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MSC Math
IF_Lecture_4.pptxLecture 4 Exchange Rate Parities
Learning Objectives
Understand what UIRP tells us about exchange rate determination and the
mechanism of international financial markets
Comprehend the relationship between inflation and interest rates and
the concept of real interest rates
Comprehend the relationship between inflation differentials, interest rate
differentials, and changes in the exchange rate
Appreciate the relationships between these parities and the respective
focuses of the individual parities
Reading: Madura and Fox, Ch 8
Peijie Wang, Ch3
Uncovered Interest Rate Parity
UIRP states that
there is a relationship between
the expected change in the spot exchange rate
and the interest rate differential between the two countries
and
the expected change in the spot exchange rate
is equal to the two countries' interest rate differential.
Requires an understanding of what we mean by ‘expected’
What is the expected value?
In probability theory, the expected value of a random variable
Is the weighted average of all possible values that this random variable can take
Suppose that the current spot rate (S0 ) = $1.6/£,
and the possible spot rates next year are shown in the table.
What is the expected exchange rate next year?
E0(S1 ) = 0.5 *1.8 + 0.5 * 1.5 = $1.65/£
| pi (probability) | Possible spot rates next year (S1) |
| 0.5 (50%) | $1.8/£ |
| 0.5 (50%) | $1.5/£ |
Uncovered Interest Rate Parity
You have to choose
whether to invest £1 at home or abroad and consider
the simplest possible asset -bank deposits:
What is the rate of return (r.o.r.) on £ deposits?
£(1+ r£ )
What is the rate of return on $ deposits?
To be able to calculate the r.o.r. of $ deposits in terms of £ we can follow three steps:
a) first you need to convert £ to $ at S£/$, the amount of $ you get:
£1 * (1/ S£/$)
Uncovered Interest Rate Parity
Invest $ in a US bank for one year
(1 + r$) * (1/ S£/S )
In one year you liquidate the $ deposit and convert the proceeds into £
at E0(S1)
So you will have
In equilibrium the two r.o.r. should be equalized, that is
Uncovered Interest Rate Parity
Uncovered Interest Rate Parity
Uncovered Interest Rate Parity therefore means:
(1)
Where E0(S1) is the expectation of the future spot rate at time 1, formed at time 0.
Deducting 1 from both sides of eq (1):
Re-arranging:
(2)
9
Uncovered Interest Rate Parity
A simplified version of UIRP:
(3)
UIRP states that the expected change in the spot rate is equal to the two countries’ interest rate differential.
In other words, differences between interest rates
are matched by an offsetting expected change in the exchange rate
Graphic Illustration of UIRP
Expected depreciation of home currency is greater than interest rate differential
E(S) > rh – rf
Expected depreciation of home currency is smaller than interest rate differential
E(S) = rh – rf
rh – rf
E(S)
Uncovered Interest Rate Parity
UIRP implies that :
a) In equilibrium
or
-- investing in the home country is equal to investing in the foreign country
b) If or
-- the expected depreciation of the home currency is greater than the interest
differential, so invest in the foreign currency.
c) If or
-- the expected depreciation of the home currency is smaller than the
interest differential, so invest in the home currency.
Uncovered Interest Rate Parity Example
The Chinese interest rate is and will remain 5% pa for the next 12 months;
The Euro interest rate is and will remain 3.25% pa for the next 12 months;
The current spot CNY/EUR rate is 7.7512.
What is the expected spot rate in 12 months time?
Answer:
E0(S1) = S0(1+rh)/(1+rf)
= 7.7512 (1+0.05)/(1+0.0325) = CNY 7.8826/EUR
Exercise -- UIRP
Suppose
The UK interest rate
is and will remain 0.5% pa for the next 12 months;
The US interest rate
is and will remain 0.25% pa for the next 12 months;
The current spot £/$ rate is 0.6277.
Questions:
What is the expected spot rate in 12 months time?
If the UK interest rate is expected to rise in six months, what will the expected spot rate be?
(4 minutes)
Uncovered Interest Rate Parity & Covered Interest Rate Parity
Recall Covered Interest Rate Parity:
Uncovered interest rate parity
Forward rate as an unbiased predictor of the future spot rate and FX market efficiency
From UIRP and CIRP we can easily see that:
i.e., the market expectation of the future spot rate should be equal to the
forward rate
If the market is efficient (prices reflect all available information) we should
expect that the forward rate should be an unbiased predictor of the future
spot rate .
Fisher Effect
We have examined parities based on two characteristics
Purchasing Power Parity
Based on the difference between inflation rates in two countries
Interest rate parities
Whether covered or uncovered
Are based on interest rates
We might reasonably ask
Are these two types of parity contradictory?
Answer is “not necessarily”
If inflation rates and interest rates are closely correlated
Then there may be little difference between them
However this is not very satisfactory
So Fisher proposed the idea that
Investors are interested in the real return that they can make on investment
In essence combining PPP and interest rate parity
Fisher Effect
The Fisher effect is based on three assumptions:
Investors across countries require the same real return/real interest rates.
The expected inflation rate is embedded in the nominal interest rate
The exchange rate adjusts to the inflation rate differential according to PPP.
Assumption (1) is consistent with some theories on general investment return – including the consumption CAPM
18
Fisher Effect
Denote
a as the real interest rate,
r as the nominal interest rate,
and the inflation rate, which we expect will occur E0()
1+r =(1+a) * [1+E0()]
An approximation can be made
1+r =1+a + E0() + a* E0()
≈ 1+a + E0()
So if we expect inflation to be higher, the nominal interest rate will rise
r ≈ a + E0()
20
Fisher Effect
Assumes that real interest rates are equalised across countries
rh = interest rate in home country
E0(h) = inflation rate expected in home country
rf =interest rate in foreign country
E0(f) = inflation rate expected in foreign country
rh = a + E0(h)
rf = a + E0(f)
rh - rf = E0(h) - E0(f)
So the interest rate difference is equal to the difference in the expected
inflation rates
International Fisher Effect (IFE)
Fisher effect:
A version of PPP-in-expectations (i.e., PPP applies not to actual S and P, but rather their market expectations)
So the International Fisher Effect:
IFE suggests that the expected change in exchange rates be equal to the interested rate differential / the expected inflation rate differential between the two countries.
Note that:
As we can see that IFE and UIRP come up with the same equation, the only difference is that these two models are derived under different circumstances.
Different Parity Conditions
International Parity Conditions
CIRP – Covered Interest Rate Parity
Links forward rates, spot rates, and interest rate differentials
UIRP or Unbiasedness – Uncovered Interest Rate Parity
Sometimes called the International Fisher Effect/Relationship
Links expected exchange rate changes and interest rate differentials
PPP
Links inflation rates and rates of changes in foreign exchange rates
If the international parity conditions hold, real interest rates are the same everywhere.
Relationships between Parities
There are, in two countries, relationships between
the spot exchange rate
the forward exchange rate
the interest rates
inflation rates
These give rise to the parities and parity conditions
However there are possible tensions between some of these parities
For example PPP may hold but the International Fisher Effect does not
i.e., if the assumptions (1) and (2) of the Fisher effect (see previous slide) do not hold, PPP may still hold, the IFE would be refuted.
12/10/2017
Graphic Illustration of Relationships between Parities
Conclusion
Introduced concepts of expectations
To understand determination of the exchange rates
And a variant of the interest rate parity that we discussed last time
The relationship between interest rates and expected exchange rates
Also how forward rates
Might be used as an (unbiased) forecast of future spot rates
The relationship between different parties
Also addressed
By using the concept of parity in real interest rates
Business School
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