GLOBAL PARTNERSHIP OF ASIAN COLLAGES

GPAC 2014 International finance

NATIONAL CHENGCHI UNINVERSITY page 1

By Paul, Carina, Jennifer, Wendy, Benson

GLOBAL

PARTNERSHIP

OF

ASIAN

COLLAGES

International Finance

Does Interest rate parity hold?

Paul Lin / Carina Liao / Jennifer Li

Wendy Hsu / Benson Chen

Supervisor: Prof. Hsieh




Abstract

Many literatures have discussed whether IRP exist empirically, some papers had

the conclusion that IRP was rejected in the reality. In practice, it is often the case that

people had a greater demand in high interest rate currencies and push them to the edge

of appreciation rather than depreciation. Therefore, Burnside et al. (2011) had found

that the carry trade creates a sizable return and a Sharp ratio more than twice of the

U.S. stock market.

In our study, however, we test IRP in a more straight forward method. We use

empirical data and a regression analysis to test the IRP equation directly. And then we

calculate the return from the currencies that highly deviated from the prediction of the

theory.

We test the data of eight major currencies around the world and among

Asian-Pacific area. The result isn’t surprise that IRP does not hold between most of

the countries. Nevertheless, when we calculate the return we do find negative or

economically insignificant returns in some portfolios.




1. Introduction

Many literatures have discussed whether IRP exist empirically, such as Bilson

(1981) and Fama (1984). Both of them had the conclusion that IRP was rejected in the

reality. In practice, it is often the case that people had a greater demand in high

interest rate currencies and push them to the edge of appreciation rather than

depreciation. Therefore, Burnside et al. (2011) had found that the carry trade creates a

sizable return and a Sharp ratio more than twice of the U.S. stock market. Other

papers researched in the carry trade strategy include, Fama and French (1993),

Brunnermeier et al. (2009), Farhi et al. (2009), Lustig et al. (2011), Mueller et al.

(2012). Most of the work done on interest rate parity tested the theory in a somewhat

indirect way. They first identified that there is an excess return, and then they had the

conclusion that IRP does not hold empirically.

There has long been an argument that whether interest rate parity (IRP) holds in

reality. According to an article Carry on trading published on Economist August 10th

2013, around $5 trillion is traded on the foreign-exchange markets every single day,

and that compares with global trade in goods and services of $18.3 trillion a year, or

about $50 billion a day. Apparently, shifting capital around the world moves

currencies more than trading on goods and service. The article continued to conclude

that the mean factor for investors to prefer one currency over another is the carry trade.




To us, it implies that the carry trade must be overall profitable, so that investors

around the world keep conducting these kinds of currency arbitrage strategies.

The carry trade is one of the oldest and most popular currencies trading strategy

that involves in borrowing money from a lower interest rate country and investing in a

high interest return market. The return will then be determined by interest rate

differences as well as exchange rate gaps. In other words, the carry trade is profitable

only when the interest rate parity does not hold. If IRP holds, the return we gain form

interest rate differences will then be on average offset by a compensatory depreciation

of the high interest rate currencies, and the expected return from these currency

speculation strategy will then turn out to be zero.

In this paper, however, we test IRP in a more straight forward method. We use

empirical data and a regression analysis to test the IRP equation directly. And then we

calculate the return form the currencies that highly deviated from the prediction of the

theory.

We test the data of eight major currencies around the world and among

Asian-Pacific area. Our study covered the period from 1995 to 2014; all of the data

are monthly average. The result isn’t surprise that IRP does not hold between most of

the countries. Nevertheless, when we calculate the return we do find negative or

economically insignificant returns in some portfolios.




The paper is organized as follows. In section 2 we describe the methodology we

used in this paper. In section 3 we explain the empirical data, show the result of

regression, and calculate the portfolio returns. In the final section, we conclude our

findings and contributions.

2. Methodology

This section contents of three parts. First, we introduce the IRP theory. Second, we

describe the statistics. Third, we identified the return gain from the carry trade.

