A Resolution of Uncovered Interest Rate. Parity Puzzle: the Case of Korean Won/ the. United States Dollar

Transcription

1 A Resolution of Uncovered Interest Rate Parity Puzzle: the Case of Korean Won/ the United States Dollar By Chung, Dae Hyun Major in International Finance GRADUATE SCHOOL OF INTERNATIONAL STUDIES, SOGANG UNIVERSITY December 2003

2 A Resolution of Uncovered Interest Rate Parity Puzzle: the Case of Korean Won/ the United States Dollar By Chung, Dae Hyun Advisor: Prof. Dr. Im, Joon Hwan A thesis submitted to the faculty of Sogang University in fulfillment of the requirements for the degree of Master of International Studies Major in International Finance GRADUATE SCHOOL OF INTERNATIONAL STUDIES, SOGANG UNIVERSITY, Seoul, Korea December 2003

3 GRADUATE SCHOOL OF INTERNATIONAL STUDIES, SOGANG UNIVERSITY COMMITTEE APPROVAL of a master s thesis submitted by Chung, Dae Hyun This thesis has been read by each member of the supervisory committee and by majority vote has been found to be satisfactory. December 23, 2003 Referee: Prof. Dr. Yoon Soo Kim Referee: Prof. Dr. Joon Hwan Im Referee: Prof. Dr. Hae Sik Park

4 Acknowledgements First of all, I give all glory to God for His endless love, grace, and blessing on me. Without the help of God, I would not have been able to complete my studies. I give all credit to God. Second, I am deeply indebted to my mentor Professor Im, Joon Hwan for his academic contribution, his constant encouragement, and his selfless work for the accomplishment of this thesis. I appreciate his time and pain to supervise this paper. His suggestions and comments have enriched my work. Third, I also want to express my deep appreciation to Professor Kim, Yoon Soo and Doctor Park, Hae Sik who read my whole manuscript and provided valuable comments on it. In a real sense their competent suggestions and advice sharpened my mind. My thesis is better in many ways because of their critical suggestions and comments. Fourth, I would like to express great thanks to my best English teacher and friend Ron Somerville for his sincere teaching, commenting, and proofreading about my thesis. Words are not sufficient to express my appreciation to him who has provided creative points and has helped for my paper. Fifth, I appreciate my friends and classmates at Sogang University with whom I have studied with for two memorable and academically i

5 fulfilling years. Especially I appreciate my junior Koh, In Hae for introducing good statisticians to me. Lastly, but not the least, the deepest gratitude and thanks goes to my parents who have taken care of me for 29 years. Without my parents constant prayer, constant support, and sacrifice, my studies would have never been finished. There are numerous people to whom thanks are due, but it is impossible to name all the helpers and supporters. However, I would like to express my deep appreciation for those to whom I am deeply indebted. ii

6 Abstract The Uncovered Interest Rate Parity (UIP) is very significant for determining expected future foreign exchange rates. But so far many researchers have experienced the empirical failure of UIP. Thus this thesis is motivated to attempt for addressing the UIP puzzle. To resolve the failure of UIP, this thesis considers reducing risk premium which is a decisive factor in the resolution for the UIP puzzle.. There are three important strategies contributing to reducing risk premium. First, tests in the thesis develops methods of a short-term time window spanning a cut-off time of banks for creating the discrete interest payment which Chaboud and Wright (2003) exploited. The second strategy is that the restriction on Korean currency transaction is lifted for Korean won/ the U.S. dollar trades in New York. 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. However, to draw up the discrete interest payment in a short overnight period, the won currency account is assumed to be opened in the New York market. The reason is a time difference between the United States and Korea. Third, prefixed interest rate should be assumed so that an investor may iii

