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2. Purchasing Power Parity (PPP)
There is a relation between level of price and the exchange rate which is determined by the
famous theory named Purchasing Power Parity (OECD, n.d.). It is often abbreviated as
PPP. There are two versions of theory of purchasing power parity:
1. The Absolute PPP.
2. The Relative PPP.
2.1. Absolute PPP
Absolute Purchasing Power Parity is a theory that works with the same logic as that of
Law of One Price or in other words, the price at which the goods are sold in different
markets are same after providing the adjustment for rate of exchange or exchange rate. It is
a pure theory of price-level which considers the same basket of goods in every country
ignoring any other factors. According to this concept, the currency’s exchange-rate would
gradually change over a period of time until the goods hold an equal value because without
any trade barriers there should be equilibrium in the goods’ prices (IG, n.d.).
As per Absolute PPP, rate of exchange between the currencies of two different nations is
always equal to the ratio of levels of price of basket of goods.
where,
two nations are, (AUD/USD)
foreign price level is, (USA).
Therefore,
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Domestic Price Level (P) = [Exchange rate between two
nations (S)] x [Foreign (USA) Price Level (P*)]
S=P/P*

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2.1.1 Methodology
The ratio of Australia and USA prices are considered for computing the implied Purchase
Power Parity exchange rate. The issue is that the price level given by CPI for Australia and
USA is dependent on different base years. Hence, there arises a requirement to base both
nations’ CPI to the same time-period. Since, our analysis is based upon a ten years period,
the selected base-period for our analysis is March 2010. Therefore, implied Purchase
Power Parity spot rate is computed using the below formula:
where,
P0 = CPI of Australia in Mar-2010.
P*o = CPI of USA in Mar-2010.
Plotting the ratio of CPI of USA and Australia based upon Mar-2010 against the
AUD/USD actual spot exchange rate gives the following the graph:
Figure - 2.1.1
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St/So=(Pt/Po)/(P*t/P*o)

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Figure - 2.1.2
The above Figure (2.1.1) represents the existing relation between the exchange rate
implied by Purchasing Power Parity and the actual spot exchange rate of AUD/USD spot
rate over ten years’ time-period. The above figure depicts that the rate implied by
Purchasing Power Parity has mere fluctuations, but throughout the observed period the
market spot rate has been highly volatile. This volatility can also be seen in the Figure
2.1.2, that shows deviation of the market spot rate from the exchange rate implied by
Purchasing Power Parity in this time-period. From the year 2010 to year 2013 the
deviation was really small but it widens from the year 2014 and then happened a
significant deviation between the year 2015 and year 2019. Therefore, on the basis of this
observation it can be inferred that the theory of absolute Purchasing Power Parity fails to
explain the AUD/USD market spot rate fluctuations in the observed time-period. .
2.2. Relative PPP
There is always a difference between the inflation rates of two different nations and these
differences are considered by the Relative PPP theory. It means, the relative rate of change
existing between foreign price-level & domestic price-level would depict the rate at which
exchange rates will change (Nasdaq, n.d.).
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∆S=∆P- ∆P*

