a change in
  PPP. Here Indonesias competitiveness shot up.

21
A 2nd Example of PPP RER

• Use q formula from previous page.
• (1pUS) 1.024
• (1pCan) 1.039
• (1e) 0.9876
• q (1.024)/(1.0390.9876)
• 0.9979
• Note this is a more common example of a change in
  PPP. Here Canada has a very minor competitive
  advantage vis-à-vis the US.

22
Big Mac Index
Source Vincenzo Quadrini
23
How can we use PPP and the RER?

• For the most part PPP is used to figure out if a
  currency is fairly valued. To that extent,
  economists regularly report the real exchange
  rate and how that compares to the nominal
  exchange rate. Here, the gap indicates that q 1 for Indonesia.

Source ADB
24
Politics of PPP RER

• International organizations report countries GDP
  in US terms. What do you use to report the GDP?
  PPP or nominal exchange rates?
• Many analysts say PPP is more useful as it gives
  a better indicator of the true strength of an
  economy. This is especially relevant in
  discussing countries such as China and India
  (large but relatively poor economies).
• Note that even these governments switch
  methodologies depending on their target audience!

25
The Fisher Effects

• An increase (decrease) in the expected rate of
  inflation will cause a proportionate increase
  (decrease) in the interest rate in the country.
• For the U.S., the Fisher effect is written as
• i ? E(?)
• Where
• ? is the equilibrium expected real U.S.
  interest rate
• E(?) is the expected rate of U.S. inflation
• i is the equilibrium expected nominal U.S.
  interest rate

Source McGraw/Hill
26
International Fisher Effect

• If the Fisher effect holds in the U.S.
• i ? E(?)
• and the Fisher effect holds in Japan,
• i ? E(?)
• and if the real rates are the same in each
  country (this assumes that unrestricted capital
  flows have forced the rates to be equal)
• ? ?
• then we get the International Fisher Effect
• E(e) i - i .

Source McGraw/Hill
27
International Fisher Effect

• If the International Fisher Effect holds,
• E(e) i - i
• and if IRP also holds,

then forward parity holds
Source McGraw/Hill
28
Equilibrium Exchange Rate Relationships
IFE
FP
PPP
IRP
FE
FRPPP
? - ?
Source McGraw/Hill
29
Forecasting Techniques

• Let 100 flowers bloom ????
• Mao (but not in such a capitalist context!)
• 3 general types of forecasts
• Intuitive expectations should be sufficient ?
  efficient market approach
• Monetary policy ? fundamental approach.
• History ? technical approach.

30
Efficient Market Approach

• Markets are efficient and fully reflect all
  available information.
• Markets will follow a random walk by changing
  only when unpredicted events occur (i.e. new
  information is received). This implies St
  ESt1.
• PPP can be interpreted as the markets consensus
  forecast of the future exchange rates if the
  markets are efficient. Ft ESt1 It.
• Assuming markets are efficient, these two
  equations contain all the necessary info to make
  forecasts.

31
Fundamental Approach

• Exceedingly technical. Widely used in banks.
• Heavy econometrics 3-step process
• Estimate structural model.
• Estimate future parameter values.
• Use the model to develop forecasts.

32
Technical Approach

• History repeats itself.
• Data mining in search of patterns.
• Largely reliant on short-term and long-term
  moving averages and divining patterns in the
  graphs.
• Not well-regarded in academia but extremely
  popular among traders.

33
Example of Technical Analysis
Source http//www.investavenue.com/article.html?I
D5761
34
Chap 6 International Banking

• How are international and domestic banks
  different?
• Types of services offered
• Why would a domestic bank aspire to be
  international?

35
Structures of International Banks

• Correspondent bank
• Representative office
• Small service facility
• Foreign branch
• Operate like a local bank but legally part of
  parent bank subject to home and host country
  banking regulation.
• Branch bank loan limit is based on the capital of
  the parent bank, not of the branch.
• Most popular way for US banks to expand overseas.

36
Structures of Intl Banks (2)

• Subsidiary and affiliate banks
• Sub Locally incorporated bank that the foreign
  parent either fully owns or partly-owns w/control
  rights.
• Aff Partially-owned but not controlled by its
  foreign parent.
• Both (1) operate under the laws of country of
  incorporation (2) allowed to underwrite
  securities
• Edge Act banks
• Federally chartered subsidiaries of US banks that
  are physically located in the US that are allowed
  to engage in intl banking activities.
• Unlike domestic commercial banks, these are
  allowed to own equity in business corporations.
  This allows US banks to own foreign banking
  subsidiaries and take ownership stakes in foreign
  banking affiliates.

37
Structures of Intl Banks (3)

• Offshore banking centers
• Countries whose banking system is organized to
  permit external accounts beyond the normal scope
  of the country.
• IMF recognizes the Bahamas, Bahrain, the Cayman
  Islands, Hong Kong, the Netherlands Antilles,
  Panama and Singapore. Note HK and Singapore
  have evolved into full service international
  banking centers.
• Virtually total freedom from host country
  governmental banking regulations. Note this is
  not the same as no regulation.
• International banking facilities
• A separate set of accounts that are segregated on
  the parent banks books.
• Not a unique physical or legal identity.
• Any US bank may have one only take deposits and
  make loans to foreigners.

