Description
The purpose of this study is to test the validity of the UFH (Unbiased Forward Rate Hypothesis). To test this hypothesis, the conventional method uses an Ordinary Least Squares (OLS) regression, with the spot rate as the dependent variable, while the one-period lagged forward rate as the independent variable.
Are Forward Rates An Efficient Indicator of Future Spot Rates
An Empirical Study
International Financial Management
Contents
Contents......................................................................................................2 Introduction.................................................................................................3 Literature Review.........................................................................................4 Exchange Rate..........................................................................................4 Spot Rate..................................................................................................4 Forward Rate............................................................................................4 Significance Of The Forward Rate.............................................................5 Unbiased Forward Rate Hypothesis (UFH)...................................................6 Hypothesis Testing......................................................................................8 Null Hypothesis H0 : UFH Holds True........................................................8 Alternative Hypothesis H1 : UFH Does Not Hold True...............................8 Results Of Hypothesis Testing.....................................................................9 1-Month Forward Rate As A Predictor Of Future Spot Rate.......................9 3-Month Forward Rate As A Predictor Of Future Spot Rate.....................11 6-Month Forward Rate As A Predictor Of Future Spot Rate.....................12 Conclusion.................................................................................................14 References.................................................................................................15 Appendix: Data Used In Study...................................................................17
Are Future Rates An Efficient Indicator Of Future Spot Rates | 2 Appendix: Data Used In Study
Introduction
The purpose of this study is to test the validity of the UFH (Unbiased Forward Rate Hypothesis). To test this hypothesis, the conventional method uses an Ordinary Least Squares (OLS) regression, with the spot rate as the dependent variable, while the one-period lagged forward rate as the independent variable. To support the UFH, the constant term would not differ from zero, the coefficient of the oneperiod lagged forward rate would not significantly differ from one, and the error term would not exhibit any serial correlation. Monthly exchange rate data was used from January 2003 to July 2007. The equation is applied to exchange rate equations for the US Dollar, Euro, British Pound and Japanese Yen. Both the spot and forward exchange rates are measured as units of currency per INR. To run the regression, the Ordinary Least Squares Method (OLS) was used.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 3 Appendix: Data Used In Study
Literature Review
Exchange Rate
It is the price of one country's money in relation to another’s. Exchange rates may be fixed or flexible. An exchange rate is fixed when two countries agree to maintain a fixed rate through the use of monetary policy. Historically, the most famous fixed exchange-rate system was the gold standard; in the late 1850s, one ounce of gold was defined as being worth 20 U.S dollars and 4 pounds sterling, resulting in an exchange rate of 5 dollars per pound. An exchange rate is flexible, or "floating," when two countries agree to let international market forces determine the rate through supply and demand. The rate will fluctuate with a country's exports and imports. Most world trade currently takes place with flexible exchange rates that fluctuate within relatively fixed limits.
Spot Rate
The present conversion price of one currency into another, being the exchange rate for immediate delivery (ie. within two business days) of currencies to be exchanged. The spot rate is the exchange rate existing in the market at any given moment in time. It is the rate you would be able to buy foreign currency at "now".
Forward Rate
The N-day forward rate is the rate which appears in a contract to exchange a currency for another N days in the future. It is distinguished from the spot rate, which is the rate used in agreements to exchange one currency for another immediately. No currency changes hand between the parties in a forward contract at the time it is signed; the currency is exchanged at the maturity date of the contract N days in the future.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 4 Appendix: Data Used In Study
According to Eugene Fama (1984), a forward rate can be interpreted as the sum of a premium and the expected future spot rate. The forward exchange rate Ft-1 observed for an exchange at time 't' is the market determined certainty equivalent of the future spot exchange rate St.”