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where,
∆S = % change in AUD/USD rate.
∆P= % change in Australia Price-Level.
∆P* = % change in USA Price-Level.
As per Relative PPP, the country which has a higher rate of inflation would depreciate.
2.2.1 Methodology
In order to test the Relative Purchasing Power Parity, difference existing between the price
level of US and Australia is plotted against the % changes in AUD/USD spot-rate. The
graph is presented below:
Figure - 2.2
In the above Figure (2.2), it can be seen that from 2006 to 2016 there is very small
fluctuations in the relative changes between price-levels of these counties but there exist
huge changes in the market spot exchange-rate. So, based upon this graph it can be
concluded that the theory of relative Purchasing Power Parity doesn’t explain AUD/USD
spot rate fluctuations.
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2.3. Limitations of PPP
There are certain limitations related to this theory named Purchasing Power Parity (PPP)
which may assist to explain deviations in the movement of actual rate of exchange against
the ones implied through the means of purchasing power parity (PPP).
Certain trade related barriers and discrepancies in values of non-traded items
internationally might act as an origin of price differences arising among the nations and
thereby rejects the hypothesis of purchasing power parity (PPP). Imperfect competition can
even lead to price variations because it’s possible that the same item is selling at some
different prices in many other markets with an objective to maximize the profit of firms.
Additionally, difference in weights and statistical differences while computing price
indices would give a different value of price index, leading to deviations from Purchasing
Power Parity (PPP) (Moon, Page, Rodin and Roy, 2010).
Due to commodity arbitrage, prices would be needed to adjust but since the prices are
usually considered sticky in the short-run, it could adjust but little slowly and gradually
over the period of time. In the long-run, exchange-rate can be predicted using the theory of
PPP because arbitrage turn out to be highly efficient and therefore higher goods are traded.
As visible from the graph depicted above, in short-run, the theory of Purchasing Power
Parity (PPP) can hardly describe movement of exchange rate.
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3. Interest Rate Parity
Interest-rate parity refers to the theory as per which differences in interest-rate between
two nations is equivalent to the differences between the forward and spot-rate of exchange.
Interest rate parity has a significant role to play in foreign exchange rates, connecting
interest rates, foreign exchange markets, and spot exchange rates (Levich, 2013).
IRP has two components namely, Covered Interest Parity and Uncovered Interest Parity.
3.1. Covered Interest Parity (CIP)
As per the idea of CIP, once the risk associated with exchange rate is covered using the
forward market there should not exist any differences in returns of two nations. Any
difference existing in the interest rates of two nations will be converted to the exchange
rate (forward exchange rate and spot exchange rate) movement in the equal proportion
(Efstathiou, 2019). Hence, the chance of arbitrage would be removed or abolished.
It is expected that a country offering higher rate of interest would will sell at a forward
discount and vice-versa.
where
it = domestic rate of interest
it* = foreign rate of interest
Ft = forward exchange rate
St = spot exchange rate
In order to test for Covered Interest Parity (CIP), difference in interest-rate has been
plotted against percentage change in forward exchange-rate. Due to non-availability of
forward exchange-rate data it would not be possible to test the CIP.
3.2. Unbiased Expectation Theory
It is a theory which assumes that the market stands efficient due to which individual would
be neutral to risk. Therefore, conversion of currency using forward-rate today or expected
spot-rate in future would make no difference to an investor (The Motley Fool, 2016).
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(1+ it) / (1+ it*) = Ft / St

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where,
Ft = Forward exchange rate
St +1
e = expected future spot rate
3.3. Uncovered Interest Parity (UIP)
Like Covered Interest Parity, UIP has the notion that all the return on investments in the
domestic country and foreign countries must be equal or same. Still, UIP does not cover
long currency position and thereby leave it open to exchange rate fluctuations (Saadon and
Sussman, 2018). Uncovered Interest Parity accepts that both unbiased expectation theory
and Covered Interest Parity theory actually holds.
Thus, uncovered interest rate can be defined as change in relative rate of interest between
the two nations is equivalent to the expected change in exchange rate.
where,
it
❑ = Domestic rate of interest
it
¿ = Foreign rate of interest
St +1
e = expected future spot rate
St = spot exchange rate
3.3.1. Methodology
For testing theory of Uncovered Interest Parity, we are required to subtract differences in
rate of interest between two nations from % change in the exchange-rates. However,
regarding future spot rate, data related to forward-rate as well as expected future spot-rate
is unavailable. Since, we did not get the data related to expected future spot rates, we
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Ft = St +1
e
(1+it) (1+it*) = ¿ ¿) / (St)

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would assume that market is efficient as well as rational. Efficient and rational market
means actual spot exchange-rate in time t+1 would be similar to the expected future spot-
rate of an investor.
The above assumption can be represented as follows:
where,
St +1
e = Expected future spot rate
St+1 = Actual future spot rate
Therefore, Uncovered Interest Parity can be computed by:
Where
it = domestic interest rate
it
¿ = foreign interest rate
St+1 = actual future spot rate
St = spot exchange rate
For testing the validity of the theory of UIP, we will use here standard deviation with
confidence interval of 95 per cent. Therefore, we need to use ±2σ and will see whether the
graph would fall within it.
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St +1
e
= St+1
[it-it*]-[St+1-St/St] = 0

