Covered interest parity CIP Notation

1
Covered interest parity (CIP)Notation

• r interest rate (per period) on baht
  denominated security
• r interest rate (per period) on US
  denominated security
• s exchange rate (Bht/)
• f one period forward exchange rate (Bht/)

2
The forward rate and the spot rate

• The spot exchange rate s baht/
• The exchange between the two currencies takes
  place at once (or actually, within two days).
• The forward rate f baht/
• The exchange takes place at a date in the
  future that is specified in the contract between
  the two parties to the exchange. It is often 30
  or 90 days ahead but may be more than one year
  ahead.

3
Futures contracts and forward contracts

• Forward contracts are usually written between two
  banks, or between a bank and a large firm, or
  between two large firms.
• Futures contracts are written between a customer
  and an exchange, such as the Chicago Futures
  Exchange.

4
Default risk

• Suppose that in June 1997, when the spot rate was
  Bht 25/, I had agreed to sell dollars to you six
  months later (December 1997) for Bht 26/.
• Six months later, the actual spot rate was Bht
  45/ and I find myself in a very awkward
  situation Im contracted to give you dollars for
  not much more than half their current value! You
  would have to be worried that I might go
  bankrupt, or flee the country.

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Futures markets the good news

• A firm, or even a bank, might default on its
  forward obligations, but it is very unlikely that
  the Chicago Futures Exchange will default.
• This means that futures contracts are less risky
  than forward contracts.
• They are also more liquid because the futures
  exchanges operate secondary markets in which
  firms and banks can buy and sell futures
  contracts.

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Futures markets the bad news

• Given the extra liquidity and reduced default
  risk of futures markets, why does anyone deal in
  forward markets?
• Futures exchanges are philanthropic
  organisations. In return for their liquidity and
  good reputation they are able to charge a wider
  spread between buy and sell rates than a
  commercial bank.
• If banks and customers have confidence in each
  other it is cheaper to deal in the forward
  market. If they are worried about default risk,
  it is better to deal in futures

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Back to CIP

• Consider an investor (arbitrageur) who holds
  Bht 1 and chooses between the following two
  options
• Invest in baht to get Bht (1 r) after one
  period.
• (a) Sell Bht on spot market to get (1/s) today,
  invest the dollars to get (1 r)/s after one
  period
• (b) Sell these dollars forward. That means, enter
  into a contract to deliver this quantity of
  dollars in the next period in exchange for baht
  at the rate of Bht f per 1 in the future period.
  
• By contracting to deliver (1 r)/s the
  investor will receive Bht f (1 r)/s.

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The CIP condition

• If the amount received after one period
  from option 2 (that is, at the end of step b in
  the previous slide) is equal to the amount
  received after one period from option 1, then
• (1 r) f (1 r)/s.
• This is the covered interest parity
  condition.
• The forward premium on the dollar, p, is
  defined by
• p (f s)/s
• Therefore
• f/s 1 p

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• The CIP condition can therefore be re-written
  as
• p r r/1 r
• Provided that r is small, this can be
  approximated by
• p r r
• Empirical studies show that CIP holds to a
  very close approximation.

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• To confirm that pr is relatively unimportant,
  note that the 3 month repo-rate of the Bank of
  Thailand is
• r 4.78 per year 1.17 per quarter
• The corresponding interest rate in the USA is
  about
• r 2.5 per year 0.62 per quarter.

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CIP formula and approximation

• The value of the forward premium implied by the
  CIP formula is
• r r
  r r p(rr)/(1r)
• Per year 4.78 2.50 2.28
  2.22
• Per quarter 1.17 0.62 0.55
  0.55
• Provided that the interest rate are low, the
  approximation is OK. If interest rates are large,
  as in the 1997/98 crisis, it would be necessary
  to use the exact formula, not the approximation.

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Why doesnt CIP hold exactly?

• Transactions costs buy-sell margins on spot and
  forward trades.
• Default risk will the parties contracted to
  deliver and baht in the future fulfil their
  contracts? Will the borrowers repay the
  contracted loans in baht and dollars?
• But, in markets for the major currencies,
  involving the worlds largest banks, the margins
  are small and the risk of default is even
  smaller. In emerging markets, such as Thailand,
  CIP does not always hold because markets are much
  thinner, largely because of the restrictions on
  lending (or implicit lending) by on-shore banks
  to non-residents. These restrictions can stop
  banks taking advantage of arbitrage opportunities
  offered by any deviation from CIP

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• Traders in the forward markets for the major
  currencies (and even fairly small ones like
  A/US and NZ/US) have the two interest rates,
  the spot rate and the CIP formula programmed into
  their computers. The implied value of the forward
  rate shows on their screens and they deviate from
  it only to avoid, or reduce, transactions costs
  for themselves and their customers.