7 know interest differential between Korean and the U.S. on the beginning day of a trade, t. Actually, if an investor does not prefix interest rate on day t, he will not calculate interest cost and gain interest applying on day t+2 due to a settlement lag. But if an investor can agree to contract terms on concerning interest rate differential between Korea and the U.S. in advance on beginning day of a trade, he can assume that risk premium is diminished. To implement these three strategies, this thesis exploits high frequency data that is the exchange rate Korean won relative to the U.S. dollar covering the years from 2000 to Test results are divided by the length of the period. The longest period test is the period from 2000 to 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. 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 are favorable toward the UIP hypothesis. 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 iv

8 Table of Contents 1. Introduction Implications of UIP Hypothesis Discrete Timing of Interest Payment Empirical Plans UIP tests for prefixing interest differential between Korea and the U.S UIP tests on the four hour time window UIP tests on the single day time window UIP tests on the multi-day time window UIP tests for non-prefixing interest differential between Korea and United States UIP tests on the four hour time window UIP tests on the single day time window UIP tests on the multi-day time window Empirical Results UIP tests for prefixing interest differential between Korea and the U.S UIP tests on the four hour time window UIP tests on the single day time window UIP tests on the multi-day time window UIP tests for non-prefixing interest differential between Korea and the U.S UIP tests on the four hour time window UIP tests on the single day time window UIP tests on the multi-day time window Implications of Empirical Results Conclusion...23 <References>...26 v

9 List of Figure Figure 1: Actual time data scheme of UIP regression for pre-fixed interest rate differential on the smallest window...29 Figure 2: Actual time data scheme of UIP regression for pre-fixed single day interest rate differential from time 16:00 on day t to 16:00 on day t+1 in New York...30 Figure 3: Actual time data scheme of UIP regression for pre-fixed multi-day interest rate differential from New York time 16:00 on day t to 20:00 on day t+ n in New York...31 Figure 4: Actual time data scheme of UIP regression for non-pre-fixed interest rate differential on the smallest window...32 Figure 5: Actual time data scheme of UIP regression for non-pre-fixed single day interest rate differential from time 16:00 on day t to 16:00 on day t+1 in New York...33 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 day t + n in New York...34 List of Table Table 1: Time Difference between New York and Seoul to construct a 4-hour time window...12 Table 2: UIP regression test results for pre-fixed interest differential on overnight intraday data...35 Table 3: UIP regression test results for pre-fixed interest differential on daily data...36 Table 4: UIP regression test results for pre-fixed interest differential on multi-day data...37 Table 5: UIP regression test results for non-pre-fixed interest differential on Overnight intraday data...38 Table 6: UIP regression test results for non-pre-fixed interest differential on daily data...39 Table 7: UIP regression test results for non-pre-fixed interest differential on multi-day data...40 vi

10 1. Introduction The Uncovered Interest Rate Parity (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 1

11 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 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 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 2

12 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 thesis is designed to contribute to address the UIP puzzle, alone the lines of discrete interest payment that Chaboud and Wright consider in their paper. Interest rates are discretely paid because no interest payment are made during intraday trading. 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 thesis 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 idea in the thesis 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. This is like a window of a house. If you close the window, you will not be exposed to the wind outside. On the other hand, if you open the window for a long time, you will be completely vulnerable to the wind, but you open the window slightly for a short time, you will not be completely exposed to the wind. 3

13 Thus a house is analogous to underwriting assets; the degree of window opening is the holding period for investing; the length of time a house resident opens the window is the testing data period; and the wind is the time-varying risk. Therefore, in order to protect himself from the wind, the house resident either has to close the window tightly or open the window slightly for a short time. Likewise, to diminish risk premium, this thesis designs tests using short holding periods of investment in a currency, exploiting high frequency data which is the exchange values of Korean won relative to the U.S. dollar. And actually five tests and six tests among the 12 tests show favorable results toward the UIP hypothesis in the smallest time window. The plan for the remainder of this thesis is as follows. Section 2 lays out the implication of UIP. Section 3 contains interpretation 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 4

14 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 1- year 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 5

15 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 paid, 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 6