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Figure 3.3.1
It can be seen in the above graph that UIP fluctuates over-time but it however, remains
between the confidence-interval. Here issue is that few collected data may not follow
random distribution’s assumptions and this is explained further in the following part.
3.3.2. Empirical Evidence
By employing z test it was noticed that calculated value of Zcal is 0.1758 (appendix 1
shows the calculations) is lower than Zstats (1.96). So, we have accepted the null-
hypothesis and therefore rejected alternative hypothesis. Hence, it can be stated that mean
is statistically equal to the zero. So, it could be said that the data set follows the normal-
distribution variance and it lies in between ± two standard deviations. But there are few
outliers in the observed period that were due to some macro actions. So, according to this
empirical evidence and above graphical observations (3.3.1) we conclude that the
Uncovered interest parity holds.
3.3.3. Limitations of IRP
No doubt that usually assumptions of IRP holds true but there also exist few barriers that
leads to differences in return of domestic country as well as foreign countries and violates
assumptions of IRP.
Government policies may affect change in net return among the nations but it never
changes and impact position of exchange rate. Due to difference in tax, the assumptions of
IRP might not be valid because arbitrager would long position financial instruments in the
nation with a lower rate of tax and short position in a nation with higher rate of tax
(Lemke, 2019).
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IRP assumes that there exists an infinite fund for currency arbitrage which cannot be held
realistic. When future contracts and forward contracts are not available for the hedging
means, uncovered interest-rate parity cannot be held in the actual world.
References
1. Efstathiou, K. (2019). The breakdown of the covered interest rate parity condition.
[online] Available at: https://www.bruegel.org/2019/07/the-breakdown-of-the-
covered-interest-rate-parity-condition/ [Accessed 23 Mar. 2020].
2. IG. (n.d.). What is purchasing power parity (PPP)?. [online] Available at:
https://www.ig.com/en/trading-strategies/what-is-purchasing-power-parity--ppp---
191106. [Accessed 23 Mar. 2020].
3. Lemke, T. (2019). What Is Interest Rate Parity?. [online] Available at:
https://www.thebalance.com/what-is-interest-rate-parity-4164249 [Accessed 23
Mar. 2020].
4. Levich, R.M. (2013). Interest Rate Parity. [online] Available at:
https://www.sciencedirect.com/topics/economics-econometrics-and-finance/
interest-rate-parity [Accessed 23 Mar. 2020].
5. Moon, S. Page, S. Rodin, B. and Roy, D. (2010). Purchasing Power Parity
measures: advantages and limitations. [online] Available at:
https://www.odi.org/sites/odi.org.uk/files/odi-assets/publications-opinion-files/
6018.pdf [Accessed 23 Mar. 2020].
6. Nasdaq. (n.d.). Glossary of Stock Market Terms. [online] Available at:
https://www.nasdaq.com/glossary/r/relative-purchasing-power-parity. [Accessed 23
Mar. 2020].
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7. OECD. (n.d.). Purchasing power parities (PPP). [online] Available at:
https://data.oecd.org/conversion/purchasing-power-parities-ppp.htm [Accessed 23
Mar. 2020].
8. Saadon, Y. and Sussman, N. (2018). Nominal exchange rate dynamics and
monetary policy: Uncovered interest rate parity and purchasing power parity
revisited. [online] Available at: https://voxeu.org/article/uncovered-interest-rate-
parity-and-purchasing-power-parity-revisited [Accessed 23 Mar. 2020].
9. The Motley Fool. (2016). How to Calculate Unbiased Expectations Theory.
[online] Available at: https://www.fool.com/knowledge-center/how-to-calculate-
unbiased-expectations-theory.aspx [Accessed 23 Mar. 2020].
Appendix
To ensure UIP validity, we have performed hypothesis testing:
1st step
H0: μ = 0
H1: μ ≠ 0
2nd step
X = 0.01
σ = 0.0569
3rd step
Z0.05/2 = 1.96
If Calculated Z > Zstat, we reject H0
If calculated Z < Zstat, we do not reject H0
4th step
Zcal = 0.1758
5th step
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Calculated Z of 0.1758<1.96, So we do not reject H0. Hence, it can be concluded that
mean is statistically equal to zero. So, Uncovered interest parity holds.
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