Interest rate parity and law of one price

Prüfungsvorbereitung, 2016

9 Seiten


Table of contents

1 Solution to Q1 a)

2 Solution to Q1 b)

3 Solution to Q2

4 References

List of tables and figures

1 Solution to Q1 a)

2 Solution to Q1 b)

3 Solution to Q2

4 References

1 Solution to Q1 a)

The interest rate parity states that the difference in national interest rates in absence of transaction costs is equal to the forward rate premium or discount, which is the percentage difference between the spot and forward exchange rate (Eiteman/Stonehill/Moffett 2016, p. 177). Knowing that, the answer to the first question can be determined with the help of the given information:

If we assume that EUR is our domestic currency, we can exchange 1 EUR at the current spot rate of 0.80 USD/EUR and receive 0.80 USD. They are invested at the given 5% USD rate for one year, so we get 0,84 USD at the end of that period. Because we sold the USD amount beforehand via the given forward rate of 0.78 USD per EUR, we now receive 0,84 USD: 0.78 USD/EUR = 1.0769 EUR. Consequently, the current EUR one year interest rate is 7.69%. Even without calculating it is apparent that the EUR rate has to be higher than the USD rate, because the EUR is depreciating over that period which has to be compensated with a higher interest rate. ‘Any differences in interest rates must be offset by the difference between the spot and forward exchange rates’ (Ibid., p. 179), which is shown by the following formula:

Using our data we get the result, that our calculated one year EUR interest rate is correct:

2 Solution to Q1 b)

If the interest parity described in Q1 a) does not hold and spot and forward markets are not in equilibrium, the possibility of riskless arbitrage emerges. This is possible by choosing to invest in the currency with the highest interest return and exchanging it back with the guaranteed forward rate. Because the return of such an investment is known beforehand, the arbitrage deal is covered and therefore known as covered interest arbitrage (Eiteman/Stonehill/Moffett 2016, p. 179). The ‘arbitrage rule of thumb’ states that one should invest in the higher interest yielding currency, if the difference in interest rates is greater than the forward premium/discount or the expected change in the spot rate (Ibid., p. 181). The forward premium/discount is calculated this way:

The positive sign indicates that the USD is selling forward at a yearly premium of 2.56% (Ibid., p. 177). Because that is less than the new interest difference of 10% EUR minus 5% USD, we follow the precedent rule and invest in EUR, the higher yielding currency. We have to conduct the following steps to benefit from the arbitrage opportunity:

At first, we borrow 1 USD for one year at the given rate of 5%, so we know that we have to pay back 1.05 USD in one year. We change the 1 USD into EUR at the spot rate and receive 1 USD : 0.80 USD/EUR = 1.25 EUR. This amount is immediately invested in a one-year EUR-account, so we can be sure to receive 1.25 EUR * 1.10 = 1.375 EUR at maturity. Furthermore at the beginning, we sell EUR vs. USD forward to ensure the repayment of our USD loan. Because the USD is anticipated to get stronger, we will need more EUR than at the beginning to buy back the 1.05 USD, interest included. 1.05 USD divided by the forward rate of 0.78 USD/EUR results in 1.3462 EUR payable in one year. Fortunately, this is less than the proceeds of our EUR account, so that we earn the difference of 1.375 EUR – 1.3462 EUR = 0.0288 EUR without taking any market risk. In relation to the invested 1.25 EUR there is an arbitrage profit of 2.3%.

3 Solution to Q2

The second question starts with an anecdote of a special goods offer (cheap diapers) in southern Norway, which led to frequent journeys of foreigners aiming to profit from arbitrage with the result of a shortage of this good eventually. It has to be examined if the described situation is an example of a possible ineffectiveness of the purchasing power parity (PPP). Furthermore, the usage of the PPP theory shall be evaluated in general. Before discussing that, PPP and the relating “law of one price” (LOP) will be defined.

The LOP states that in a frictionless world, the price of two identical goods in two different countries should be the same, even after a necessary currency conversion. In other words: Assuming efficient markets, the price of the product in currency A is its price in currency B multiplied by the spot exchange rate, which in turn is dependent on both prices (Eiteman/Stonehill/Moffett 2016, p. 168).

