1. International Parity Conditions
Chapter 04
International Parity Conditions

2. International Parity Conditions
Foreign exchange rate quotations
Measuring a change in spot rates
Prices and exchange rates
Law of one price
Absolute Purchasing Power Parity (PPP)
Relative Purchasing Power Parity
Interest rates and exchange rates
The Fisher effect
International Fisher effect
Forward rate
Interest Rate Parity (IRP)
Covered/Uncovered Interest Arbitrage
Forward rates as an unbiased predictor of future spot rates

3. Foreign Exchange Rates & Quotations
Direct and Indirect Quotes
A direct quote is a home currency price of a unit of a foreign currency
Sfr1.6000/$ is a direct quote in Switzerland
An indirect quote is a foreign currency price of a unit of the home currency
Sfr1.6000/$ is an indirect quote in the US,
$0.6250/Sfr is a direct quote in the US and an indirect quote in Switzerland

4. Measuring a Change in Spot Rates
Assume that Swiss franc is quoted at Sfr1.6000/$ (same as $0.6250/Sfr). Suddenly it strengthens to Sfr1.2800/$ (same as $ /$). What is the percentage change in the dollar value of the franc? (Home currency is dollar)
Using Direct Quotes:
Using Indirect Quotes:
What if Home Currency is Sfr in this example. (What is the percentage change in the Sfr value of the dollar?)
Direct Quote %Δ = [ (Sfr1.2800/$ – Sfr1.6000/$) / Sfr1.6000/$ ] x 100 = –20%
Indirect Quote %Δ = [ ($0.6250/Sfr – $ /Sfr) / $ /Sfr ] x 100 = –20%
SAME

5. Prices and Exchange Rates
The Law of one price states that all else being equal (no transaction costs) a product’s price should be the same in all markets
The law of one price states that
Where the price of the product in US dollars (P$), multiplied by the spot exchange rate (S, yen per dollar), equals the price of the product in Japanese yen (P¥)
Conversely, if the prices were stated in local currencies, and markets were efficient, the exchange rate could be calculated from the relative local product prices

6. Prices and Exchange Rates
What if you have the following scenario:
You live in Switzerland and observe that a product costs Sfr6.20 in Switzerland while the same product costs $2.65 in the US
Also assume that Homer trades Sfr and $ from his couch and that he stands ready to sell you one dollar for Sfr1.36 – This is also to say he is going to buy Sfr1.36 for a buck
Can you make any arbitrage profits?
Buy the product in the US and sell it in Switzerland
Buy: need to spend $2.65 for the purchase. Since you are a Swiss person ask Homer to sell you dollars for Sfr. You need to pay him $2.65 x Sfr1.36/$ = Sfr3.604
Sell: receive Sfr6.20 for the sale of the product that you just spent Sfr3.604 for
What is your profit (Sfr6.20/Sfr3.604) – 1 = + 72%
Thanks to Homer!!!
If you are a Dollar based investor then procedure would be slightly different.
Buy the product and spend $2.65.
Sell it in Switzerland for Sfr6.20.
Sell Sfr6.20 to Homer for Dollar. Homer would give you: (Sfr6.20) / (Sfr1.36/$) = $4.5588
Your profit is [ $ / $2.65 ] – 1 = +72%

7. The Big Mac Hamburger Standard
The Economist developed the Big Mac Standard to track PPP:
Assuming that the Big Mac is identical in all countries, it serves as a comparison point as to whether or not currencies are trading at market prices
Big Mac in Switzerland costs Sfr6.20 while the same Big Mac in the US costs $2.65
The implied PPP of this exchange rate is

8. The Big Mac Hamburger Standard (Continued)
If the actual exchange rate is Sfr1.36/$, then we can determine relative valuation
The Swiss franc is overvalued against dollar by
Above equation applies when we have an “Indirect Quote” (FC/$) to measure Sfr value against the dollar