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CIP and arbitrage

• Suppose in the earlier example where r 4.8 and
  r 2.5, that instead of CIP holding we had p
  1.0. How could you make an arbitrage profit? To
  keep the maths simple, assume s 40 Bht/ and f
  40.4 Bht/.
• Borrow 100 that is, contract to repay 102.50
  next year.
• Buy 102.50 forward contract to deliver
• Bht 102.50 x 40.4 Bht 4141

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• Use the 100 youve borrowed to buy Bht 4,000 in
  the spot forex market. Invest the baht at 4.8
  that is, be guaranteed of receiving
• Bht 4,000 x 1.048 Bht 4192. Next period you are
  only contracted to deliver Bht 4141 to redeem you
  forward market commitment.
• You are ahead by Bht 51. Ignoring default risk
  and transactions costs, this is a guaranteed no
  risk profit. Why not borrow 100 million and be
  guaranteed Bht 51 million? The sky is the limit
  for arbitrage profits if the CIP condition does
  not hold.

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Arbitrage helps ensure CIP

• How will arbitrage activities impact on markets
  in the above example? Note that initially
• p lt r r.
• Buying baht forward will raise f selling dollars
  spot will reduce s. This will tend to raise p
  f/s 1.
• Borrowing dollars will tend to raise r and
  lending in baht will depress r. Both factors will
  tend to depress
• r r.
• Raising p and reducing r r will help restore
  CIP.

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Uncovered interest parity (UIP)

• Let p denote the expected rate of depreciation
  of the baht against the dollar
• p (s s )/s, where s is the expected value,
  this period, of the spot exchange rate in the
  next period.
• UIP is the condition that
• p r r
• or more exactly p (r r)/(1 r).

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Implications of UIP

• Since CIP holds UIP implies that
• p p and s f.
• Lets look at three ways to think about UIP

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The risk neutral US investor and UIP

• An American who invests in a baht security at r
  and expects the baht to depreciate at p per cent
  per period expects to get a return in dollars
  (after selling the depreciated baht) of about r
  p. Investing in dollars gives a dollar return of
  r. IF, investors are risk neutral, the two
  returns must be the same. That is
• p r r.

r p.
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The risk neutral Thai investor and UIP

• A Thai investor who invests in a dollar security
  at r and expects the baht to depreciate at p
  per cent per period expects to get a return in
  baht (after selling the appreciated dollars) of
  about r p. Investing in baht gives a sure
  return in baht of r. IF, investors are risk
  neutral, the two returns must be the same. That
  is
• p r r.

r p.
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The pure speculator

• If f gt s, a speculator who contracts to sell
  100 forward (and who does not cover the exchange
  risk), will have to buy dollars next period in
  order to fulfill the contract.
• The speculator expects the price of dollars next
  period to be s Bht and therefore expects to make
  a profit of f s. Since f gt s, the
  speculator expects to make a profit.

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Testing for UIP

• Define the error in the forecast of s(t1) as
  u(t1)
• s(t1) s(t) u(t1)
• u(t1) is the forecast error, and if exchange
  rate forecasts are efficient, s(t) will
  incorporate all information available at time t
  and u(t1) will therefore be uncorrelated with
  s(t). Under UIP, s(t) f(t)

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Testing for UIP (cont)

• Therefore
• s(t1) f(t) u(t1)
• with f(t) and u(t1) uncorrelated. Under UIP, it
  would therefore be legitimate to run the
  regression
• s(t1) a(0) a(1)f(t) u(t1)
• since the residual is uncorrelated with the
  explanatory variable, f(t).
• Under UIP, a(0) 0 and a(1) 1.
• Usually, the regression is transformed and the
  rate of change of the exchange rate (from t to
  t1) is regressed on a constant and the forward
  premium.

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Failure of UIP using high-frequency data

• When this regression is estimated for the major
  currencies using 3 month interest rates and the
  3-month forward premium, a(1) is always
  significantly less than unity and is usually
  negative.
• Therefore UIP certainly does not hold exactly for
  high frequency (short period) data.

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UIP does not do too badly in cross-country
studies using long-run data

• But in cross-country comparisons, over the
  long-term, UIP does hold to a rough
  approximation. Consider the US, A, Bht and Rp.
  Over the last 20 years, the Rp has depreciated
  relative to Bht the Bht has depreciated relative
  to the A (actually this depends on exactly how
  the period is defined, in the 20 years before
  1997, the A depreciated relative to the Bht)
  and the A has depreciated relative to the US.
  In conformity with UIP, Rp interest rates are the
  highest, Bht interest rates are slightly higher
  than A interest rates and US rates are lowest
  of all.