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A Resolution on UIP Puzzle:
The Case of Korean won/The United States dollar
Joon-hwan Im
Graduate School of International Studies, Sogang University
Dae-hyun Chung
Graduate Student of GSIS, Sogang University
ABSTRACT
This paper draws on an empirical model of Chaboud and Wright (2003)
to address the Uncovered Interest Rate Parity (UIP) puzzle, employing a high
frequency exchange rate dataset of the U.S. dollar versus the Korean won
during the period from 2000 to 2002.This paper develops methods of a shortterm time window spanning discrete timing of interest payment in order to
concentrates on abating risk premium.. There are two major empirical
results; firstly quarterly periods and over short windows of high frequency
data enhance supporting UIP hypothesis, although the yearly window data
are not enough to support it. Secondly, the regression test designed for prefixed interest differential has a more positive slope than the one for non-prefixed interest differential, indicating the former is more supportive than the
latter. The implication of the results is that as the time window spanning
discrete timing of interest payment becomes shrunk, the test results tend to
support UIP hypothesis, because the holing period of uncovered position is
diminished.
1. Introduction
This paper addresses the Uncovered Interest Rate Parity (UIP) puzzle,
employing a high frequency exchange rate dataset of the U.S. dollar versus
the Korean won during the period from 2000 to 2002.This paper develops
methods of a short-term time window spanning discrete timing of interest
payment in order to concentrates on abating risk premium. There are two
major empirical results; firstly quarterly periods and over short windows of
high frequency data enhance supporting UIP hypothesis, although the yearly
window data are not enough to support it. Secondly, the regression test
designed for pre-fixed interest differential has a more positive slope than the
one for non-pre-fixed interest differential, indicating the former is more
supportive than the latter. The implication of the results is that as the time
window spanning discrete timing of interest payment becomes shrunk, the test
results tend to support UIP hypothesis, because the holding period of
uncovered position is diminished.
The UIP hypothesis states that the difference between domestic and
foreign interest rates should be a feasible predictor of future changes in
exchange rates. Unfortunately, this assumption has been and is generally
rejected by much empirical research, for example, Hodrick (1980), Fama
(1984), Hodrick (1989), Frankel and Froot (1989), and Froot and Thaler
(1990). So, this empirical failure of UIP has been a puzzle to economists
working in international finance.
Fama interpreted that this empirical failure is attributable to the
evidence of risk premium. According to him, the usual domestic-foreign
interest difference can be divided into the expected future change in the
exchange rate and a non-zero risk premium with the two terms being
negatively correlated. Frankel and Foot attribute this bias to a systematic
forecast error stating that this systematic forecast error leads to a violation of
the rational expectations hypothesis.
McCallum (1994) argued that monetary-policy behavior could be
responsible for the apparent empirical failure of the UIP hypothesis. He
investigated whether optimizing policy behavior can account for the
observed regime-dependence of UIP evidence. The main result is the
tradeoff between interest-rate and exchange-rate stability is a potential
candidate for the explanation of the apparent failure of UIP. And Peter Anker
(1999) further investigated whether a model with monetary-policy reactions
along the lines in McCallum accounts for this observed regime-dependence
of UIP evidence. According to his argument the failure of UIP can be
rationalized as a consequence of systematic monetary-policy reactions in
order to smooth interest rates. And Froot and Thaler added the explanations
on empirical failure of UIP such as the “peso problem.”1
Lyons and Rose (1995) found that currencies which were under
speculative attack actually appreciated intraday. Their interpretation of this
finding is that investors must be compensated for the risk of devaluation.
Especially overnight, they can be compensated by an interest differential.
However, intraday there are no interest differentials. Thus Chaboud and
Wright (2003) developed the idea of the compensation from an interest
differential that Lyons and Rose seriously considered. Rather than looking at
high frequency exchange rate movement over an intraday period when no
1
More generally, peso problems can arise when the possibility that some infrequent or
unprecedented event may occur affects asset prices. Peso problems may occur when the
economy faces this sort of instability. In this environment, using historical data to
predict the future is difficult because the future may be much different from the recent
past
interest rate is paid, they focus on the overnight period when interest accrues.
In addition, they add the settlement lag which the vast majority of UIP
literature ignores. Although Bekaert and Hodrick (1993) had already
considered a settlement lag, they did not find settlement lag as a significant
factor in the failure of UIP in their paper. However, according to Chaboud
and Wright considering a settlement lag seems to give a little more favorable
result toward the UIP hypothesis.
This paper is designed to contribute to address the UIP puzzle, alone
the lines of discrete interest payment that Chaboud and Wright consider in
their paper. Discrete interest payment is a very important factor in reducing
the failure of UIP. The violation of UIP is determined by many different
factors which have already been pinpointed by previous studies of UIP. Thus,
this paper does not comprehensively deal with all the causes of UIP failure.
Instead, it focuses on factors to reduce risk premium which is an essential
element in the violation of UIP.
A key assumption in the paper is that if test schemes reduce risk
premium, it can enhance the UIP hypothesis. In addition risk premium is
assumed to be reduced as the holding period of the securities diminishes.