Significance Of The Forward Rate
Insurance against exchange rate risk can be obtained through contracts in the forward market. Such activity is called hedging. A hedge is the offset of a given position in a separate bu parallel market by an equal and opposite position in which the effect of the offset reduces or eliminates the effects of a value change in both positions. In simple terms, a hedge locks in the current value in a contract. The instrument for a hedge is often a currency swap in which a spot contract is offset by an equalamount forward contract.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 5 Appendix: Data Used In Study
Unbiased Forward Rate Hypothesis (UFH)
According to Cornell (1987) there is often the belief that the forward rate must be an unbiased predictor of the spot rate, otherwise speculators could profit from the bias by taking one position in the spot market and the opposite position in the forward market. For example, if the US dollar forward rate systematically under-predicted the future spot rate, speculators could buy US dollars while simultaneously taking a short forward position. On the day when the forward contract falls due, the position could, on average, be closed out at a profit because the spot rate would be above the rate specified by the forward contract. Therefore, the argument runs, the existence of such bias is inconsistent with the concept of an efficient market. The asset approach to exchange rate determination, explored by Fama (1984) and others, emphasizes the role of new information on exchange rate movements and poses two alternative hypotheses for the predictions of future spot rates. One popular hypothesis is the expectations theory of a forward rate model. In the “simple efficiency” specification of forward exchange markets, it is often argued that the forward rate “fully reflects” available information about the exchange rate expectations; consequently the forward rate is usually viewed as an unbiased predictor of the future spot rate. The expectations theory posits that the economic agents are able to process information rapidly. Through the arbitrage activities of the economic agents and market adjustments, the forward rates reflect the information that is expected to determine future exchange rates. In perfectly efficient markets the forward rate equates to the market’s expectation of the future spot exchange rate (with no-arbitrage, risk neutrality and market rationality). This relationship is known as the ‘Unbiased Forward Rate Hypothesis’ (UFH). Simply, the UFH states that
Are Future Rates An Efficient Indicator Of Future Spot Rates | 6 Appendix: Data Used In Study
the forward rate should provide an unbiased and efficient forecast of future spot exchange rates such that: St = Ft-1 + ?
Are Future Rates An Efficient Indicator Of Future Spot Rates | 7 Appendix: Data Used In Study
Hypothesis Testing
Monthly exchange rate data was used from January 2003 to July 2007. The data was taken from the ICRA bulltein. The equation is applied to exchange rate equations for the USD, EURO, GBP, JPY. Both the spot and forward exchange rates are measured as units of currency per INR. To run the regression, the Ordinary Least Squares Method (OLS) was used. The results of the OLS are contained in the tables given below.
Null Hypothesis H0 : UFH Holds True
• • The constant term would not differ from zero The coefficient of the one-period lagged forward rate would not significantly differ from one • The error term would not exhibit any serial correlation
Alternative Hypothesis H1 : UFH Does Not Hold True
This study examines the effectiveness of the forward exchange rate (lagged one period) in determining the spot exchange rate. The equation utilized is: St = ß0 + ß1*Ft-1 + ? Where St is the current spot exchange rate and Ft-1 is the one-period lagged forward rate. The linear form of the variables was used.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 8 Appendix: Data Used In Study
Results Of Hypothesis Testing
1-Month Forward Rate As A Predictor Of Future Spot Rate