9. The Big Mac Hamburger Standard (Continued)
If Direct Quotes ($/FC) are used the equation would become
Since home currency is $, Direct Quotes are:
Theoretical = 1 / Sfr2.34/$ = $0.4274/Sfr and
Actual = 1 / Sfr1.36/$ = $0.7353/Sfr
Again we are measuring the value of Sfr against the dollar
What about the value of dollar against Sfr? (Sfr is Home Currency)
IQ = [ Theoretical / Actual ] – 1 = [ $0.4274/Sfr / $0.7353/Sfr ] – 1 = –42%.
DQ = [Actual / Theoretical ] – 1 = [ Sfr1.3600/$ / Sfr2.3400/$ ] – 1 = –42%.
Dollar is undervalued against the Sfr by 42%.

10. Homer’s Solution
Homer should change his conversion rate, Spot Exchange Rate, to Sfr2.34/$ = (Sfr6.20/$2.65)
Buy the product in the US and sell it in Switzerland
Buy = need to spend $2.65 for the purchase. Since you are a Swiss person ask Homer to sell you dollars for Sfr. You need to pay him $2.65 x Sfr2.34/$ = Sfr6.20
Sell = receive Sfr6.20 for the sale of the product that you just spent Sfr6.20 for????
What is your profit (Sfr6.20/Sfr6.20) – 1 = 0%

11. Purchasing Power Parity & The Law of One Price
If the Law of One Price were true for all goods, the purchasing power parity (PPP) exchange rate could be found from any set of prices
Prices of individual products can be determined through the PPP exchange rate
This is the absolute theory of purchasing power parity
Absolute PPP states that the spot exchange rate is determined by the relative prices of similar basket of goods

12. Relative Purchasing Power Parity
If the assumptions of absolute PPP theory are relaxed, we observe relative purchasing power parity
The idea is that the relative change in prices between countries over a period of time determines the change in exchange rates
Moreover, if the spot rate between 2 countries starts in equilibrium, any change in the differential rate of inflation between them tends to be offset over the long run by an equal change in the spot rate. Higher inflation currency should depreciate
Using the direct quotes mathematically the following relationship should hold:
Using indirect quotes, we have:
Exchange rate does not change in line with inflation in one currency.
Time Є Cost FX Rate $ Cost
0 Є $1.3000/Є $130.00
1 Є $1.3000/Є $136.50
2 Є $1.3000/Є $143.00
Exchange rate should change with inflation in one currency.
1 Є $1.2391/Є $130.00
2 Є $1.1818/Є $130.00

13. Relative Purchasing Power Parity
High inflation currency should depreciate
Home inflation rate is higher, but home currency does not depreciate as much (direct quote goes up). Foreign goods become relatively cheaper to US consumers.
π$ – πFC 1
Increased purchasing power of foreign goods. Cheaper to buy foreign goods. or
Let’s consider some possibilities: 1. Price of a product is $100 in the US and ¥100 in Japan. For simplicity also assume that exchange rate is $1.00/¥. Now suppose that due to inflation product’s price increase to $110 in the US and to ¥105 in Japan (10% inflation in the US and 5% in Japan). At the same time the new exchange rate is $1.02/¥. What are the implications of these in terms of PPP?
Arbitrage is possible: Japanese product is relatively cheaper. A US based person now needs $110 for the product if purchased in the US and only ¥105 x $1.02/¥ = $ if purchased in Japan. Therefore buy it in Japan spending $ in dollars for purchase and sell it in the US for $110. Your profit is $ If exchange rate had changed to $1.05/¥ (representing 5% inflation difference) then $ cost would be ¥105 x $1.05/¥ = ~$110.00
2. A different example: Original prices are $100 and ¥100. Exchange rate is $1.00/¥. In one year $103 (3%) and ¥106 (6%). Inflation difference is –3%. Exchange rate becomes $0.99/¥ (–1%). Product costs now are $103 in the US and ¥106 x $0.99/¥ = $ in Japan. Now, it is cheaper to buy in the US.
Decreased purchasing power of foreign goods. Cheaper to buy domestic goods. 2