Once a price in something, somewhere, falls below the price of that same thing elsewhere plus transport costs, then people will buy it and ship it and sell it. This will raise the price in the original location, lower it in the second, and things will always end up costing the same (accounting for transport costs) everywhere. (Worstal 2013)

That sounds comprehensible, but only for tradeable goods. The classic example for the LOP is the “Big Mac Index”. Here we have a product with identical ingredients (but mostly of local origin) all over the world. If we regard its price in different countries after currency conversion and compare it with the domestic USD price, we can test if the LOP is working, what is often not the case because of constraints like transportation costs and tariffs. Beyond that, we can derive a real valuation of the specific currency in terms of purchasing power (Eiteman/Stonehill/Moffett 2016, p. 168).

That leads us to the definition of the interrelated PPP: It is the exchange rate which results from identical products in different currencies (price in currency B divided by price in currency A), which can differ from the actual exchange rate. In other words, it is the “rate at which the currency of one country would have to be converted into that of another country to buy the same amount of goods and services in each country”. (Callen 2012) If we refer to a basket of goods, we have “absolute PPP” (Ibid). PPP helps us to get the implied exchange rate which is needed if we want to buy similar goods in a foreign country. On the other hand, it works as a price index, giving us information of the under- or overvaluation of a currency, similar as with the “Big Mac Index”, not just for one product or commodity but for the price level in general. A practical example is the calculation of salaries for foreign staff: If the home salary is just multiplied by the spot exchange rate, the amount could be too less in terms of purchasing power because of the assumed higher costs of living. Using PPP, there would be the result of a conversion at a higher rate leading to similar financial living conditions as in the home country (Vachris/Thomas 1999, p.4).

On top of that, we have relative PPP, which states that the relative change of prices between two countries over time is the basis for the change in their exchange rates. It goes without saying, that if a country has rising prices, its exchange rate should modify to the same relative extent, if its competitiveness should stay at the same level (Eiteman/Stonehill/Moffett 2016, p. 170f.). An important advantage of relative PPP is, that it doesn’t need the same basket of goods with equal weights for both observed countries as only the general change in price levels is regarded (Pakko/Pollard 2003, p.10).

Looking back to the previously described situation in Norway, it can be said that the behavior of the arbitrageurs can be explained by the “law of one price” theory. It has been estimated, that the trip of a Lithuanian to Norway buying lots of diapers costs approximately 600 USD, which is amortized quickly by a profit margin of 50% selling thousands of them back at home (O’Brien 2013). In a normal economic environment, the price gap should be closed quickly by these trades, because a shortage of a good as a sign of extraordinary demand leads to higher prices. In our case, it seems that this did not happen as fast as assumed, because the lower prices in southern Norway were implemented and apparently hold low on purpose for a longer time by the retailers – to gain additional market share. Thus it is questionable, if we really have a clear violation of the law of one price – maybe there are just not enough people who actually have the time and capacity to conduct the arbitrage. Furthermore, some retailers implemented buying limits per costumer and in Norway, all exporting goods with value over 5,000 NOK have to be declared anyway (Burglund 2014). That increases the risks for the trading foreigners, leading to a slower price adjustment.

This slower adjustment is also a serious problem of PPP in general – and not only for our Norway case - as PPP is a weak measure for shorter time periods (Eiteman/Stonehill/Moffett 2016, p. 172). In fact, there are large deviations from real exchange rates in the short run. Combined with high fluctuations they are diminishing only at a rate of 15% per year (Rogoff 1996, p. 647). The same is true for the law of one price where strong and permanent deviations are usual, mainly because of huge nominal exchange rate movements. (Ibid., p. 652). If we think of our Big-Mac-Example, these deviations sound unrealistic as we have nearly the same product ingredients worldwide and it should have a similar price after conversion. One reason for the tremendous local differences in its converted price lies in the effect of non-traded goods which are needed to deliver the final meal, e.g. operating costs like rent and the wages. They are not interchangeable (i.e. workers are restricted to move to higher paying countries) and in our special case they account for 94% of the product price (Pakko/Pollard 2003, p. 17). “The Big Mac simply costs more where income is higher.” (Ibid., p. 21) That can be explained by the fact that rich countries mostly have overvalued currencies (Taylor/Taylor 2004, p. 20). The described effect is true for many other consumer goods offered in supermarkets, like bananas from Africa (Rogoff 1996., p. 653) or the diapers from the previous example. Another reason for deviations could be government spending, which happens usually more for non-traded goods. Excessive spending can result in a currency appreciation combined with rising price levels, leading to further deviations (Pakko/Pollard 2003, p. 21).


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Interest rate parity and law of one price
School of Oriental and African Studies, University of London  (CeFIMS)
ISBN (eBook)
547 KB
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Arno Hetzel (Autor), 2016, Interest rate parity and law of one price, München, GRIN Verlag,


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