2.1 Interest parity theory

Researchers have long been curious about how exchanges are determined, and

had proposed lots of theories and possible explanations. Examples include

International Indebtedness Theory (Goschen 1861), and the Purchasing power parity

(e.g. Cassel 1922). The Interest Rate Parity was formalized and brought to people’s

attention by the famous Keynes (1923). For the covered interest rate parity (CIP), the

forward exchange rate of a currency can be expressed as follow:

𝐹𝑡 = (1 + 𝑟1 + 𝑟∗⁄ )

𝑡𝑆𝑡,

where 𝐹𝑡 is the forward exchange rate of a certain currency for time t+1 at time t; 𝑟

and 𝑟∗ represent the risk free interest rate at home and in foreign country

respectively; 𝑆𝑡 stands for the spot exchange rate at time t.

2.2 Multi-regression analysis

(1)




In this paper, we used the multiple regression analysis to test if equation (1) holds

empirically. Multiple regression analysis is a widely used statistical technique for

researches of Economics. It can help us speculate the relationship between two or

more variables. For example, to describe the overall pattern of a dependent variable

(Y) to a single independent or explanatory variable (X), the general multiple

regression equation can be stated as:

y = a + b1X1 +b2X2 + . . . + bkXk

Where a is the intercept, the value of Y when all the X’s are zero and bj is the amount

by which Y changes when that particular Xj increases by one unit, with the values of

all the other independent variables held constant. Following the general multiple

regression equation are the basic assumptions for regression analysis: 1. Given each

value of X, there is a group of Ys, and y is the estimation of the mean of those Ys. 2.

The probability distribution of Ys’ values follows the normal distribution. 3. The

means of these normal distributions (y) is a linear function of X. 4. The standard

deviations of these normal distributions are all the same. 5. The observations (X1,

Y1), … ,(Xn, Yn) are statistically independent.

3. Empirical results

In this section, we will first show the data we selected. And then we will reveal our

empirical finding.

(2)




3.1 Data and descriptive statistics

Spot exchange rates and one-year forward exchange rates as well as risk-free

interest rates in eight selected countries are all taken from Datastream provided by

Thomson Financial. The eight selected currencies are New Taiwanese Dollar, Korean

Won, Japanese Yen, Australian Dollar, United Kingdom Pound, Euro, Chines Yuan

and the U.S dollar. We used three month LIBORs as risk-free interest rate for most of

the countries, and for those who don’t have LIBORs we used average three month

certificate deposit rate. The data are all in monthly average terms. There are 230

observations during the sample period January 1995 to March 2014. Figure 1 shows

the trends of spot and forward exchange rate of each currency as well as the risk-free

interest rate in each country.

Exchange rate Interest rate

Taiwan

Australia

0

10

20

30

40

1995 1998 2002 2006 2010

NT $ TO US $

0

2

4

6

8

10

1995 1998 2002 2006 2010

MONEY MARKET 90 DAYS RATE

0

0.25

0.5

0.75

1

1.25

1995 1998 2002 2006 2010

US $ TO AUSTRALIAN $

0

2

4

6

8

10

1995 1998 2002 2006 2010

INTERBANK RATE - 3 MONTH




Japan

Korea.

U.K.

Euro

China

Figure1. Exchange rates and interest rates of the seven countries

00.25

0.50.75

11.25

1.5

1995 1998 2002 2006 2010

US $ TO 100 JAPANESE YEN

0

0.5

1

1.5

2

2.5

1995 1998 2002 2006 2010

INTERBANK RATE-3 MONTH

0

500

1000

1500

2000

1995 1998 2002 2006 2010

KO KOREAN WON TO US $

0

10

20

30

1995 1998 2002 2006 2010

NCD 91 DAYS MIDDLE RATE

0

0.5

1

1.5

2

2.5

1995 1998 2002 2006 2010

US $ TO UK POUND

0

2

4

6

8

10

1995 1998 2002 2006 2010


0

0.5

1

1.5

2

1995 1998 2002 2006 2010

U.S. $ TO EURO

0

2

4

6

8

1995 1998 2001 2004 2008 2011


0

2

4

6

8

10

1995 1998 2002 2006 2010

CHINESE YUAN TO US $

02468

1012

1995 1998 2002 2006 2010

3M DEPOSIT - MIDDLE RATE




We easily analyze the figures above. As you can see, Taiwan had a significant drop

during 2000~2002 when Taiwan were going through the Dot-com bubble. Korea and

China had a big interest rate drop in 1997 when the huge financial crisis, Asian

Financial Crisis exploded. This crisis started in Thailand, raised fears of a worldwide

economic meltdown. After that, there is no obvious interest rate fluctuation in Korea.