The plan for the remainder of this paper is as follows. Section 2 lays out the
implications of UIP. Section 3 contains interpretations of discrete interest
payments. Section 4 includes empirical plan considering time difference
between Korean and the U.S., prefixed/non-prefixed Interest differential,
and value date of trades. In Section 5 empirical results are presented. Section
6 contains the conclusions.
2. The Implication of UIP Hypothesis
The Uncovered Interest rate Parity (UIP) hypothesis has similar
implications as the Covered Interest rate Parity (CIP). If UIP is true for the
foreign exchange market, an investor will have the same return regardless of
whether an investor invests in Korea or the United States, thus no arbitrage
occurs even though he is shifting markets. But some assumptions are
required to meet the needs for UIP application. First, the market should be
an “efficient capital market” where the current price of a security fully
reflects all the information currently available about that security including
risk. An “efficient capital” market is one in which security prices adjust
rapidly to new information. Second, an investor is assumed to be risk neutral.
If these two assumptions are satisfied, investors can predict the expected 1year future exchange rate, Es(t+1), exploiting the UIP equation,
Es(t+1) = S(t) (1 + i)/(1 + i*)
(1)
S(t) is the spot exchange rate, and i and i* is the annualized Korean interest
rate and the U.S. interest rate respectively. A numerical example will clarify
the meaning of UIP. Suppose that S(t) is KRW 1200/USD; i is 2.5%; and i*
is 1.0%. If UIP holds in the market, an investor can calculate that Es(t+1) is
KRW1217/USD).
The interpretation of this hypothetical example is that if the Korean
interest rate is higher than the United States’ interest rate, the won currency
will appreciate rapidly due to capital inflow from the U.S. to Korea, the
current value of the Korean won adjusts to this new information rapidly
according to the “efficient capital market” hypothesis. In addition, if an
investor is rational or risk neutral, he will not expect the Korean won to
continue to appreciate; instead, he expects the Korean won to depreciate in
the future. As a consequence, the expected future exchange rate, Es(t)
becomes higher than the spot exchange rate, S(t). Therefore, both the
differential between Es(t+1) and S(t), and the differential between i and i*
have a positive correlation coefficient. On the other hand, if an investor is
not risk neutral but a risk taker, the equation will not have a positive
coefficient because the value of Es(t+1) is lower than that of S(t).
3. Discrete Timing of Interest Payments
Because interest rates are discretely quoted, no interest payments are
made during intraday trading. Interest payments are made near the end of the
business day at what is known as the cutoff time. If a position is open at the
cutoff time then discrete interest is paid. Thus, opening a position right
before the payment of interest may provide a good opportunity to investors
for gaining interest. This cutoff time in New York is 17:00 and is the end of
business for off-line banks. The value date of currency trades on day t in the
foreign exchange market is performed on day t+2, which is the conventional
settlement2 period in both Korea and the United States. On holidays, the
foreign exchange market is closed.
Empirical tests in this paper are conducted on the basis of a selffinancing strategy. An investor shorts the Korea won on day t at time h1,
investing the proceeds in a dollar currency account. And then the investor
buys Korean won on the next day (t+1) at time h2, unwinding the position.
Through these trades, the investor will receive the interest differential
prevailing between the day of settlement for day t trades and the day of
settlement for day t+1 trades and interest rates differential is assumed to be
2
Parties to a trade are free to fix settlement at any time they both agree to, but the two
business day settlement lag is a very strong convention. Some countries such as Canada
use a t+1 settlement.
known by the investor on day t.
s(t, h) denotes the spot exchange rate (Korean currency won per
dollar) on day t at time h. Let i and i* represent the Korean (call rate) and
US overnight interest rate (Federal fund rate), respectively. Let the ex-ante
expected return on this transaction be defined to be equal to risk-premium,
RP (t, h1; t + 1, h2). By definition, in the equation
{s(t+1, h2) - s(t, h1)}/ s(t, h1) - (i t - it*)/(1+ it*) = RP(t, h1; t+1, h2) + ut
(2)
the error term must be uncorrelated to the interest differential set on day t at
time h1 which is an independent variable. In the null hypothesis for UIP
tests,
{s(t + 1, h2) - s(t, h1)}/ s(t, h1) = α + β(i t - it*)/(1+ it*) + RP(t, h1; t + 1, h2) + ut
(3)
the intercept coefficient α is zero, and the slope coefficient β is unity. And
The UIP equation assumes that the risk premium will become zero if the exante expected return on the carry trade3 is zero. By this assumption,
3
A carry trade in which an investor borrows in the currency with the low interest rate
and invests in the currency with a high interest rate is profitable on average .
{s(t + 1, h2) - s(t, h1)}/ s(t, h1) = α + β(i t - it*)/(1+ it*) + ut
(4)
the intercept and slope coefficients should be zero and one, respectively. The
hypothesis that the slope coefficient in the UIP regression is unity has been
tested by many researchers, but decisively rejected over many different
horizons. The common interpretation of the results is that risk premium
exists. That is specifically a time varying risk that correlates with the interest
differential. In this paper, high frequency intraday data is exploited. Let λ
denote the time elapsed between time h1 on day t and time h2 on day t+1.
