International Parity Conditions

In the previous sessions, Sessions 17 and 18 (Exchange Rate Theories: Purchasing Power Parity & Exchange Rate Pass Through), we discussed rate parity conditions like

Purchasing Power Parity and Law of One Price, REER (Real Effective Exchange Rate) and NEER (Nominal Effective Exchange Rate System) aspects.

Besides these parity conditions, macroeconomic factors like inflation rate, exchange rate and interest rates of countries are intertwined to create equilibrium. These equilibrium conditions can popularly to known as Interest Rate Parity, Fischer Effect, International Fischer Effect. Understanding the basis of these parity conditions forms the basis of exchange rate movement. When macroeconomic factors governing these parity conditions deviate, arbitrage opportunity is possible.

Hence in the remaining part of this session as well as next session (Session 20), these parity conditions are discussed in detail. The parity conditions are Fischer effect,

International Fischer effect, Covered and Uncovered Interest Rate Parity, Real Interest Parity and Forward Rate to be an unbiased predictor of Future Spot Rate.

In these two sessions, theoretical underpinnings for these parity conditions, whether these parity conditions hold true in real life or not and how arbitrage opportunity ensures that these parity conditions do not deviate over long period of time are also discussed.

The importance of effect of parity conditions on exchange rate can be understood from the details given in  19.1. Though it is little dated, but clearly shows the importance of these parity conditions on exchange rate.

  19.1 Exchange Rate Management: Dilemmas

Inaugural Address by Dr. Y.V. Reddy, Deputy Governor,

Reserve Bank of India

Inaugural Address by Dr. Y.V. Reddy, Deputy Governor, Reserve Bank of India at XIth National Assembly Forex Association of India at Hotel Cidade De Goa, Goa, on August 15, 1997.

Source: http://rbidocs.rbi.org.in/rdocs/Speeches/PDFs/2511.pdf

Mr Chairman and friends,

I am thankful to the organisers of the XI th National Assembly of the Forex Association of India for giving me an opportunity to share with you the dilemmas that we face in foreign exchange management. The fifty years since independence have seen significant changes in our exchange rate regime. The exchange rate policy has evolved from the rupee being pegged to the pound sterling until 1975, pegged to an undisclosed currency basket until 1992 and after a year's experience with dual exchange rate system to a market-related system by March 1993. This has helped to bring about flexibility in exchange rate management. A couple of years ago, my predecessor, distinguished Dr. S. S. Tarapore, addressed this Assembly on some of the burning issues of foreign exchange markets. Today, I will address the dilemmas that we, as policy makers face, in the conduct of exchange rate policy.

International Parity

2. I will briefly as a backdrop, revisit the four parity conditions, that you are familiar with.

•       First, the Purchasing Power Parity (PPP) which links the spot exchange rate and inflation.

•       Secondly, the International Fisher Relation which links interest rates and inflation.

•       Thirdly, the Foreign Exchange Expectations which link forward exchange rates and expected future spot exchange rates.

•       Fourthly, the Interest Rate Parity, which links spot exchange rates, forward exchange rates and interest rates.

The four parity relations could be combined in several ways to throw light on

the four critical variables that are often used in exchange rate management policies, viz., the interest rate differential, the inflation differential, the forward discount/premium, and the exchange rate movement. The theories built around the parity relations help us to understand the foreign exchange markets better, but, they rarely give us ready made solutions to the problems that arise.

It is clearly evident from the contents of Box 19.1 that these parity conditions are important to understand exchange rate movement

19.2: Fischer Effect: Relationship between the Nominal and Real exchange Rate.

In the “Session 16.4 Exchange Rate Arithmetic” we discussed how forex traders undertake exchange rate arbitrage when the relationship between forward exchange rate, spot rate and interest rate between two currencies deviate from the fundamental relationship.

Hence we know that exchange rate between two currencies pair is linked to the interest rate. But before we discuss this fundamental relationship, we need to understand a little more on the relationship between real & nominal interest rate and inflation rate in an economy.

In an economy, the relationship between the real interest rate, nominal interest rate and inflation is known as “Fischer Effect”.

Irving Fischer postulated that the nominal interest arte in an economy is equal to real rate of return and inflation rate. Mathematically,

(1+i) = (1+r)(1+Inflation Rate) ….. Eq(19.1)

Where  i= nominal interest rate and r = real interest rate.

The nominal interest rate is the interest rate we get when we approach bank for a fixed deposit. If a bank informs us that nominal interest rate is 7.25% per annum that means that an investor would receives INR1070.25 after one year on an investment of INR 1000

The real interest rate is the nominal rate after the effect of inflation is adjusted. The real interest rate tells us how fast the purchasing power of your savings account will rise over time.

Let us take some numerical example to understand this:

Nominal interest rate is 10%, i.e an bank fixed deposit holder is earning 10% per annum as interest rate Expected Inflation rate during this period is 6%.

(1+10%) = (1+r)(1+6%). Solving for r, the real rate (r) is 3.77%.

Many a times we come across and easy estimation of real interest rate i.e, real interest rate is the nominal interest rate minus the expected inflation rate.