As for china, due to government controls the interest rates after 1997 were almost the

same. The curve is very flat. Australia and U.K. both had a bigger interest rate

fluctuation during 2008~2009 because of the Global financial crisis. Euro is

constantly fluctuating, and the most obvious drop was also in 2008.The crisis resulted

in the threat of total collapse of large financial institutions, downturns in stock

markets worldwide, and changed the global financial environment a lot. Last, the

interest rate fluctuation in Japan. There is a drop around the year of 1996. Since 1990s,

Japan went into a recession often referred as The Lost Tow decade. Therefore the

government drew down interest rate to stimulate consumption in 1996. Japan had zero

interest rate during 2001~2006, it was a policy carried out by the Japan government,

which wanted to eliminate the serious deflation problems at that times. Because of the

Japan zero interest rate, many people borrowed Japan yen to gain profit from carry

trade.




3.2 Results from regression analysis

From (1) we can take the nature log on the both side, and rewrite it into:

𝑙𝑛𝐹𝑡 = 𝑙𝑛𝑆𝑡 + 𝑡𝑙𝑛(1 + 𝑟) − 𝑡𝑙𝑛(1 + 𝑟∗),

The reason why we take the nature log is just for simplicity. In this study, we do

not deal with the dynamic problems, so t can be ignore for the time being. To further

analyze the empirical data we use a multi-regression analysis. Consider the

regressions of 𝑙𝑛𝐹𝑡 on 𝑙𝑛𝑆𝑡, 𝑙𝑛(1 + 𝑟) and 𝑙𝑛(1 + 𝑟∗),

𝑙𝑛𝐹 = 𝛼𝑖 + 𝛽𝑖1𝑙𝑛𝑆 + 𝛽𝑖2𝑙𝑛(1 + 𝑟) + 𝛽𝑖3𝑙𝑛(1 + 𝑟∗),

Estimates from (4) tell us whether spot exchange rate (S), interest rate at home

(1+r) and interest rate in foreign country (1+r*) together have the power to predict

forward exchange rate of time t+1 (observed at time t). Evidences suggest that 𝛽𝑖1 is

significantly non-zero means that spot exchange has an influence on forward

exchange rate. Likewise, evidences suggest that 𝛽𝑖2 and 𝛽𝑖3 are reliably away from

zero tell us that interest rate at home and abroad have the power to predict F.

Given a rational or efficient exchange market, and the assumption that IRP holds

between the observed two countries, the regression coefficients in (4) should be:

𝛼𝑖 = 0 𝛽𝑖1 = 1 𝛽𝑖2 = 1 𝛽𝑖3 = −1,

To test the estimated coefficients, we will then use a one-Sample T Test to see

whether the empirical result is reliably different from the prediction of the Interest

(5)

(4)

(3)




Parity Theory. The T statistic from (4) and (5) will then be,

𝑇𝛼𝑖=

𝛼𝑖−0

𝑆𝐸𝛼𝑖

,

𝑇𝛽𝑖1=

𝛽𝑖1−1

𝑆𝐸𝛽𝑖1

,

𝑇𝛽𝑖2=

𝛽𝑖2−1

𝑆𝐸𝛽𝑖2

,

𝑇𝛽𝑖3=

𝛽𝑖3−(−1)

𝑆𝐸𝛽𝑖3

,

where the null hypothesis is that 𝛼𝑖 = 0, 𝛽𝑖1 = 1, 𝛽𝑖2 = 1, 𝛽𝑖3 = (−1), while the

alternative hypothesis is 𝛼𝑖 ≠ 0, 𝛽𝑖1 ≠ 1, 𝛽𝑖2 ≠ 1, 𝛽𝑖3 ≠ (−1). T and SE are the t

statistic and the standard error of estimate for the four coefficients respectively.