14. Does PPP Hold?
Empirical tests of both relative and absolute purchasing power parity show that for the most part, PPP is not accurate in predicting future exchange rates
Reasons:
Price indexes include non tradable goods
Goods baskets are not similar
Differential inflation rates might be inaccurate
Test periods are subject to government interventions
Two general conclusions can be drawn from the tests:
PPP holds up well over the very long term but is poor for short term estimates
The theory holds better for countries with relatively high rates of inflation and underdeveloped capital markets

15. Exchange Rate Indices: Real and Nominal
In order to evaluate a single currency’s value against all other currencies in terms of whether or not the currency is “over” or “undervalued,” exchange rate indices were created
These indices are formed by trade-weighting the bilateral exchange rates between the home country and its trading partners
The nominal exchange rate index uses actual exchange rates to create an index on a weighted average basis of the value of the subject currency over a period of time

16. Exchange Rate Indices: Real and Nominal
The real effective exchange rate index indicates how the weighted average purchasing power of the currency has changed relative to some arbitrarily selected base period
The real effective rate for the US dollar
The nominal rate index
US dollar costs
Foreign currency costs (CFC)
If changes in exchange rates just offset differential inflation rates – if purchasing power parity holds – all the real effective exchange rate indices would stay at 100
If a rate strengthened (overvalued) or weakened (undervalue) then the index value would be above or below 100, respectively

17. Real Effective Exchange Rate Indices IMF’s Real Effective Exchange Rate Indexes for the United States & Japan (2000 = 100)
Overvalued
Undervalued

18. Exchange Rate Pass-Through
Incomplete exchange rate pass-through is one reason that country’s real effective exchange rate index can deviate from it’s PPP equilibrium point
The degree to which the prices of imported & exported goods change as a result of exchange rate changes is termed pass-through
Example: assume BMW produces a car in Germany and all costs are incurred in euros. When the car is exported to the US, the price of the BMW should be the euro value converted to dollars at the spot rate
Where P$ is the BMW price in dollars, P€ is the BMW price in euros and S is the spot rate

19. Exchange Rate Pass-Through
If the euro appreciated 20% against the dollar, but the price of the BMW in the US market rose to only $40,000 from $35,000, and not $42,000 as is the case under complete pass-through, the pass-through is partial
The degree of pass-through is measured by the proportion of the exchange rate change reflected in dollar prices
The degree of pass-through in this case is partial, 14.29% ÷ 20.00% or approximately Only 71.0% of the change has been passed through to the US dollar price

20. Fisher Effect
Prices between countries are related by exchange rates and now we discuss how exchange rates are linked to interest rates
The Fisher Effect states that nominal interest rates in each country are equal to the required real rate of return plus compensation for expected inflation. As a formula, The Fisher Effect is
Where i is the nominal rate, r is the real rate of interest, and is the expected rate of inflation over the period of time
The cross-product term, , is usually dropped due to its relatively minor value

21. Fisher Effect
Applied to two different countries, like the US and Japan, The Fisher Effect would be stated as
It should be noted that this requires a forecast of the future rate of inflation, not what inflation has been, and predicting the future can be difficult!
International Fisher Effect assumes that the real rates across countries are the same.

22. International Fisher Effect (IFE)
The International Fisher Effect, or Fisher-open, states that the spot exchange rate should change in an amount equal to the difference in interest rates between countries
if we were to use the US dollar and the Japanese yen, the expected change in the spot exchange rate between the dollar and yen should be
Using direct quotes:
Using indirect quotes:

23. International Fisher Effect (IFE)
Justification for the international Fisher effect is that investors must be rewarded or penalized to offset the expected change in exchange rates
The international Fisher effect predicts that currencies with low interest rates are expected to appreciate relative to currencies with high interest rates
This reasoning is due to the fact that low interest rates imply low expected inflation rates
Similar to PPP except that expected inflation rather than past inflation figures are incorporated