Nominal Interest Rate = Real Interest Rate + Inflation rate.

So when Nominal interest rate is 10%, expected inflation rate during this period is 6%, the real interest rate is 4%. If the expected inflation rate increases to 13%, then real interest rate is -3%.

The following Business Standard Article (dated March 20, 2009) given in 19.2 succinctly explains the relation among real nominal and inflation rate.

 19.2 Lower inflation means higher real interest rates

March 20, 2009, Business Standard http://www.business-standard.com/india/news/lower-inflation-means-higher-real-interest-rates/352352/

With the inflation measured by the wholesale price index (WPI) ruling close to zero, real interest rates have shot up to around 12 per cent, as against around 4.5 per cent a year ago, prompting bankers to say that there was more room for the Reserve Bank of India to lower rates.

Real interest rate is the difference between WPI-based inflation and the prevailing benchmark prime lending rate (BPLR).

While inflation dropped to 0.44 per cent for the week- ended March 7, the BPLR of the top five Indian banks was in the range of 12.25-16.75 per cent. In the corresponding period last year, inflation was estimated at 7.78 per cent, while lending rates were in the range of 12.25-12.75 per cent.

On the deposit side, with inflation at near zero levels, you can hope to earn around 7.5 Empiricalpercent onstudiesanonehave-yearshowndeposit.hatIn contrast,Fischer effectthereturnsholdsweretrue negativemostly forwhenshortinflationduration governmentwasclosetosecurities13percent. in August.

Country specific Fischer effect is expressed as

  

Though all us understand what is inflation and how inflation rate is measured, in this Section we briefly discuss what inflation is and how it is measured?

19.3: International Fischer Effect:

International Fisher Effect postulates that the estimated change in the current exchange rate between any two currencies is directly proportional to the difference between the two countries' nominal interest rates at a particular time. In other words, the percentage change in the spot exchange rate over time is governed by the difference between the nominal interest rate for the two currencies.

Mathematically, International Fischer effect is expressed as

For example, if the nominal interest rate in India is 12% per annum and it is 8% in USA, then INR is expected to depreciate vis-a vis USD. Plugging the interest rate in the right hand side of Equation 19.1, we get,

This indicates that the left hand side of the Equation 9.2 should also be equal to -3.57%. Hence, percentage difference between the spot rate prevailing today and spot rate to prevail after a year should be equal to -3.57%.

Elaborating the example given above, suppose a Government of India issued a G-Sec on 1^st January 2010 having a maturity of 1 year has a coupon rate of 12% per annum. Govt. of USA paper with a maturity of 1 year is available at 8%. The differential in the nominal interest rate prevailing in Indian and USA indicates that INR will depreciate by 3.57% by the end of one year i.e, 1^st January 2011.

In other words

^{INR40 /USD − spot} after a   year             _{= −3.57%}

^spot after   a year

Solving the above equation, Spot rate after a year will be INR41.48

Intuitively, International Fisher effect works like this:

Suppose on 1^st January 2010, the exchange rate is INR 40/USD. On this date an investor invest INR 1600 at his disposal. He invests INR 800 on a Govt. of India paper at 12% interest per annum. He converts the other INR 800 to USD (USD 20) and invests in Govt. of USA paper for 1 year. After a year, he has INR 896 and USD21.6 from INR and USD investment respectively.

According to the International Fisher’s effect, the spot exchange rate on 1^st January 2011 will be decided by these two investment returns i.e USD 21.6 = INR 896. Hence the spot rate on 1^st January 2011 will be INR41.48/USD.

 

Now let us find out what would be the % appreciation/depreciation of USD/INR . The nominal interest rate in India is 12% per annum and it is 8% in USA, then USD is expected to appreciate.

The USD appreciation amount is governed by

In other words, USD is expected to appreciate by 3.7%. 

Suppose on 1^st January 2010, the exchange rate is INR 40/USD or USD 0.025/INR. On this date an investor invest INR 1600 at his disposal. He invests INR 800 on a Govt. of India paper at 12% interest per annum. He converts the other INR 800 to USD (USD 20) and invests in Govt. of USA paper for 1 year. After a year, he has INR 896 and USD21.6 from INR and USD investment respectively. According to the international Fisher’s effect, the spot exchange rate on 1^st January 2010 will be INR 41.48/USD or USD0.024108/INR.

The International Fisher’s effect relates the nominal interest rate between two countries and the movement of exchange rate between the currencies of two countries. It indicates that the country with lower nominal (higher) interest rate will appreciate (depreciate) compared to the other currency.

If the spot rate is INR40/USD and 1 year interest rate is 12% and 8% in India and US respectively, then INR is expected to depreciate or USD is expected to appreciate. The % appreciation and depreciation will be governed by Interest rate differential.

19.3.1: Empirical Validity of International Fischer

So far so good. But does International Fischer Effect holds true? Many empirical studies have been undertaken to test the validity of international Fischer effect. One of research finding details are given below.

Sundqvist ( 2002) conducted a study to test the International Fischer effect empirically. The purpose of this research is to describe the theory of the International Fisher Effect and test its empirical validity in the long run. The question asked in this research is if there is a tendency for nominal interest differentials to offset exchange rate changes? The International Fisher effect states that the future spot rate of exchange can be determined from the nominal interest differential.