By (4) to (9), we can test the empirical data to see whether the reality is really

deviated from the prediction of the IRP Theory. In this way we are different from

most of the studies regarding this topic in which we test the IRP directly. If the

coefficients of the regressions really deviate from the predicted value, we can come to

the direct conclusion that the Interest Rate Parity is rejected empirically.

Table 1 summarized the results for the regression of 𝑙𝑛𝐹𝑡 on 𝑙𝑛𝑆𝑡, 𝑙𝑛(1 + 𝑟)

and 𝑙𝑛(1 + 𝑟∗). The anomalous numbers in the table are the estimated coefficients.

And the numbers in ( ) are the p value of the coefficients, which test the hypothesis of

𝐻0: 𝛼𝑖 = 0, 𝛽𝑖1 = 1, 𝛽𝑖2 = 1, 𝛽𝑖3 = (−1) ,and 𝐻1: 𝛼𝑖 ≠ 0, 𝛽𝑖1 ≠ 1, 𝛽𝑖2 ≠ 1,

𝛽𝑖3 ≠ (−1)

We test the IRP between seven countries and the U.S. These currencies are

(6)

(7)

(8)

(9)




selected because they are widely traded either around the world or among Asia-Pacific

area. The reason why we test these currencies against America is because all of the

data are denoted in U.S. dollar. So we first determined whether IRP exist between

these seven countries and America. From Table 1 we can observe that in Japan, U.K.,

and the Euro zone, we cannot reject the null hypothesis. Thus, according to our result,

we cannot reject that IRP holds between these three countries and the U.S. For the rest

of the observations, Taiwan, Australia, Korea and China, the empirical results tell us

that IRP does not exist between these countries and the U.S. Furthermore, by

observing the estimated coefficients and the respective p value, two countries, China

and Korea, deviated largely from our expectations.

After finding the fact that the results from China and Korea are highly deviated

from IRP theory, we review the original data and find out that interest rate in these

two countries are extremely high. These too countries maintain high interest rates

while most of the major economies are experiencing an era of zero interest rate. The

reasons behind might be government want to attract foreign investors. With a higher

interest rate, they might be able to attract more foreign capitals. After, observed this

phenomenon, we then came up with an idea that we can determine the countries with

the highest and the lowest interest rates, and test the interest rate parity between the

high interest rate countries and low interest rate countries. We expected the result will




Tab

le 1

OL

S r

egre

ssio

ns:

01/1

995

-03/2

014, N

=230

𝑙𝑛𝐹

⬚=

𝛼𝑖

+𝛽

𝑖1𝑙𝑛

𝑆⬚

+𝛽

𝑖2𝑙𝑛

( 1+

𝑟)+

𝛽𝑖3

𝑙𝑛( 1

+𝑟

∗)

ountr

y

T

aiw

an

Aust

rali

a Ja

pan

K

ore

a U

K

Euro

pe

Chin

a A

&JP

K

&JP

C

hin

a&JP

R

squar

e 0.9

860

0.9

995

0.9

959

0.9

203

0.9

820

0.9

895

0.9

245

0.9

976

0.9

671

0.9

392

𝛼𝑖

-0.0

160

(0.6

92

6)

0.0

036

(0.0

905)

-0.0

178

(0.4

728

)

1.5

957

(0.0

002)

0.0

022

(0.7

081

)

-0.0

028

(0.4

418)

0.2

873

(0.0

007

)

-0.0

282

(0.0

548)

-0.2

726

(0.0

000)

0.0

607

(0.3

357

)

𝛽𝑖1

1.0

032

(0.3

88

5)

0.9

971

(0.0

740)

1.0

030

(0.2

837

)

0.7

819

(0.0

001)

0.9

919

(0.2

150

)

0.9

971

(0.3

567)

0.9

107

(0.0

054

)

1.0

061

(0.0

340)

0.9

084

(0.0

000)

0.9

538

(0.0

228

)

𝛽𝑖2

0.8

625

(0.0

86

0)

0.9

572

(0.0

376)

1.0

774

(0.2

980

)

-0.2

777

(0.0

082)

0.9

304

(0.2

335

)

0.9

885

(0.4

470)