24. International Fisher Effect (IFE)
High interest rate currency should depreciate
Home interest rate is higher, but home currency does not depreciate (direct quote goes up) as much. It is better to invest in the US. Foreigners will do the same.
i$ – iFC
Lower returns from investing in foreign deposits. Invest in the US. 1 or
Let’s consider an example: 1. Annual interest rates are 5% and 3% in the US and Japan, respectively. For simplicity also assume that the current exchange rate is $1.00/¥ and the one-year forward exchange rate is $1.03/¥. What are the implications of this in terms of International Fisher Effect?
Arbitrage is possible: Borrow $100 in the US and sell ¥103 forward at $1.03/¥. Convert dollars into ¥ and receive ¥100. Invest Yen for one year at 3%. Investment will be worth ¥103 in one year. Sell ¥103 for dollar at forward rate of $1.03/ ¥ and receive $ Repay the US loan for $105 and keep $1.09 as profit.
Higher returns from investing in foreign deposits. Invest abroad.

25. Does International Fisher Effect Hold?
Empirical studies indicate that the IFE theory holds during some time frames. However, there is also evidence that it does not consistently hold
Since the IFE is based on PPP, it will not hold when PPP does not hold
For example, if there are factors other than inflation that affect exchange rates, the rates will not adjust in accordance with the inflation differential

26. Interest Rates and Exchange Rates
The Forward Exchange Rate
A forward rate is an exchange rate quoted today for settlement at some future date
The forward exchange agreement between currencies states the rate of exchange at which a foreign currency will be bought or sold forward at a specific date in the future (typically 30, 60, 90, 180, 270 or 360 days)
The forward rate is calculated by adjusting the current spot rate by the ratio of euro currency interest rates of the same maturity for the two subject currencies

27. Interest Rates and Exchange Rates
The Forward Rate (using direct quotes)
The equation for determining the Forward Rate
Equilibrium condition where the investment return in $ is the same regardless where the investment is made after taking into account the change in exchange rate
Another way of stating equilibrium condition
Note each one of these equations can be driven from one another

28. Interest Rates and Exchange Rates
The Forward Rate example with spot rate of Sfr1.4800/$, a 90-day euro Swiss franc deposit rate of 4.00% p.a. and a 90-day euro-dollar deposit rate of 8.00% p.a. Home currency is US $.

29. Interest Rates and Exchange Rates
The forward premium or discount is the percentage difference between the spot and forward rates stated in annual percentage terms
When stated in direct terms (home currency per foreign currency units, $/FC) then formula is
For indirect quotes (FC/$), then (S – F) / F should be applied

30. Interest Rates and Exchange Rates
Using the previous Sfr example, the forward discount or premium would be as follows:
The positive sign indicates that the Swiss franc is selling forward at a premium of 3.96% per annum (it takes 3.96% more dollars to get a franc at the 90-day forward rate – it would be the same if direct quotes are used)

31. Interest Rates and Exchange Rates
Same example with direct quotes:

32. Interest Rate Parity (IRP)
Interest rate parity theory provides the linkage between foreign exchange markets and international money markets
The theory states that the difference in the national interest rates for securities of similar risk and maturity should be equal to the forward rate discount or premium for the foreign currency, except for transaction costs
If not true then there exists risk-free profit opportunities (arbitrage)

33. Interest Rate Parity (IRP)
In the diagram in the following slide, a US dollar-based investor with $1 million to invest, is shown indifferent between dollar-denominated securities for 90 days earning 8.00% per annum, or Swiss franc-denominated securities of similar risk and maturity earning 4.00% per annum, when “cover” against currency risk is obtained with a forward contract

34. Interest Rate Parity (IRP)
Dollar money market
$1,000,000
$1,020,000
 1.02
Start
End
i $ = 8.00 % per annum
(2.00 % per 90 days)
S = SF /$
SF 1,480,000
F90 = SF /$
$1,019,993*
90 days
Swiss franc money market
SF 1,494,800
 1.01
i SF = 4.00 % per annum
(1.00 % per 90 days)
Note that the Swiss franc investment yields $1,019,993, $7 less on a $1 million investment.