38
Basle Accord History

• July 1988 current accord published
• End-1992 deadline for implementation
• Jan 1999 began discussion on new accord
• End-2001 publication of new accord
• 2004 scheduled implementation of revised accord

39
Why have the Basle Accord?

• Bank regulators and depositors are all concerned
  with the safety of bank deposits.
• The accord created the concept of bank capital
  adequacy to ensure that banks are reasonably
  prepared to meet obligations. This is designed
  to minimize the probability of bank failure and
  the resultant damage if one occurs anyway.
• Banks capital ratio (min 8) total capital
  divided by sum of credit risk, market risk, and
  operational risk.
• The idea behind the denominator is that not all
  loans are equally risky loans are therefore
  weighted according to their intrinsic risk.

40
Problems with Original Basle Accord

• One method doesnt fit all systems
• Should there be one global system or different
  ones for developed and developing nations?
• Business cycle
• Risk varies according to state of economy
• Ex US in 1999 vs. today.
• Didnt account for range of activities undertaken
  by some banks (e.g. trading equities and
  derivatives).
• Prime example of why this system needed
  modification Barings Bank, which collapsed in
  1995 from derivative losses, looked good on paper
  relative to capital adequacy standards.

41
Proposed New Accord

• Places greater emphasis on banks own internal
  methodologies
• Greater flexibility in how risk is assessed and
  capital adequacy measured
• More risk sensitivity.

42
International Money Market

• Eurocurrency is a time deposit in an
  international bank located in a country other
  than the country that issued the currency.
• For example, Eurodollars are U.S.
  dollar-denominated time deposits in banks located
  abroad.
• Euroyen are yen-denominated time deposits in
  banks located outside of Japan.
• The foreign bank doesnt have to be located in
  Europe. The prefix Euro applies even if the
  bank is located elsewhere.

43
Eurocurrency Market

• External banking system that parallels but is
  separate from the domestic banking system of
  the country that issued the currency. Thus,
  Eurodollar market has a lower cost structure (no
  FDIC requirements apply) ? therefore it is
  popular.
• Operates at the interbank and/or wholesale level.
• Usually transactions are US1mn.
• Transaction rate is usually LIBOR London
  Interbank Offered Rate.

44
Eurocredits

• Eurocredits are short- to medium-term loans of
  Eurocurrency.
• The loans are denominated in currencies other
  than the home currency of the Eurobank.
• Often the loans are too large for one bank to
  underwrite alone. Therefore banks will form a
  syndicate to share the risk of the loan.
• Eurocredits feature an adjustable rate. On
  Eurocredits originating in London the base rate
  is LIBOR.
• Lending rate is LIBOR X where X is the lending
  margin that is set based on the borrowers
  creditworthiness.

45
Example Pricing of a Eurocredit

• Same s as book example (p139) but using current
  rates.
• Borrow 3mn at LIBOR .75/annum on 1-month
  rollover basis.
• 1-month LIBOR 1.34
• Therefore in 1 month Teltrex owes interest of
  3,000,000 (.0134 .0075)/12 5,225
• Suppose the loan was instead on a 3-month
  rollover basis
• 3-month LIBOR 1.35
• Then in 3 months Teltrex would owe interest of
  3,000,000 (.0135 .0075)/4 15,750

46
Forward Rate Agreement (FRA)

• A major risk in the Eurodeposit/Eurocredit market
  is interest rate risk arising out of a possible
  mismatch in deposit and credit maturities.
• Example bank makes a 3-month loan using money
  from a 6-month deposit. How will the deposit be
  repaid if the 3-month loan doesnt generate
  enough interest?
• Forward Rate Agreements can be used to
• Hedge assets that a bank currently owns against
  interest rate risk.
• Speculate on the future course of interest rates.

47
FRA contd

• An interbank contract in which
• the buyer agrees to pay the seller the increased
  interest cost on a notional amount if interest
  rates fall below an agreed rate.
• The seller agrees to pay the buyer the increased
  interest cost if interest rates increase above
  the agreed rate.
• FRAs are bought (sold) when one believes rates
  will be higher (lower) in the future.

48
Calculate FRA

• It is the absolute value of
• NA (SR AR) (N/360) / 1 (SR N/360)
• NA Notional Amount Value of loan
• AR agreement rate LIBOR on day of pricing
  (e.g. today)
• SR settlement rate LIBOR on day of collection
  (e.g. in 3 months)
• N term-length (e.g. 90 days for 3 month
  contract)
• Called a X against Y FRA for a X-month loan that
  is made against a Y-month deposit. (Ex 6-month
  loan against 12-month deposit ? Six against
  Twelve FRA.)