-3.6

753

(0.0

000

)

0.8

003

(0.1

034)

4.6

296

(0.0

015)

1.4

241

(0.3

021

)

𝛽𝑖3

-0

.8032

(0.0

46

1)

-1.0

632

(0.0

080)

-0.9

874

(0.6

641

)

-1.9

493

(0.0

000)

-0.8

528

(0.1

195)

-0.8

263

(0.0

706)

-0.3

230

(0.0

001

)

-1.0

143

(0.3

825)

0.3

721

(0.0

016)

1.6

985

(0.0

000

)

also largely deviate from the prediction of IRP. Since there are huge interest rate

differences between these countries, if IRP doesn’t hold, the return from the carry

trade should be large. In the next section, we will calculate the return from the carry

trade.




After we reviewed the original data, we determined that the countries with the

highest interest are China, Korea and Australia. In contrast, the country with a lowest

interest rate is Japan. As a result, we test the IRP between these three countries which

have a relatively high interest rate and the country with a very low interest rate which

is Japan. All of the exchange rate data are dominated in Japanese Yen.

The outcome was not surprise that in all of the three combinations, we find that

the Interest Rate Parity does not exist. To sum up, according to our experiment, the

Interest Rate Parity does not hold between Taiwan and the U.S., Australia and the U.S.,

Korea and the U.S., as well as China and the U.S. Moreover, IRP does not exist

between Australia and Japan, Korea and Japan, and also China and Japan.

3.3 Portfolio Returns

After proving that the Interest Rate Parity does not hold between some selected

countries, we then want to calculate the actual profit from carry trading. We pick five

combinations of countries and build five portfolios. Each portfolio contains of only

one combination of countries; in other words in one portfolio, we only speculate

between two countries. In this way, we can see between which country combinations,

the carry trade is the most profitable. Figure 2 summarized the results from each

portfolio.

A currency is having a forward premium when 𝐹𝑡 excess 𝑆𝑡. On the other hand,




a currency is said to be at a forward discount when 𝑆𝑡 excess 𝐹𝑡. The return from the

carry trade using a forward contract can then be written as:

𝑅𝑡+1 = (𝐹𝑡 − 𝑆𝑡+1),

where 𝑅𝑡+1 is the return of the carry trade form time t to time t+1. This is a comment

way to calculate the profit from the carry trade (e.g. Burnside et al. 2011).When IRP

holds, investors will gain a zero return from the carry trade.

Monthly Return Accumulated Monthly Return

-300

-200

-100

0

100

200

300

400

2002 2003 2005 2006 2008 2009 2011 2012

KOREA to U.S.

-2000

-1500

-1000

-500

0

2002 2004 2006 2008 2010 2012

KOREA to U.S.

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

2002 2003 2005 2006 2008 2009 2011 2012

CHINA to U.S.

-5

0

5

10

15

20

25

2002 2003 2005 2006 2008 2009 2011 2012

CHINA to U.S.

(9)




Figure 2. In the right column shows the returns of differ periods in each portfolio and

in the left column shows the accumulated returns.

As shown in the Figure 2, three out of five portfolios appear to be profitable. In

portfolios, China to U.S., Australia to Japan and Korea to Japan, both monthly returns

and accumulated returns are positive almost in ever period. For China to U.S., the

carry trade is profitable in most of the observed periods. However, during the period

of global financial crisis, returns become very volatile. Returns in this period of time

-15

-10

-5

0

5

10

15

1995 1997 1999 2001 2004 2006 2008 2010

AUSTRALIA to JAPAN

0

200

400

600

800

1000

1995 1997 2000 2003 2006 2008 2011

AUSTRALIA to JAPAN

-0.03

-0.02

-0.01

0

0.01

0.02

2002 2003 2005 2007 2009 2010 2012

KOREA to JAPAN

0

0.1

0.2

0.3

0.4

2002 2003 2005 2006 2008 2009 2011 2012

KOREA to JAPAN

-2

-1

0

1

2

2002 2003 2005 2006 2008 2009 2011 2012

CHINA to JAPAN

-15

-10

-5

0

5

2002 2003 2005 2006 2008 2009 2011 2012

CHINA to JAPAN




drop from a historical high level to the lowest point among the periods. But after the

financial crisis the returns bounced back to a positive level again. The accumulated

return of the portfolio China to U.S. is overall positive, despite a slight deduction

between 2008 and 2009. Moreover, the carry trade profit in recent years drop to a

negative level as well.