35. Covered Interest Arbitrage (CIA)
Because the spot and forward markets are not always in a state of equilibrium as described by IRP, the opportunity for arbitrage exists
The arbitrageur who recognizes this imbalance can invest in the currency that offers the higher return on a covered basis
This is known as covered interest arbitrage (CIA)
The following slide describes a CIA transaction in much the same way as IRP was transacted

36. CIA – Example Assume that you observe the following (HC is $):
i$ = 8% p.a. and i¥ = 4% p.a.
S¥/$ = ¥106.00/$ and six-month F¥/$ = ¥103.50/$
Compare interest differential to forward premium/discount
Interest differential = i$ – i¥ = 8% – 4% = 4%
Forward premium/discount:
This observation would be below the IRP line, therefore we borrow $ and invest in ¥

37. CIA – Example Start End Eurodollar rate = 8.00 % per annum
Dollar money market
$1,000,000
$1,040,000
 1.04
Start
End
F180 = ¥ /$
Arbitrage
Potential
$1,044,638
S = ¥ /$
¥ 106,000,000
180 days
Yen money market
¥ 108,120,000
 1.02
Euroyen rate = 4.00 % per annum

38. Uncovered Interest Arbitrage (CIA)
A deviation from CIA is uncovered interest arbitrage, UIA, wherein investors borrow in currencies exhibiting relatively low interest rates and convert the proceeds into currencies which offer higher interest rates
The transaction is “uncovered” because the investor does not sell the currency forward, thus remaining uncovered to any risk of the currency volatility

39. Uncovered Interest Arbitrage (UIA): The Yen Carry Trade
Investors borrow yen at 0.40% per annum
Japanese yen money market
¥ 10,000,000
¥ 10,040,000 Repay
 1.004
Start
End
S360 = ¥ /$
¥ 10,500,000 Earn
¥ ,000 Profit
Then exchanges
the yen proceeds
for US dollars,
investing in US
dollar money
markets for
one year
S = ¥ /$
$ 83,333.33
360 days
US dollar money market
$ 87,500.00
 1.05
Invest dollars at 5.00% per annum
Note that the final outcome is determined by future spot rate. It is likely to test some nerves!!!
¥ appreciates to below ¥114.74/$ you face losses.

40. Does Interest Rate Parity Hold?
Various empirical studies indicate that IRP generally holds
While there are deviations from IRP, they are often not large enough to make covered interest arbitrage worthwhile
This is due to the characteristics of foreign investments, including transaction costs, political risk, and differential tax laws

41. Forward Rates as an Unbiased Predictor
If the foreign exchange markets are thought to be “efficient” then the forward rate should be an unbiased predictor of the future spot rate
This is roughly equivalent to saying that the forward rate can act as a prediction of the future spot exchange rate, and it will often “miss” the actual future spot rate, but it will miss with equal probabilities (directions) and magnitudes (distances)
Evidence indicate that forward rates are biased predictors of future spot rates
Forecasting services should have value otherwise would not exist

42. Forward Rates as an Unbiased Predictor
Exchange rate
Time S2
Error F2 S3 S4 F1
Error S1 F3
Error
t 2
t 3
t 4
t 1
The forward rate available today (Ft,t+1), time t, for delivery at future time t+1, is used as a “predictor” of the
spot rate that will exist at that day in the future. Therefore, the forecast spot rate for time St2 is F1; the actual spot rate turns out to be S2. The vertical distance between the prediction and the actual spot rate is the forecast error. When the forward rate is termed an “unbiased predictor,” it means that the forward rate over or underestimates the future spot rate with relatively equal frequency and amount, therefore it misses the mark in a regular and orderly manner. The sum of the errors equals zero.