49
FRA Example

• This is a Three against Six FRA where the bank
  has made a 3-month Eurodollar loan against an
  offsetting 6-month Eurodollar deposit.
• Notional amount US5mn. 3-month LIBOR (AR) is
  1.3. Let the SR be 1.5. Say there are 91 days
  in the 3-month period.
• The bank would expect to receive US5mn .013
  (91/360) 16,431 as the base amount of interest
  when the loan is rolled over in three months.
  (NA AR N/360)
• But SR AR ? the bank will actually receive
  US5mn .015 (91/360) 18,958. (NA SR
  N/360) (Profit 2,527)

50
FRA Example

• Since SR AR the purchasing bank profits from
  the FRA it bought. In 91 days it will receive
  the absolute value of this gain.
• Suppose the purchasing bank accurately predicted
  the SR. It would want to know what the present
  value of the gain from the FRA is worth. The
  absolute present value is US5mn (.015-.013)
  91/360 / 1 (.015 91/360) 2,518. NA
  (SR-AR) (N/360) / 1 (SR N/360)
• But, what if SR would have been paid by the buyer exactly the
  same amount of money it would have made had it
  done absolutely nothing with the sum of money.
  In short, this wouldve been a zero-sum game.

51
Return briefly to the Basle Accord

• Why are we paying so much attention to the
  possibility that a bank might lose money if the
  interest rates on loans deposits arent in its
  favor?
• If banks miscalculate their exposure and assume
  too much risk, possible implosion of system could
  occur.
• If banks in one country have too high a default
  rate, it could have an international ripple
  effect.

52
So why Basle?

• So, to prevent the occurrence of an international
  debt crisis, the Basle accord requires banks to
  maintain an 8 capital adequacy ratio.
• The ratio ensures that banks hold enough equity
  capital and other securities as reserves against
  risky assets. This reduces the probability of
  bank failure.

53
Technical Result of Basle VAR

• VAR value at risk the loss that will be
  exceeded with a specified probability over a
  specified time horizon.
• This determines the capital adequacy ratio.
• VAR (Portfolio value) (Daily standard
  deviation of return) (Confidence Interval
  Factor) (Horizon length)1/2
• Imprecise concept as the inputs cant be measured
  precisely. Hence, the CAR is useful but not
  perfect.

54
Suppose the safety net breaks?

• If a bank failed even with all these safety
  procedures in place, how would this play out?
• Look at Mexico and the resultant Latin American
  Crisis in the 80s.
• Led to development of debt-for-equity swaps as
  part of debt rescheduling agreements among bank
  lending syndicates and debtor nations.

55
Debt-for-equity swaps

• Creditor banks sell loans for US at discounts
  from face value to MNEs.
• The MNEs want to make equity investments in
  subsidiaries or local firms in the less developed
  countries.
• The local countrys central bank then buys the
  bank debt from the MNE at a smaller discount than
  the MNE paid but in the local currency.
• The MNE then uses the local currency to make a
  pre-approved investment in the country.

56
Example of Debt-for-equity swap

• Honda buys 100mn of local debt from the Mexican
  central bank at 55 of face value. Cost to MNE
  55 mn.
• The Mexican government then buys the debt from
  Honda at 75 of face value. Cost to govt 75
  mn.
• Honda then has 75 mn in local currency and opens
  Honda Mexico, which is a pre-approved investment
  in the tropical country.

57
Another example(based on p.145)

• Volkswagen paid 170 mn for 283 mn in Mexican
  debt, which it swapped for the equivalent of 260
  mn of pesos.
• What is the discount from face value that
  Volkswagen paid? 170/283 .60 ? 40 discount.
• What is the discount that the govt paid?
  260/283 .919 ? 8.1 discount.

58
Who gains and why?

• Creditor bank removes an unproductive loan from
  its books. Gets some portion of the principal
  repaid. (Repays most when discount is lowest.)
• MNE gets bid-ask spread on the loan (how much
  more does the govt give for the loan then you
  paid for it?).
• Host country can pay off a hard currency loan
  with the capital raised by sale of loan to MNE.
  In addition, the host country is positioned to
  make long-term gain from productivity of the
  MNEs new investment.

59
Brady Bonds

• Alternative to the debt-for-equity mechanism we
  just examined. Brady bonds arose from an effort
  in the 1980s to reduce the debt held by
  less-developed countries that were frequently
  defaulting on loans.
• U.S. dollar-denominated bond issued by an
  emerging market, particularly those in Latin
  America, and collateralized by U.S. Treasury
  zero-coupon bonds.

60
Brady Bonds (2)

• Defaulted loans were converted into bonds with
  U.S. zero-coupon Treasury bonds as collateral.
  Because the Brady bonds were backed by
  zero-coupon bonds, repayment of principal was
  insured.
• The Brady bonds themselves are coupon-bearing
  bonds with a variety of rate options (fixed,
  variable, step, etc.) with maturities of between
  10 and 30 years. Issued at par or at a discount,
  Brady bonds often include warrants for raw
  materials available in the country of origin or
  other options.