16 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 settlement 2 period in both Korea and the United States. On holidays, the foreign exchange market is closed. Tests in this thesis are conducted on the basis of a self-financing 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 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 - i t *)/(1+ i t *) = RP(t, h1; t+1, h2) + u t (2) 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. 7

17 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 - i t *)/(1+ i t *) + RP(t, h1; t + 1, h2) + u t (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 trade 3 is zero. By this assumption, {s(t + 1, h2) - s(t, h1)}/ s(t, h1) = α + β(i t - i t *)/(1+ i t *) + u t (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 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. 8

18 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 record 4. The assumptions for UIP equation in this thesis 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 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. 9

19 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 Korean won relative to the U.S. dollar provided by Olsen and Associates, covering the entire calendar years from 2000 to In order to design these data, Olsen and Associates record all Reuters quotes, average the bid and ask. I 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. 10

20 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 4- hour 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. 11

21 Table 1: Time Difference between New York and Seoul to construct a 4- hour 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 closed closed open closed Greenwich Mean Time (GMT) t, 07:00 t, 11:00 t, 21:00 t+1, 01:00 Seoul time t, 16:00 t, 20:00 t+1, 06:00 t+1, 10:00 Seoul market open closed closed open 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 12

22 In this thesis, 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 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 (i t i* t ) / (1 + i* t ) + u t (6) is an ex-ante return for the pre-fixed interest rate differential on day t with 13

23 the difference between Es(t+1, h2) and S(t, h1) 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 U.S. currency account on day t+2, so he is supposed to gain a day U.S. 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 (i t i* t ) / (1 + i* t ) + u t (7) 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 14

24 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 (i t i* t ) / (1 + i* t ) + u t (8) Actual time data scheme of UIP regression for pre-fixing multi-day 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 3.1. The only difference is that the investor unwinds the position at the day t + n, so the value date of 15

25 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 (i t i* t ) / (1 + n t *) + u t (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) 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 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: 16

26 {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) 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 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) Actual time data scheme of UIP regression for pre-fixing multi-day 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 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) + u t+2 (13) 17

27 5. Empirical Results Test results are divided by the length of the period. The longest period test is the period from 2000 to 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 t- statistics 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 18

28 beginning day of a trade, t UIP regression test results for pre-fixing the interest differential between Korea and United States 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 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 and t- statistic is shows the most favorable results for the UIP hypothesis. Refer to Table 2 presenting the results of estimated slope coefficients and t- statistics. 19

29 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 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 Refer to Table 3 presenting the results of estimated slope coefficients and t- statistics 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 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

30 and yearly period tests, especially from the fourth quarter of 2000 to the third quarter of Refer to Table 4 presenting the results of estimated slope coefficients and t-statistics UIP regression test results for non-prefixing the interest differential between Korea and United States 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 , 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 t- statistics 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 And 21

31 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 and t-statistic is That result does not reject the UIP hypothesis. Refer to Table 6 presenting the results of estimated slope coefficients and t- statistics 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 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 and t-statistic is , which is favorable toward the UIP hypothesis. Refer to Table 7 presenting the results of estimated slope coefficients and t-statistics. 22

32 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 thesis experiments with UIP tests concentrating on abating risk premium which is a decisive factor in the violation of the UIP hypothesis. 23

33 There are three proposals to consider reducing risk premium. First, tests in the paper exploit methods of a short-term time window spanning the cut-off time of off-line banks for creating the discrete payments of interest introduced by Chaboud and Wright. Interest is paid only when a position is rolled over from one day to the next. The number of interest days that accrue depends on how many days the value date moves when a position is rolled over. The common rollover time is determined by market convention. The second proposal is that the restrictions on Korean currency transactions are lifted. The second one is very important to designing discrete timing of interest payments in the test schemes. In reality, an investor does not open a Korean won currency account in New York because Korean foreign exchange law bans won currency from circulating outside the country so that it is not be used for speculative or criminal purposes. However, for discrete interest payments, the won currency account is assumed to be opened in the New York market and a beginning trade should commence there because of the time difference between the United States and Korea. Third, a prefixed interest rate should be assumed so that an investor knows the interest differential between Korea and the U.S. on the beginning day of a trade, t. If an investor does not fix the interest rate on day t, he will 24