The assumption about the risk premium is that it will be smaller as the time
window of investing a currency is contracted. Specifically, the risk premium
is expressed in the equation,
lim λ→0 RP(t, h1; t + 1, h2) = 0
(5)
Nevertheless, no matter how little time elapses between time h1 on day t and
time h2 on day t + 1, the carry trade includes a fixed interest differential.
This discrete interest payment performs a similar role as that of the
ex-dividend date in the stock market. An ex-dividend date is the cut-off date
for receiving stock dividends. The ex-dividend date is two business days
before the date of record4. The assumptions for UIP equation in this paper
will be α = 0 and β = 1 if time h1 is sufficiently late on day t, and time h2 is
sufficiently early the next day. It is obvious that an investor is less exposed
to a time-varying risk when time window of uncovered position is
diminished.
Ignoring transactions costs, under the condition in equation (5), the
strategy of shorting the lower-interest rate currency at very late on day t and
then buying the higher-interest rate at the start of day t+1 is not likely to be
profitable because transactions costs exist in the market. The presence of
transaction costs might well hinder investors from accepting the UIP
hypothesis on a short time window around discrete timing of the interest
payment; but, for an investor who deposits a significant amount of proceeds
in a currency account, the transaction costs will not be a serous obstacle if
the predicted profits from capital gain or interest gain overwhelm the
transaction costs.
4. Empirical Plans
Our spot exchange rate data is composed of the exchange rate of
4
On date of record, the shareholders of record are designated; thus, stock price
increases right before ex-dividend date and the price falls on or right after the exdividend.
Korean won relative to the U.S. dollar provided by Olsen and Associates,
covering the entire calendar years from 2000 to 2002. In order to design
these data, Olsen and Associates record all Reuter’s quotes, average the bid
and ask. we discard weekend data because there is virtually no foreign
exchange trading during this time. All quotes in the tests in this paper are
based on Reuters indicative quotes, not transaction prices. Danielsson and
Payne (2002) compared Reuters indicative quotes with transactions prices,
and they found that the five-minute returns on the two series are very highly
correlated.
Korea and the U.S. spot overnight interest rates are acquired from the
Bank of Korea and Federal Reserve in the United States. These are
annualized rates. So to create a day interest rate, the annualized interest rates
are divided by 365. For single-day interest differential tests, a day interest
rates prevailing in both countries are exploited. And for multi-day interest
differential test, a day interest rates are multiplied by n, multi-day.
New York times 16:00 and 20:00 were selected as trade days
respectively to construct the smallest possible time window around 17:00
New York time. Even though an investor shorts Won currency in Seoul at
16:00 on day t, he cannot trade Korean Won at Seoul time 20:00, because at
this time New York time is 06:00 when Both Seoul and New York markets
are closed. Seoul time is 14 hours ahead of New York time. Seoul time is 9
hours ahead of Greenwich Mean Time (GMT). New York time is 5 hours
behind GMT. Therefore, to create the single interest differential over a 4hour holding period, the first trade must be commenced in New York. (New
York time16:00, a day t trade should occur in New York) and then at New
York time 20:00, the second trade should shift to the Seoul market whose
time is 10:00 at day t+1 when market is open. Consequently, transactions on
a four-hour time window create a day of interest from transactions between
day t and day t+1 according to GMT. Refer to Table 1.
Although an investor’s position remains uncovered to time-varying
risk, if he takes advantage of time difference between countries, he can take
discrete interest differential gain faster than other people who do not
consider time discrepancies between countries. As a consequence, the
position is far less vulnerable to time-varying risk, because he can
significantly curtail his uncovered position. However, to draw up this
discrete interest payment in a short overnight period, the Won currency
account is assumed to be opened in New York market But in reality, an
investor does not open a Korean won currency account in New York
because Korean foreign exchange law bans won currency to circulate
outside Korea so that the won may not be used for speculative or criminal
purposes
In this paper, the interest differential in the settlement system for
foreign currency trade is measured two ways. One is the prefixed interest
rate differential prevailing between day t and day t+1 trades. The other
method is performed for an investor who does not recognize the UIP
equation. A spot loan rates are not entered into on day t.
4.1. UIP tests for prefixing the interest differential between Korea and
the U.S.
A spot loan contract rates are entered into on day t of the trade. But
the spot loan rates are applied in two business days after the currency trade
on day t. The investor can fix the interest rate in advance on day t to apply
them between day t and day t+1 trades. As a result, on t day, the investor
acquires three variables, the Korean and the U.S. interest rate, and the spot
exchange rate among all the four variables for conducting the UIP test. Thus
he can predict the future expected exchange rate Es(t+1), if the UIP
hypothesis is true for the markets of his investment. By this assumption, the
equation
{Es(t + 1, h2) - s(t, h1)} / s(t, h1) = α + β (it – i*t ) / (1 + i*t) + ut
(6)
is an ex-ante return for the pre-fixed interest rate differential on day t with
the difference between Es(t+1, h2) and S(t, h1).
