Purchasing Power Parity Interest Rate Parity

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Purchasing Power ParityInterest Rate Parity

• International Corporate Finance
• P.V. Viswanath

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Learning Objectives

• Law of One Price
• How arbitrage links good prices and asset returns
• Relations between spot and forward exchange
  rates, inflation rates and interest rates
• Difference between real and nominal exchange rates

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Arbitrage

• Law of One Price in competitive markets with
  many buyers and sellers with low-cost access to
  information, exchange-adjusted prices of
  identical tradable goods and financial assets
  must be within transaction costs worldwide.
• Risk-adjusted expected returns on financial
  assets in different markets should be equal.

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Law of One Price

• In the absence of frictions, the same good will
  sell for the same price in two different
  locations.
• Either because of two-way arbitrage or
• Because buyers will simply go to the lower cost
  seller
• If goods are sold in different locations using
  different currencies, then
• The law of one price says after conversion into
  a common currency, a given good will sell for the
  same price in each country.
• If 10.8 (11.25), and a bushel of wheat
  sells for 15, it must sell for (15)(0.8) or 12
  in the UK.

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Static PPP

• If e is the / exchange rate (i.e. the number of
  needed to buy 1, then
• P e.P
• Hence, e P/P
• The static PPP is difficult to test because
  different baskets of goods are consumed in
  different countries indexes reflect different
  consumptions.

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Dynamic PPP

• The dynamic PPP simply states that the absolute
  PPP relationship will hold in terms of changes
  if ? refers to the inflation rate, then
• (et1-et)/et (?- ?)/(1?)
• Thus, if a unit of consumption costs 15 in the
  US and 12 in the UK, we have seen static PPP
  holds.
• If inflation is 10 in the UK and 20 in the US,
  then, prices will be 18 in the US and 13.2 in
  the UK. Then, static PPP will require that e
  18/13.2 or 1.36.
• The percentage change in e is (1.36-1.125)/1.125
  9.09
• The RHS is also (0.2-0.1)/1.1 9.09

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Static vs. Dynamic PPP

• In the above example, both static and dynamic PPP
  holds.
• But, suppose the original exchange rate were not
  1.25, but 1.3/, due to some friction.
• Then dynamic PPP would assert that the exchange
  rate would increase by 9.09 or rise to
  1.3(1.0909) or 1.4182/.
• If price changes are not too large, then approx.,
• (et1-et)/et (?- ?)
• If we take the expectation of both sides, we find
• E(et1-et)/et E(?- ?)
• The expected change in interest rates will be
  equal to the expected differential in inflation
  rates.

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Causes for deviation from PPP

• PPP is reinforced by two-way arbitrage
• If transportation of goods is costly, static PPP
  is violated.
• Import tariffs and quotas can cause static PPP
  violations.
• Many items cannot be traded such as on-site
  services (haircuts), perishable goods, etc.
  Hence PPP measured with standard price indexes
  can be violated.
• Movement of buyers can compensate for movement of
  goods, sometimes. For example, vacations.
• Movement of producers can also compensate.
  Producers will move to places where the goods
  price is high.
• In the long run, PPP should hold even if there
  are non-traded goods.

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Covered Interest Rate Parity

• Investing 1 for 1 year will generate (1r),
  where r is the rate quoted on dollar-denominated
  investments.
• Investing 1 for 1 year in pound-denominated
  investments will generate (1/e0)(1r). If e1
  is the future exchange rate, this will equal
  (e1/e0)(1r). However, the value of this
  expression depends on e1 and is unknown at t0.
• If f1 is the forward exchange rate for delivery
  at t1, then the pound value, which is known in
  advance can be converted to (f1/e0)(1r).
  Hence, we find
• 1r (f1/e0)(1r) or equivalently,
  (1r)/(1r) f1/e0
• Or approx. the forward premium, (f1- e0)/e0 r
  - r

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Uncovered Interest Rate Parity

• The Unbiased Expectations Hypothesis says that
  the forward rate is equal to the expected future
  spot rate.
• If the forward rate is greater than the expected
  future spot rate, then speculators will sell the
  foreign currency forward. If the forward rate is
  lower than the expected future spot rate, then
  they will buy forward contracts on the foreign
  currency.
• Putting this together with the covered interest
  rate parity condition, we derive the uncovered
  interest rate parity condition (also known as the
  International Fisher Equation)
• E(e1- e0)/e0 r - r

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Deviations from Covered Interest Parity

• Although covered interest parity generally holds,
  there could be deviations because of
• Transactions costs
• Politifal Risks
• Potential tax advantages to foreign exchantge
  gains versus interest earnings
• Liquidity differences between foreign and
  domestic securities.

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Fisher Open condition

• Take the uncovered interest rate parity
  condition, E(e1- e0)/e0 r - r together with
• the expectations form of the PPP E(e1- e0)/e0
  E(?- ?). This gives us
• r - r E(?- ?)
• This is known as the Fisher Open Condition

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The Fisher Effect

• Irving Fisher decomposed the nominal interest
  rate into the real interest and the expected
  inflation rate.
• If capital is mobile across countries, then real
  interest rates should equalize.
• This implies that differences in nominal interest
  rates across countries should reflect differences
  in expected inflation.
• Combining this with the expectations form of the
  PPP, we have the International Fisher Effect
• the interest rate differential between two
  countries is an unbiased predictor of the future
  change in the spot rate of exchange.