34 not know the incurred interest cost and will gain interest applied on day t+2 due to settlement lag. But if an investor can agree to contract terms concerning interest rate differentials between Korea and the U.S. in advance on the beginning day of a trade, he can assume that the risk premium is reduced. And exploiting a high frequency exchange rate dataset of the U.S. dollar versus the Korean won enhances the results for supporting the UIP hypothesis. As a consequence, during quarterly periods and over short windows of high frequency data, estimated slope coefficients in the UIP regression become close to unity. And the regression model of pre-fixed interest differential before the value date of day t trades on short-term windows yields similar favorable results for the UIP hypothesis as the one for non-fixed interest differential before value date of day t trades. The regression test designed for pre-fixed interest differential has a more positive slope than the one for non-pre-fixed interest. Non-pre-fixed interest differential tests are conducted for an investor who does not consider the UIP equation before beginning a trade on day t. On the other hand, pre-fixed interest differential models indicate that an investor in advance can shield his investment time window from time-varying risk. 25

35 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 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 Bekaert, G. and R.J. Hodrick (1993): On Biases in the Measurement of Foreign Exchange Risk Premiums, Journal of International Money and Finance, 12, pp.115~138 Engel, C (1996): The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence, Journal of Empirical Finance, 3, pp123~192 Hansen, L.P. and R.J. Hodrick (1980), Forward Change Rates as Optimal Predictors of Future Spot Rates: an Economic Analysis, Journal of Political 26

36 Economy, 88, pp Hodrick, R. J. (1989): Risk, Uncertainty, and Exchange Rates, Journal of Monetary Economics. 23, Danielsson, J. and R. Payne (2002): Real Trading Patterns and Prices in Spot Foreign Exchange Markets, Journal of International Money and Finance, 21, pp.203~222. Fama, E.F. (1984): Forward and Spot Exchange Rates, Journal of Monetary Economics, 14, pp Flood, R.P. and A.K. Rose (2002): Uncovered Interest Parity in Crisis, IMF Staff. Papers, 49, pp Frankel, J.A. and K.A. Froot (1989): Forward Discount Bias: Is It an Exchange Risk Premium, Quarterly Journal of Economics, 104, pp Froot, K.A. and R.H. Thaler (1990): Anomalies: Foreign Exchange, Journal of Economic Perspectives, 4, pp

37 Fujii, E, and M. Chinn (2001): Fin de Siecle Real Interest Parity, Journal of International Financial Markets, Institutions and Money, 11, pp Lyons, R.K. (1995): Tests of Microstructural Hypotheses in the Foreign Exchange Market, Journal of Finance Economics, 39, pp.321~351. Lyons, R.K. and A.K. Rose (1995): Explaining Forward Exchange Bias, Journal of Finance, 50, pp McCallum, B.T. (1994): A Reconsideration of the Uncovered Interest Rate Parity Relationship, Journal of Monetary Economics 33, Meredith, G. and M. Chinn (1998): Long-Horizon Uncovered Interest Rate Parity, National Bureau of Economic Research Working Paper

38 Seoul time t+1, 06:00 t+1, 10:00 New York time t, 16:00 t, 20:00 Korean won currency account U.S. dollar currency account Short selling KRW in New York market Buying KRW in Seoul market (unwinding position) Value date of a day t trade, t + 2 Settlement of Short Selling KRW A day interest cost from borrowing KWR accrues. ( t i t+1 ) A day interest gain from deposing USD accrues. ( t i* t+1 ) Value date of a day t+1 trade, t + 3 Settlement of Buying KRW(and delivering KRW to a lender) Figure 1: Actual time data scheme of UIP regression for pre-fixed interest rate differential on the smallest window * Note: ( t i t+1 ) indicates that interest rate during period from day t to day t