A regression analysis has been applied to quarterly nominal interest differentials and exchange rate changes for five country pairs between the years 1993-2000, except for US-Germany, which contains data for the years 1993-1998. The investigated country pairs are US-Sweden, US-Japan, US-UK, US-Canada and US-Germany. The regression tests whether nominal interest differentials are a good forecast for changes in the future spot rates of exchange for the tested time frame and respective country pair. The result shows that only for US-Japan are the nominal interest differentials, on average, offset by exchange rate changes. This means that the exchange rate movements react to other factors in addition to nominal interest differentials for the other country pairs.

19.4: Interest Rate Parity & Covered Interest Rate Arbitrage:

Interest rate parity is one of the most important fundamental economic relation relating differential interest rate and forward exchange rate between a pair of currency. The parity condition requires that the spot price and the forward or futures price of a currency pair would be governed by interest rate differentials between the two currencies. In other words, the interest rates paid on two currencies should be equal to the differences between the spot and forward rates.

For example, Let us assume that interest rate prevailing in India is 8% per year while in USA it is 3% per year. Suppose the spot rate INR 47/USD. The interest parity says, that one year forward rate would be governed by the interest rate differential.

Spot _{( INR / USD)} * ⁽(^{1 + r Dom})⁾ = fwd ( _INR ^/_USD) ...... ( Eq.19.3) 1+ r _for

This indicates as on today, the 1 year forward rate will be

INR 47 /USD * ^{(1+ 8 %)} = INR 49.28 / USD (1+ 3 %)

Intuitively, it is a very simple concept. Suppose spot rate prevailing on today is INR47/USD. A person intends to invest INR 47 for year at 8% interest in India. Otherwise, he can convert INR 47 to 1 USD and invests in USA at 3% per annum and simultaneously buys a forward cover to sell 1.03 USD after a year. In both options, the investor should have the same return.

Option 1: investing in INR at 8% would result in INR 50.76.

Option 2: Investing in USD would result in USD 1.03.

The forward exchange rate must be such that, if the investors sell USD 1.03, he must earn INR 50.76. Hence the 1-forward rate prevailing in the spot date would be INR49.28/USD.

If the forward rate prevailing today is different than INR 49.28, it would give rise to interest rate arbitrage. In other words, the 1 year forward rate and interest rate in both

 countries should adjust in such a manner that this relationship holds true. If the actual forward rate differs from the interest rate parity, the arbitrage will happen.

Now let us take two scenarios: actual forward rate is either INR 50.25/USD or INR 48/USD and see forex traders can avail the interest rate arbitrage.

19.4.1: Covered Interest Rate Arbitrage:

Forward rate governed by Interest Rate Parity: INR49.28/USD.

Scenario 1: Actual forward rate prevailing: INR 50.25/USD.

When actual forward rate INR 50.25/USD, an investor converting INR to USD and investing in US market and then selling USD forward is better off compared to investing in India at 8% interest rate.

INR 47 investment in India at a rate of 8% results in INR 50.76. However, if investor converts it to USD and invests in US market, the investor receives USD1.03.

The investor sells in forward market at a rate of Rs.50.25, he receives INR 51.75.

Hence, everybody would like to borrow money in Indian market, sell INR and buy USD, invest in USD and simultaneously enter into a contract to sell USD forward.

With many investors trying to benefit from the arbitrage, borrowing in INR would increase. Hence interest rate prevailing in India would increase. Simultaneously, interest in USA would go down and many arbitrageurs would be willing to lend USD. Simultaneously investors in USA would also be entering into contract to sell USD forward thus reducing the forward rate. This would result in adjustment in spot rate, interest rates prevailing in both countries as well as the forward rate.

Scenario 2: Actual forward rate prevailing: INR 48/USD.

When actual forward rate INR 50.25/USD, an investor converting borrowing in USD and converting INR at the spot rate and buying forward USD ( equivalent to selling forward INR) is better off compared to investing in USA at 3% interest rate.

Suppose an investor borrows 1 USD. He has to pay USD 1.03 after 1 year. He converts 1 USD to INR 47 at the prevailing spot rate. Invests in India at a rate of 8%. Earns INR50.76. Converts INR to USD at a rate INR 48/USD. Receives USD1.0575. Pays back USD 1.03 to the US lender. Makes a profit of USD0.0275 for every 1USD. If he borrows 1mn USD, he would make neat profit of USD 27,500.

With many investors trying to benefit from the arbitrage, borrowing in USD would increase USD interest rate. Hence interest rate prevailing in USA would increase. Simultaneously, interest in India would go down and many arbitrageurs would be willing to lend INR. Simultaneously investors in USA would also be entering into contract to sell INR forward thus reducing the forward rate. This would result in adjustment in spot rate, interest rates prevailing in both countries as well as the forward rate.

As in both scenarios, the arbitrage benefit accrues to investors only when they take forward cover, this parity condition is known as “covered interest rate parity”.

Another concept related to “interest rate parity” called “uncovered interest rate parity” is discussed in Session 20.