4.1.1. Actual time data scheme of UIP regression model for pre-fixing
a day interest differential on the smallest window
At New York time 16:00 on day t, an investor shorts the Korean won.
And unwinding the position the next day, he repurchases Korean won in the
Korean market at Seoul time 10:00 on day t+1 (New York time is 20:00 at
day t). And on the day t+2 he borrows Korean won which is already
contracted on day t, so he have to be in charged of borrowing Won currency
for a day. Simultaneously the investor who shorts the Korean won on day t
deposits the proceeds (US dollars) in a US currency account on day t+2, so
he is supposed to gain a day US interest And on day t +3, the value date of a
day t+1 trade, the investor will deliver the borrowed won principal and
accrued interest. Refer to the chart presented in Figure 1 explaining the
equation below:
{Es(t , 20:00) - s(t, 16:00} / s(t, 16:00) = α + β (it – i*t ) / (1 + i*t) + ut
(7)
4.1.2. Actual time data scheme of UIP regression for pre-fixing for
single day interest differential from time 16:00 on day t to 16:00 on
day t+1 in New York.
At New York time 16:00 on day t, an investor shorts the Korean won.
And unwinding the position the next day, he repurchases Korean won in the
same New York market at 16:00 on day t +1 without shifting the market to
the Korean market. And on the day t+2 he borrows Korean won, and have to
be in charged of a day of borrowing cost of Korean won. Simultaneously,
the investor who shorts the Korean won deposits the proceeds (US dollars)
in a US currency account on the same day. And on day t+3, the value date
of a day t+1 trade, the investor delivers the borrowed won principal and
accrued interest. Refer to the chart presented in Figure 2 explaining the
equation below:
{Es(t + 1, 16:00) - s(t, 16:00)} / s(t, 16:00 ) = α + β (it – i*t ) / (1 + i*t) + ut
(8)
4.1.3. Actual time data scheme of UIP regression for pre-fixing multiday interest differential from New York time 16:00 on day t to 20:00
on day t+n in New York.
Let n denote multi-days of position remaining on currency investment.
And the procedure is the same as the one in section 3. The only difference is
that the investor unwinds the position at the day t + n, so the value date of
t+n transaction is t+n+2. Refer to the chart presented in Figure 3 explaining
the equation below:
{Es(t + n, 20:00) - s(t, h)} / s(t, 16:00) = α + β n (it – i*t ) / (1 + n t*) + ut
(9)
4.2. UIP tests for non-prefixing the interest differential between Korea and
the U.S.
The investor does not prefix the interest rates on transaction day t
when the investor shorts the Korean currency. He just uses the interest rate
differential that is to be applied between the value dates for day t and day
t+1 trades. Actually, the latter test is performed on the condition of not
exploiting the UIP equation. This measure is also meaningful, because in
reality the latter transactions are more likely to occur than transactions
considering the UIP hypothesis. The equation is
{Es(t + 1, h) - s(t, h)} / s(t, h) = α + β (i t+2 – i*t+2 ) / (1 + i* t+2) + u t+2
(10)
4.2.1. Actual time data scheme of UIP regression for non-pre-fixed
interest rate differential on the smallest window
The test is the same procedure as in section 4.1.1 except that both
countries’ interest rates are not agreed to be fixed on day t. Refer to the chart
presented in Figure 4 explaining the equation below:
{Es(t, 20:00) - s(t, 16:00} / s(t, 16:00) = α + β (i t+2 – i* t+2 ) / (1 + i* t+2) + u t+2
(11)
4.2.2. Actual time data scheme of UIP regression for non-pre-fixing
single day interest differential from time 16:00 on day t to 16:00 on
day t+1 in New York
All of the transactions equally follow that in the procedure in section
4.1.2 except that interest rates are not predetermined on day t. Refer to the
chart presented in Figure 5 explaining the equation below:
{Es(t + 1, 16:00) - s(t, 16:00} / s(t, 16:00) = α + β (i t+2 – i* t+2 ) / (1 + i* t+2) + u t+2 (12)
4.2.3. Actual time data scheme of UIP regression for pre-fixing multiday interest differential from New York time 16:00 on day t to 20:00
on day t + n in New York.
The procedure of the test is in the same sequence as that of section
4.1.3. The only difference is that the investor uses interest rates on day t+2
in the New York market. Refer to the chart presented in Figure 6 explaining
the equation below:
{Es(t + n, 20:00) - s(t, 16:00} / s(t, 16:00) = α + β n (i t+2 – i* t+2 ) / (1 + n i* t+2) + ut+2(13)
5. Empirical Results
Test results are divided by the length of the period. The longest period
test is the period from 2000 to 2002. And then the next longest tests are
followed by a yearly and quarterly periods. And in 2000 to 2002, yearly
periods testing the UIP hypothesis are completely rejected. Estimated slope
coefficients are significantly different from unity and the absolute value of tstatistics is much larger than 2. But in quarterly period tests, the UIP
hypothesis is not completely rejected, especially, in the smallest window
(New York time 16:00 to 20:00 of the same day) five tests and six tests
among the 12 tests show that the estimated slope coefficient is not
significantly different from unity regardless of fixing or non-fixing a day
interest differential in regression tests. As the time window spanning
discrete timing of interest payment becomes shrunk, test results are
decisively favorable toward UIP hypothesis.