39 Seoul time t+1,06:00 t+2, 06:00 t+3 t+ 4 Value New York date of a Value date time day t of a day t+1 t, 16:00 t +1, 16:00 trade, t +2 trade, t +3 Short selling KRW in New York market Buying KRW in New York market (Unwinding the position) Settlement of Short Selling KRW Settlement of Buying KRW(and delivering KRW to a lender) Korean won currency account U.S. dollar currency account A day interest cost from borrowing KWR accrues. ( t i t+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. 30

40 Seoul time t+1, 06:00 t+n+1,10:00 New York time t, 16:00 t + n, 20:00 Korean won currency account U.S. dollar currency account Short selling KRW in New York market Buying KRW in Seoul market (Unwinding the position) Value date of a day t trade, t + 2 Settlement of Short Selling KRW 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*t t+n+1 ) Value date of a day t+n+1 trade t + n + 3 Settlement of Buying KRW(and delivering KRW to a lender) 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. 31

41 Seoul time t+1, 06:00 t+1, 10:00 New York time t, 16:00 t, 20:00 Korean won currency account U.S. dollar currency account Short selling KRW in New York market Buying KRW in Seoul market (Unwinding the position) Value date of a day t trade, t + 2 Settlement of Short Selling KRW 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 ) Value date of a day t+1 trade, t + 3 Settlement of Buying KRW(and delivering KRW to a lender) Figure 4: Actual time data scheme of UIP regression for non-pre-fixed interest rate differential on the smallest window 32

42 Seoul time t+1,06:00 t+2, 06:00 New York time t, 16:00 t +1, 16:00 Korean won currency account U.S. dollar currency account Short selling KRW in New York market Buying KRW in the New York market (Unwinding the position) Value date of a day t trade, t + 2 Settlement of Short Selling KRW 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 ) Value date of a day t+1 trade, t + 3 Settlement of Buying KRW(and delivering KRW to a lender) 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. 33

43 Seoul time t+1, 6:00 t+n+1,10:00 New York time t, 16:00 t + n, 20:00 Korean won currency account U.S. dollar currency account Short selling KRW in New York market Buying KRW in Seoul market (Unwinding the position) Value date of a day t trade, t + 2 Settlement of Short Selling KRW 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 ) Value date of a day t+n+1 trade t + n + 3 Settlement of Buying KRW(and delivering KRW to a lender) 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 34

44 Table 2: UIP regression test results for pre-fixed interest differential on the overnight intraday time window New York time,16:00,t~20:00,t; overnight single day interest differential Period Slope t-statistics 2000~ /1/2000~12/31/ /1/2001~12/31/ /1/2002~12/31/ The first quarter of The second quarter of The third quarter of The fourth quarter of The first quarter of The second quarter of The third quarter of The fourth quarter of The first quarter of The second quarter of The third quarter of The fourth quarter of 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, the UIP hypothesis will not be rejected. 35

45 Table 3: UIP regression test results for pre-fixed interest differential on the single day time window New York Time, 16:00,t ~ 16:00, t+1; single day interest differential Period Slope t-statistics 2000~ /1/2000~12/31/ /1/2001~12/31/ /1/2002~12/31/ The first quarter of The second quarter of The third quarter of The fourth quarter of The first quarter of The second quarter of The third quarter of The fourth quarter of The first quarter of The second quarter of The third quarter of The fourth quarter of

46 Table 4: UIP regression test results for pre-fixed interest differential on the multi-day time window New York Time, 16:00,t ~20:00,t+n; multi-day interest differential Period Slope t-statistics 2000~ /1/2000~12/31/ /1/2001~12/31/ /1/2002~12/31/ The first quarter of The second quarter of The third quarter of The fourth quarter of The first quarter of The second quarter of The third quarter of The fourth quarter of The first quarter of The second quarter of The third quarter of The fourth quarter of