Which strategy is better?
Yield of (1 + i) or yield of (1+if)e/f ?
Well, if either strategy had a higher payoff, you could short one and go long the other, earning huge profits with no risk. We should make sure that the forward exchange rate is set so that the returns are equal:
(1 + i) = ( 1 + if) e/f
OR: f = e ( 1 + if) / (1 + i)
Covered interest parity condition.
Example: If the US interest rate is i = 8% and the German rate if = 6% and the exchange rate is e =2.0, then, the forward exchange rate is f = 1.96 (future Marks are more expensive, the dollar is expected to depreciate).
The covered interest parity can be also written in a simpler form:
(1 + if) = (1+i)f/e = (1 + i) [1 + (f-e)/e] = (1 + i)(1 + fp) =
= (1+ i + fp + i fp)
Where fp (the forward premium) is the percentage difference of the forward rate from the spot rate. Since the term (i fp) is close to zero, this parity condition becomes approximately:
i = if - fp
Where fp =(f - e)/e
i.e. the domestic interest rate is equal to the foreign rate less the forward premium.
This gives you a simple rule:
If the domestic interest rate is above the foreign rate by x%, the forward exchange rate (for the maturity equivalent to the interest rate) will be less than (i.e. depreciated relative to) the spot rate by x%.
If we cover the foreign positions with a forward contract, than it makes no difference whether we invest in dollars or DMs financial markets are very efficient and arbitrage keeps things the same (except for transactions costs).
But what if, in strategy two, we converted your dollar to DMs, invested in Germany and took your chances on the exchange rate?
Your actual return at the end of the year would then be
(1+itf) et / et+1
Where et+1 is the spot rate one year from now.
Suppose now that agents, are risk-neutral, i.e. they care only about expected returns. Then, expected return on investing in a domestic asset is (1 + i) while the expected return (as of today time t) of investing in a foreign asset is:
(1+itf) et / E(et+1)
Where E(et+1) is the expectation I have today (time t) of what the spot exchange rate will be one year from now.
If agents are risk-neutral and care only about expected returns, the expected return to investing in a domestic asset must be equal to the expected return on investing in the foreign asset:
(1+it ) = (1+itf) et / E(et+1)
Uncovered interest parity condition
Note: this is not a riskless arbitrage opportunity as the ex-post future spot, et, and what we expect it to be may differ; E(et+1) is uncertain as of today.
Rearranging the expression above and simplifying, we can rewrite the uncovered interest parity condition as:
i = if - [E(et+1) - et] / et = if - deexp/e
Where deexp/e is the expected rate of change in the exchange rate.
In the above example, if the expected DM exchange rate was 1.96, then the US interest rate equals the German interest rate less the expected rate of change of the exchange rate: 8% = 6% - [1.96 - 2]/2.
If the condition holds, a x% difference between the interest rate at home and abroad must imply that investors expect that the domestic currency will depreciate by x%. Given that covered interest parity works, uncovered interest parity amounts to saying that the forward rate today (delivery of currency at time t+1) is the market's expectation of what the spot rate will be a period from now:
ft = E(et+1).
This expectations hypothesis implies that if the forward rate is less than the current spot rate (ft < et, as in the example above), we should expect the spot rate to depreciate: E(et+1) < et.
Uncovered interest parity condition:
The condition implies that the expected depreciation of a currency is equal to the differential between domestic and foreign interest rates:
Expected rate of change in exchange rate = dee/e = if - i
High domestic interest rate (i > if) should lead to depreciation. If this happens we recall, the Fisher relationship.
Nominal interest rate = real rate + expected inflation rate
i = rreal + dp/p
Combining Fisher relationship and parity condition:
dee/e = (rrealf - rreal) + (dpf /pf - dp/p)
1. If the domestic real interest rate is equal to foreign real interest rates
then, the domestic nominal interest rate can be above the foreign rate only if the domestic country is expected to have a higher inflation rate than the foreign country. In this case, it makes sense to believe that higher interest rate at home will lead to a currency depreciation.
if < i because dpf /pf < dp/p and dee/e < 0 (depreciation)
This is consistent with PPP, higher inflation is associated (sooner or later) with a currency depreciation and the higher interest rate at home reflects only the higher expected inflation of the home country.
This implication is confirmed by the data: countries with high inflation have, on average, higher nominal interest rates than countries with lower inflation and, on average, the currencies of such high inflation countries tend to depreciate at a rate close to the interest rate (or inflation) differential relative to low inflation countries.
2. Domestic inflation is equal (or close to) the foreign inflation rate. In this case higher interest rates at home do not reflect higher domestic inflation but rather higher real interest rates due for example to a tight monetary policy by the central bank. In this case, we would expect that high domestic interest rates would be associated with an appreciating currency (as the high interest rates lead to an inflow of capital to the high yielding country). The prediction of the uncovered interest parity condition is not valid.
High real interest rates can lead to an appreciation of the currency, a contradiction of the uncovered interest rate parity condition.
From 1995 to 1997 the $ appreciated against the Yen by 29% (the Yen went from 94 per $ to 121). Throughout this period, interest rates in the US were higher (with a relatively tight monetary policy) than in Japan (with a loose monetary policy). The expectations hypothesis predicted a $ depreciation but it did not occur.
Good rules of thumb are (i) high interest rate currencies (of countries with low inflation) generally increase in value and therefore (ii) expected returns are higher in the high interest rate currency.
The failure to achieve exact covered interest parity could occur because in actual financial markets there are:
- Transaction costs
- Political risks
- Potential tax advantages to foreign exchange gains
- Liquidity differences between foreign securities and domestic securities.
Conclusion:
In this paper we started by giving the definitions of interest rate parity and interest arbitrage. Continuing we saw covered interest parity through examples and if we should invest dollar in US deposit or convert the $ to DM. Moreover we saw that uncovered interest parity involves risk and that interest differential should approximately equal the expected rate of the spot exchange rate. Finally, the reasons why exact interest parity is difficult to occur were given namely.
BIBLIOGRAPHY
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Cheols S. Eun, Bruce G. Resnick, International Financial Management 2nd ed 2001 Irwin McGraw-Hill
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Ephraim Clark, Michel Levasseur and Patrick Rousseau, International Finance 2nd ed 1999 Chapman & Hall
- Keith Pilbeam, International finance 2nd ed, Basingstoke : Macmillan Business, 1998
- Taecho Kim, International Money & Banking, 1997 Routledge
- Levi, Maurice D, International finance: financial management and the international economy, New York: London: McGraw-Hill, 1983
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Maurice D. Levi, International Finance; The Markets and Financial Management of Multinational Business, 3rd ed, McGraw-Hill International Editions
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