The test results denote that although every quarterly period’s tests are
not consecutively favorable toward the UIP hypothesis, the tests do not
reject UIP hypothesis during three year; five or six quarter periods which is
one and a quarter year, or one and half year respectively during three years
tests are favorable toward UIP hypothesis. And tests for prefixing have more
positive slopes than those for non-fixing a day interest differential on
beginning day of a trade, t.
5.1. UIP regression test results for pre-fixing the interest differential
between Korea and United States
5.1.1. UIP regression test on the overnight intraday time window
The results of regression tests on a day interest during time from
16:00, t to 20:00, t are far more favorable toward UIP hypothesis than
results during time from 16:00, t to 16:00, t+1 and during time from 16:00, t
to 20:00, t + n . The tests from year 2000 to 2002 show that the coefficient β
is -0.0063. And in testing by year, t-statistics reject the null hypothesis.
However, pleasant results for boosting the UIP hypothesis are presented in
quarterly period tests. The outcomes from quarterly period tests do not
wholly reject the UIP hypothesis: absolute values for five t-statistics in 12
quarterly period tests are less than 2. Particularly, the test for the first quarter
of 2002 in which period the estimated coefficient value β is 1.0956 and tstatistic is 0.1056 shows the most favorable results for the UIP hypothesis.
Refer to Table 2 presenting the results of estimated slope coefficients and tstatistics.
5.1.2. UIP regression test results on the single day time window
The results during time from 16:00, t to 16:00, t+1 utterly reject the
UIP hypothesis. The test for year 2000 to 2002 regression shows that the
coefficient β is -0.0464. And in yearly tests all the coefficients, βs are less
than –0.11; in addition, the absolute value of t-statistics is much greater than
2. Quarterly test results also reject the UIP hypothesis. However, the
absolute values of t-statistics in quarterly period tests are smaller when
compared with that of t-statistics in 2000 to 2002 and the yearly period tests,
especially from the fourth quarter of 2000 to the third quarter of 2001. Refer
to Table 3 presenting the results of estimated slope coefficients and tstatistics.
5.1.3. UIP regression test results on the multi-day time window
The results from testing on multi-day interest differential data also
reject the UIP hypothesis. The tests from year 2000 to 2002 show that the
coefficient β is -0.0416. And in yearly tests, the estimate slope coefficients
βs are less than –0.12; in addition, the absolute value of t-statistics is much
greater than 2. Quarterly test outcomes completely reject the UIP
hypothesis; however, the absolute values of t-statistics in quarterly period
tests are also smaller when compared with that of t-statistics in 2000 to 2002
and yearly period tests, especially from the fourth quarter of 2000 to the
third quarter of 2001. Refer to Table 4 presenting the results of estimated
slope coefficients and t-statistics.
5.2. UIP regression test results for non-prefixing the interest
differential between Korea and United States
5.2.1. UIP regression test results on the overnight intraday time
window
The results from quarterly period tests on the overnight intraday time
window (New York time, 16:00 ~ 20:00) are a little more favorable toward
the UIP hypothesis than that of the pre-fixed interest differential regressions
for overnight intraday tests show. But the tests from year 2000 to 2002 show
that the coefficient β is -0.0063, which differs from unity. And in yearly
period tests, the absolute value of t-statistics is much greater than 2. Refer to
the Table 5 presenting the results of estimated slope coefficients and tstatistics.
5.2.2. UIP regression test results on the single day time window
The results from tests on daily interest data reject the UIP hypothesis.
The tests from year 2000 to 2002 show that the coefficient β is -0.0489. And
in testing by year, all the coefficients βs, differ from unity; in addition, the
absolute value of t-statistics in yearly period tests are much greater than 2.
Quarterly test results also reject the UIP hypothesis except for the first
quarter of 2001 in which period the estimated coefficient value β is 0.5298
and t-statistic is -0.9551. That result does not reject the UIP hypothesis.
Refer to Table 6 presenting the results of estimated slope coefficients and tstatistics.
5.2.3. UIP regression test results on the multi-day time window
The results from testing on multi-day differential data of time from
16:00 to 20:00 reject the UIP hypothesis. And the tests from year 2000 to
2002 show that coefficient β is -0.0461. And in testing yearly period data all
the coefficients βs are different from unity and the absolute values of t-
statistics is much greater than 2. Quarterly test results also reject the UIP
hypothesis except for the first quarter of 2001, in which period the estimated
coefficient, a β is 0.4966 and t-statistic is -1.0568, which is favorable toward
the UIP hypothesis. Refer to Table 7 presenting the results of estimated
slope coefficients and t-statistics.