COEFFICIENT CURRENCY ß0 ß1 OF CORRELATIO N USD EURO GBP JPY
45.05884 (-0.001787) 11.95574 (3.408828) 10.71917 (2.148151) 0.117735 (0.047060) -0.001787 (-0.438995) 0.784171 (12.39997) 0.868497 (14.12562) 0.992622 (15.82819)
DURBINWATSON COEFFICIENT D-W
0.110240
R2
0.003623
0.743663
1.245095
0.790127
1.332391
0.825389
1.623423
(the figures in parentheses represent calculated t-statistic values) ß0: At 5 percent significance level the t-statistic from table of normal
distribution is 1.645. For Euro and GBP, since the calculated t-statistic value of ?0 is greater than the t-statistic table value, the null hypothesis is rejected and the alternative hypothesis can be accepted, concluding that the constant term does not equal zero in case of USD and Euro. Thus, the UFH does not hold true. ß1: At the 5% level of significance, the calculated t-statistic value of ? 1 is greater than the tstatistic table value for Euro, GBP and JPY. Hence, currencies. This is done as ?1 the null hypothesis is rejected for these
differs significantly from 1. Thus, the UFH does not hold true.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 9 Appendix: Data Used In Study
Durbin-Watson Method: In the Durbin-Watson method, the table indicates the value of dL as 1.50 and dU as 1.59. If the calculated D-W coefficient is less than the dL, there is evidence of serial correlation. In the observed results, for USD, EURO and GBP the D-W coefficient is between 0 and 1.50. Hence, the error term does exhibit serial correlation, so the null hypothesis is rejected. Thus, the UFH does not hold true.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 10 Appendix: Data Used In Study
3-Month Forward Rate As A Predictor Of Future Spot Rate
COEFFICIENT CURRENCY ß0 ß1 OF CORRELATIO N USD EURO GBP JPY
14.45822 (2.270781) 33.46007 (5.442149) 38.14741 (4.432297) -3.927117 (-0.714900) 0.668419 (4.767703) 0.398283 (3.610222) 0.532391 (5.029998) 1.078376 (7.936162)
DURBINWATSON COEFFICIENT D-W
0.315975
R2
0.312535
0.206774
0.538618
0.335997
0.521475
0.557454
0.538786
(the figures in parentheses represent calculated t-statistic values) ß0: At 5 percent significance level the t-statistic from table of normal
distribution is 1.645. For USD, Euro and GBP, since the calculated t-statistic value of ?0 is greater than the t-statistic table value, the null hypothesis is rejected and the alternative hypothesis can be accepted, concluding that the constant term does not equal zero in case of USD, Euro and GBP. Thus, the UFH does not hold true. ß1: At the 5% level of significance, the calculated t-statistic value of ? 1 is greater than the tstatistic table value for all four of USD, Euro, GBP and JPY. Hence, the null hypothesis is rejected for all the currencies. This is done as ?1 differs significantly from 1. Thus, the UHF does not hold true. Durbin-Watson Method: In the Durbin-Watson method, the table indicates the value of dL as 1.50 and dU as 1.59. If the calculated D-W Are Future Rates An Efficient Indicator Of Future Spot Rates | 11 Appendix: Data Used In Study
coefficient is less than the dL, there is evidence of serial correlation. In the observed results, for USD, Euro, GBP and JPY the D-W coefficient is between 0 and 1.50. Hence, the error term does exhibit serial correlation, so the null hypothesis is rejected. Thus, the UFH does not hold true.
6-Month Forward Rate As A Predictor Of Future Spot Rate
COEFFICIENT CURRENCY ß0 ß1 OF CORRELATIO N USD EURO GBP JPY
37.03276 (5.097000) 44.41145 (6.6561914) 57.30744 (5.818859) 13.40185 (1.420825) 0.167168 (1.050916) 0.203402 (1.679010) 0.301171 (2.480161) 0.640236 (2.782176)
DURBINWATSON COEFFICIENT D-W
0.176323
R2
0.022959
0.056586
0.343079
0.115730
0.296857
0.141404
0.204496
(the figures in parentheses represent calculated t-statistic values) ß0: At 5 percent significance level the t-statistic from table of normal