In respect of the portfolio Australia to Japan, the returns had been volatile.

Nevertheless, according to its accumulated return graph, the carry trade is overall

profitable throughout the covered periods. There is also a sudden drop in returns

around the year of 2008. But this does not affect the profitability of this portfolio over

long investment period.

For the portfolio Korea to Japan, investors can also own an access return. As in

the above two portfolios, there is again a significant drop of return during the global

financial recession. There is also a bounce back of returns after the financial crisis,

and remain at a profitable level. In these three portfolios, China to U.S., Australia to

Japan and Korea to Japan, the results coincide with our expectation. Investors can

earn profits through these portfolios.

For the other two portfolios, Korea to U.S. and China to Japan, the result is

however surprising. Even though IRP does not hold in these countries, we cannot gain

positive returns from carry trading. In respect of the portfolio Korea to U.S., monthly




returns are negative in most of the covering periods. However, there is a reversal

during the period of financial crisis, the returns during that particular period is

extremely high. Nevertheless after that period, returns first experienced a tremendous

fall and remain at a negative level thereafter.

For the portfolio, China to Japan, the profitability is somehow ambiguous before

the year of 2008. But after the global recession, the accumulated return becomes

negative for a long period until around 2012. However, in more recent periods, the

returns become positive again.

To sum up, investors can earn a positive return in three of our portfolios, because

IRP does not hold in these country combinations. Moreover, we observe that there is a

relationship between abnormal carry trade returns and the financial crisis. The reasons

behind is to be further study.

4. Conclusions

In this study, we test the IRP theory in a direct way. We used empirical data and

multi-regression analysis to test the IRP equation. In four of our seven selected

countries, Taiwan, Australia, Korea and China, IRP is rejected against the U.S. In

contrast, according to the result form regression analysis, IRP do exist between the

other countries and the U.S. These countries are Japan, the U.K. and the Euro zone.

We also selected other countries combinations and test whether IRP exist between




them. As a result, we also found that IRP does not hold in Australia, Korea and China

against Japan.

After testing the IRP theory between different countries, we construct five

portfolios by comparing gaps on interest rate between countries. We then find that

three of them are profitable. China to U.S., Australia to Japan and Korea to Japan, are

overall profitable during the covered period. As for the portfolio Korea to U.S., the

accumulated returns during the observed period are negative; also monthly returns are

negative in most of the months. The result from the portfolio China to Japan is

however ambiguous. In some times investors could earn profits; however in other

times they would suffer losses. What we also observed is that there is a relationship

between financial crisis and abnormal portfolio returns. The returns during the period

around 2008 become extremely volatile in all of the five portfolios. Nevertheless, the

reasons behind need further study.




Literature Cited

Anonymous. 2013. “Carry on trading” The Economist, Vol.408(8848), p.63(US).

Bilson JFO. 1981. “The ‘Speculative Efficiency’ hypothesis.” J. Bus. 54(3):435—51.

Eugene F. FAMA. 1984. “Forward and Spot Exchange Rates” Monetary Economics,

14 , p.319-338(North-Holland).

Craig Burnside, Martin S. Eichenbaum, and Sergio Rebelo. 2011. “Carry Trade and

Momentum in Currency Markets” NBER Working Paper 16942

Fama EF, French KR. 1993. “Common risk factors in the returns on stocks and bonds.”

J. Financ. Econ. 33(1):3—56.

Brunnermeier MK, Nagel S, Pedersen LH. 2009. “Carry trades and currency crashes.”

NBER Macroecon. Ann. 23:313—47.

Farhi E, Fraiberger SP, Gabaix X, Ranciere R, Verdelhan A. 2009. “Crash risk in

currency markets.” NBER Working Paper 15062.

Lustig H, Roussanov N, Verdelhan A. 2009. “Common risk factors in currency

markets.” SSRN Paper 1139447.

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