5.3. Implications of Empirical Results
Outstanding results can be seen in the quarterly test results. The
earlier h2 or the late h1 is in the day, the closer the coefficient estimate is to
one. In this short window position, currencies move in the direction
predicted by UIP, but as the time gap between h1 and h2 around the discrete
interest payment time is widened, currencies move in an unpredictable way.
Although the UIP tests in this paper predict the exchange rate
movement on over high frequency hourly interval data to overcome the
violation of UIP, they face limitations: first, the exchange rate movements
often go the wrong way if test’s period is more than a quarterly period and
the time window is exposed to more than 4 hour time-varying risk. Second,
uncovered exchange rates easily become noisy because it become vulnerable
to risk premium resulting from the protracting the time window.
6. Conclusion
UIP is very significant for creating theoretical models for determining
foreign exchange rates, but so far many researchers have experienced the
enormous empirical failure of UIP. Thus to address the UIP puzzle, this
paper experiments with UIP tests concentrating on abating risk premium
which is a decisive factor in the violation of the UIP hypothesis.
This paper draws on an empirical model of Chaboud and Wright (2003)
to address the Uncovered Interest Rate Parity (UIP) puzzle, employing a high
frequency exchange rate dataset of the U.S. dollar versus the Korean won
during the period from 2000 to 2002.Tthis paper develops methods of a shortterm time window spanning discrete timing of interest payment in order to
concentrates on abating risk premium.. There are two major empirical
results; firstly quarterly periods and over short windows of high frequency
data enhance supporting UIP hypothesis, although the yearly window data
are not enough to support it. Secondly, the regression test designed for prefixed interest differential has a more positive slope than the one for non-prefixed interest differential, indicating the former is more supportive than the
latter. The implication of the results is that as the time window spanning
discrete timing of interest payment becomes shrunk, the test results tend to
support UIP hypothesis, because the holing period of uncovered position is
diminished
REFERENCES
Chaboud, A P. and Wright J.H. (2003): Uncovered Interest Parity: It works,
but not for Long, Board of Governors of the Federal Reserve System in its
series International Finance Discussion Paper
http://www.federalreserve.gov/pubs/ifp/2003/752/ifdp752.ddf
Baillie, R. T. and T. Bollerslev (2000): The Forward Premium Anomaly is
Not as Bad as You Think, Journal of International Money and Finance, 19,
pp.471-488.
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FIGUREES
Seoul time
New York
time
t+1, 06:00
t, 16:00
Short
selling
KRW
in New
York
market
Korean
won
currency
account
U.S. dollar
currency
account
Value date
of a day
t+1 trade,
t+3
t+1, 10:00
t, 20:00
Buying KRW
in Seoul
market
(unwinding
position)
Value date of
a day t trade,
t+2
Settlement of
Short Selling
KRW
Settlement
of Buying
KRW(and
delivering
KRW to a
lender)
A day interest
cost
from
borrowing
KWR
accrues.
( t it+1 )
A day interest
gain
from
deposing
USD accrues.
(t i*t+1 )
Figure 1: Actual time data scheme of UIP regression model for pre-fixed
interest rate differential on the smallest window
* Note: ( t it+1 ) indicates that interest rate during period from day t to day
t+1.
Seoul time
t+1,06:00
t+2, 06:00
t, 16:00
t +1, 16:00
Short selling
KRW
in New
York market
Buying KRW
in New York
market
(Unwinding
the position)
New York
time
Korean
won
currency
account
U.S. dollar
currency
account
t+3
t+ 4
Value
date of a Value date
day
t of a day t+1
trade, t +2 trade, t +3
Settlement
of Short
Selling
KRW
Settlement
of Buying
KRW(and
delivering
KRW to a
lender)
A day
interest
cost from
borrowing
KWR
accrues.
( t it+1)
A day
interest
gain
from
deposing
USD
accrues.
(t i*t+1 )
Figure 2: Actual time data scheme of UIP regression for pre-fixed single day
interest differential from time 16:00 on day t to 16:00 on day t+1
in New York
* Note: Transactions are conducted without shifting market.
Value date
of a day
t+n+1
Seoul time
New York
time
t+1, 06:00
t, 16:00
Short
selling
KRW
in New
York
market
trade
t+n+3
t+n+1,10:00
t + n, 20:00
Buying KRW
in Seoul
market
(Unwinding
the position)
Korean
won
currency
account
U.S. dollar
currency
account
Value date of
a day t trade,
t+2
Settlement of
Short Selling
KRW
Settlement
of Buying
KRW(and
delivering
KRW to a
lender)
A n+1 day
interest cost
from
borrowing
KWR
accrues.
(t i t+n+1 )
A n+1 day
interest gain
from
deposing
USD
accrues.
(t i*tt+n+1 )
Figure 3: Actual time data scheme of UIP regression for pre-fixed multi-day
interest differential from New York time 16:00 on day t to 20:00
on multi-days in New York
* Note: Multi-day, n for the test is 1.72 days. The reason that multi-day is not
integer is that data constructed for the tests is not regular period data.
Seoul time
New York
time
t+1, 06:00
t, 16:00
Short
selling
KRW
in New
York
market
Korean
won
currency
account
U.S. dollar
currency
account
Value date
of a day
t+1 trade,
t+3
t+1, 10:00
t, 20:00
Buying KRW
in Seoul
market
(Unwinding
the position)
Value date of
a day t
trade, t + 2
Settlement of
Short Selling
KRW
Settlement
of Buying
KRW(and
delivering
KRW to a
lender)
A day
interest cost
from
borrowing
KWR
accrues.
( t+2 i t+3 )
A day
interest gain
from
deposing
USD
accrues.
(t+2 i* T+3 )
Figure 4: Actual time data scheme of UIP regression model for non-prefixed interest rate differential on the smallest window.
Seoul time
New York
time
t+1,06:00
t+2, 06:00
t, 16:00
t +1, 16:00
Short selling
KRW
in New
York market
Buying KRW
in the New
York market
(Unwinding
the position)
Korean
won
currency
account
U.S. dollar
currency
account
Value date Value date
of a day of a day
t trade ,
t+1 trade,
t+2
t+3
Settlement
of Short
Selling
KRW
Settlement
of Buying
KRW(and
delivering
KRW to a
lender)
A day
interest cost
from
borrowing
KWR
accrues.
( t+2 i t+3 )
A day
interest gain
from
deposing
USD
accrues.
(t+2 i* t+3 )
Figure 5: Actual time data scheme of UIP regression for non-pre-fixed
single day interest differential from time 16:00 on day t to 16:00
on day t+1 in New York
* Note: Transactions are conducted without shifting market.
Seoul time
New York
time
t+1, 6:00
t, 16:00
Short
selling
KRW
in New
York
market
Korean
won
currency
account
U.S. dollar
currency
account
Value date
of a day
t+n+1
trade
t+n+3
t+n+1,10:00
t + n, 20:00
Buying KRW
in Seoul
market
(Unwinding
the position)
Value date of
a day t trade,
t+2
Settlement of
Short Selling
KRW
Settlement
of Buying
KRW(and
delivering
KRW to a
lender)
A n+1 day
interest cost
from
borrowing
KWR
accrues.
(t+2 i t+n+3 )
A n+1day
interest gain
from
deposing
USD
accrues.
(t+2 i* t+n+3 )
Figure 6: Actual time data scheme of UIP regression for pre-fixed multi-day
interest differential from New York time 16:00 on day t to 20:00 on multidays in New York
TABLES
Table 1: Time Difference between New York and Seoul to construct a 4hour time window
Seoul time 16:00, t ~ 20:00, t
(Market shifting is impossible)
New York time
16:00, t ~ 20:00, t
(Market shifting is
possible)
New York time
t. 02:00
t. 06:00
t. 16:00
t. 20:00
New York market
Greenwich Mean
Time (GMT)
Seoul time
Seoul market
closed
closed
open
Closed
t, 07:00
t, 11:00
t, 21:00
t+1, 01:00
t, 16:00
open
t, 20:00
closed
t+1, 06:00
closed
t+1, 10:00
Open
Table 2: UIP regression test results for pre-fixed interest differential on
overnight intraday data
Period
2000~2002
New York time,16:00,t~20:00,t;
overnight single day interest
differential
Slope
t-statistics
0.0063
-68.3598
1/1/2000~12/31/2000
1/1/2001~12/31/2001
1/1/2002~12/31/2002
0.1448
-0.0269
-0.0646
-9.2244
-18.0210
-6.3806
The first quarter of 2000
The second quarter of 2000
The third quarter of 2000
The fourth quarter of 2000
0.2420
0.0528
0.0670
0.5353
-1.5713
-6.5978
-3.2849
-1.3511
The first quarter of 2001
The second quarter of 2001
The third quarter of 2001
The fourth quarter of 2001
-0.2222
-0.4095
-0.0227
-0.2549
-2.5176
-2.0376
-11.6391
-4.5563
The first quarter of 2002
The second quarter of 2002
The third quarter of 2002
The fourth quarter of 2002
0.5433
1.0956
0.8391
-0.2773
-0.3965
0.1056
-0.1054
-5.3954
Note: T-statistic is used for testing UIP hypothesis that the true value slope,
β is equal to one, the hypothesis value. [t-statistics = (estimated value-true
value under null hypothesis) / standard error for the parameter being tested].
Thus the UIP hypothesis will be rejected if estimated value is too far from
the true value, that is, if the absolute value of the t-statistic is greater than
2.0. And if the absolute value of t-statistic is less than 2.
Table 3: UIP regression test results for pre-fixed interest differential on daily
data
Period
2000~2002
New York Time, 16:00,t ~ 16:00,
t+1;
single day interest
differential
Slope
t-statistics
-0.0464
48.5846
1/1/2000~12/31/2000
1/1/2001~12/31/2001
1/1/2002~12/31/2002
-0.1009
-0.0335
-0.0003
-14.8144
-17.9552
-153.1199
The first quarter of 2000
The second quarter of 2000
The third quarter of 2000
The fourth quarter of 2000
-0.1183
-0.0063
-0.1064
-0.2139
-8.2426
-8.5783
-12.9539
-4.9676
The first quarter of 2001
The second quarter of 2001
The third quarter of 2001
The fourth quarter of 2001
-0.4370
0.0447
-0.1730
-0.1730
-3.8425
-6.4309
-6.1569
-12.7624
The first quarter of 2002
The second quarter of 2002
The third quarter of 2002
The fourth quarter of 2002
0.0029
0.0003
0.0090
-0.0107
-85.1196
-72.4687
-70.0009
-83.0940
Table 4: UIP regression test results for pre-fixed interest differential on
multi-day data
Period
2000~2002
New York Time, 16:00,t
~20:00,t+n;
multi-day interest differential
Slope
t-statistics
-0.0416
-46.4301
1/1/2000~12/31/2000
1/1/2001~12/31/2001
1/1/2002~12/31/2002
-0.1110
-0.0441
-0.0041
-14.8052
-17.8301
-146.4738
The first quarter of 2000
The second quarter of 2000
The third quarter of 2000
The fourth quarter of 2000
-0.1189
-0.0069
-0.1339
-0.2632
-7.1802
-8.3463
-11.8924
-4.3915
The first quarter of 2001
The second quarter of 2001
The third quarter of 2001
The fourth quarter of 2001
-0.6861
0.0336
-0.1981
-0.0441
-4.7453
-6.0766
-5.9751
-17.8301
The first quarter of 2002
The second quarter of 2002
The third quarter of 2002
The fourth quarter of 2002
0.0066
-0.0128
0.0034
-0.0104
-75.9800
-67.6609
-68.7832
-79.7107
Table 5: UIP regression test results for non-pre-fixed interest differential on
intraday data
Period
2000~2002
New York Time,16:00,t~20:00,t;
overnight single day interest
differential
Slope
t-statistics
0.0065
-68.1927
1/1/2000~12/31/2000
1/1/2001~12/31/2001
1/1/2002~12/31/2002
-0.0284
-0.0216
-0.0035
-11.3156
-17.3830
-5.9454
The first quarter of 2000
The second quarter of 2000
The third quarter of 2000
The fourth quarter of 2000
-0.0263
-0.0505
0.4453
-1.0031
-2.0671
-7.0304
-1.4331
-6.3855
The first quarter of 2001
The second quarter of 2001
The third quarter of 2001
The fourth quarter of 2001
-0.2036
-0.4912
-0.0244
-0.1977
-1.9470
-1.6234
-11.2115
-4.2076
The first quarter of 2002
The second quarter of 2002
The third quarter of 2002
The fourth quarter of 2002
-0.4183
2.0800
1.0764
-0.2355
-1.0953
1.1588
0.0497
-5.0035
Table 6: UIP regression test results for non-pre-fixed interest differential on
daily data
Period
2000~2002
New York Time, 16:00,t ~ 16:00,
t+1;
single day interest
differential
Slope
t-statistics
-0.0489
-48.8047
1/1/2000~12/31/2000
1/1/2001~12/31/2001
1/1/2002~12/31/2002
-0.0044
-0.0528
0.0054
-13.5926
-18.0226
-149.5115
The first quarter of 2000
The second quarter of 2000
The third quarter of 2000
The fourth quarter of 2000
0.0431
-0.0481
-0.0372
-0.1025
-6.8797
-8.6503
-11.1729
-4.2506
The first quarter of 2001
The second quarter of 2001
The third quarter of 2001
The fourth quarter of 2001
0.5298
-0.0067
-0.1141
-0.1077
-0.9551
-6.5621
-4.5212
-14.2583
The first quarter of 2002
The second quarter of 2002
The third quarter of 2002
The fourth quarter of 2002
0.0109
0.0143
0.0106
-0.0202
-71.5962
-60.9118
-58.5918
-73.2019
Table 7: UIP regression test results for non-pre-fixed interest differential on
multi-day data
Period
2000~2002
New York Time, 16:00,t
~20:00,t+n;
multi-day interest differential
Slope
t-statistics
-0.0461
-46.7257
1/1/2000~12/31/2000
1/1/2001~12/31/2001
1/1/2002~12/31/2002
-0.0092
-0.0605
0.0084
-13.9928
-17.8268
-142.0459
The first quarter of 2000
The second quarter of 2000
The third quarter of 2000
The fourth quarter of 2000
-0.0552
-0.0647
0.0002
0.1001
-6.6082
-8.5541
-9.5846
-3.0224
The first quarter of 2001
The second quarter of 2001
The third quarter of 2001
The fourth quarter of 2001
0.4966
-0.0148
-0.1102
-0.0605
-1.0568
-6.1786
-4.2633
-17.8268
The first quarter of 2002
The second quarter of 2002
The third quarter of 2002
The fourth quarter of 2002
0.0105
0.0094
0.0223
-0.0141
-63.9622
-56.2059
-57.1774
-68.8594