distribution is 1.645. For USD, Euro and GBP, since the calculated t-statistic value of ?0 is greater than the t-statistic table value, the null hypothesis is rejected and the alternative hypothesis can be accepted, concluding that the constant term does not equal zero in case of USD, Euro and GBP. Thus, the UFH does not hold true. ß1: At the 5% level of significance, the calculated t-statistic value of ? 1 is greater than the tstatistic table value for Euro, GBP and JPY. Hence, the null hypothesis is rejected for these currencies. This is done as ?1 differs significantly from 1. Thus, the UFH does not hold true. Are Future Rates An Efficient Indicator Of Future Spot Rates | 12 Appendix: Data Used In Study
Durbin-Watson Method: In the Durbin-Watson method, the table indicates the value of dL as 1.50 and dU as 1.59. If the calculated D-W coefficient is less than the dL, there is evidence of serial correlation. In the observed results, for USD, Euro, GBP and JPY the D-W coefficient is between 0 and 1.50. Hence, the error term does exhibit serial correlation, so the null hypothesis is rejected. Thus, the UFH does not hold true.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 13 Appendix: Data Used In Study
Conclusion
The study indicates that the 1-month forward rate, the 3-month forward rate and the 6-month forward rate are NOT unbiased indicators of the future spot rates. Furthermore, as the time to delivery or maturity of the forward contract increases, the ability of forward rates to predict the future spot rates decreases.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 14 Appendix: Data Used In Study
References
• • • • http://www.dictionary.bnet.com/definition/spot+exchange+rate.html http://en.mimi.hu/business/spot_rate.html http://www.answers.com/topic/exchange-rate Fama, E. F. (1984), “Forward and Spot Exchange Rates,” Journal of Monetary Economics, 14, 319 – 338. • Meese, R.A. and Rogoff, K. 1983. Empirical exchange rate models of the seventies:do they fit out of sample? Journal of International Economics, vol. 14, pp. 3-24. • Mussa, M.L. 1979. Empirical regularities in the behaviour of exchange rates andtheories of the foreign exchange market. In Karl Brunner and Allan H. Meltzer (eds).Carnegie - Rochester Conference Series on Public Policy, vol. 11, pp. 9-57. • Ngama, Y. L., 1994. A re-examination of the forward exchange rate unbiasednesshypothesis, Weltwirtschaftliches Archive. vol. 130, no. 3, pp. 447-460. • Emily Polito, Trinity College “Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate?” • Spahn, Paul B. "The Tobin Tax and Exchange Rate Stability.” Finance and Development. 33.2, 1996, pp. 24-28. • Bakshi, G. S. and Naka, A. (1997), “Unbiasedness of the Forward Exchange Rates,” Financial Review, 32, 145-162.
•
ICRA Bulletin, February 2007
Are Future Rates An Efficient Indicator Of Future Spot Rates | 15 Appendix: Data Used In Study
•
Kohlhagen, S.W. (1979), “The Forward Rate as an Unbiased Predictor of the Future Spot Rate,” Columbia Journal of World Business, 14, 77 – 85
Are Future Rates An Efficient Indicator Of Future Spot Rates | 16 Appendix: Data Used In Study
Appendix: Data Used In Study
Spot and Future Rates of USD, Euro, GBP and JPY in terms of INR for the period of Jan ‘03 to July ’07
Are Future Rates An Efficient Indicator Of Future Spot Rates | 17 Appendix: Data Used In Study
Exchange Movement Of The Rupee Spot Month Jan-03 USD 47.9 3 47.7 4 47.6 4 47.3 8 47.0 8 46.7 1 46.2 2 45.9 4 45.8 Euro 50.9 3 51.4 4 51.5 1 51.4 4 54.6 0 54.5 1 52.5 8 51.1 8 51.3 GBP 77.5 0 76.9 3 75.3 7 74.5 7 76.4 4 77.5 4 75.1 2 73.2 3 73.7 JPY 40.3 5 40.0 0 40.1 8 39.4 9 40.1 5 39.4 8 38.9 5 38.7 0 39.8 1-Month Forward USD 48.02 Euro 50.9 5 51.4 5 51.5 4 51.4 3 54.5 9 54.5 5 52.6 1 51.2 2 51.3 GBP 77.5 2 76.9 4 75.3 8 74.5 5 76.4 1 77.5 5 75.1 4 73.2 5 73.7 JPY 40.4 3 40.0 7 40.2 5 39.5 4 40.2 9 39.5 6 39.0 3 38.7 7 39.8 3-Month Forward USD 48.2 7 48.1 2 48.0 2 47.6 0 47.2 1 47.0 1 46.5 2 46.2 1 45.9 Euro 51.1 3 51.6 9 51.7 4 51.5 3 54.6 1 54.7 3 52.7 9 51.3 5 51.3 GBP 77.6 9 77.1 9 75.6 4 74.6 0 76.3 2 77.6 8 75.2 8 73.3 2 73.5 JPY 40.7 1 40.3 9 40.5 6 39.7 4 40.3 4 39.8 0 39.2 7 39.9 8 39.9 6-Month Forward USD 48.6 9 48.5 5 48.4 3 47.9 0 47.3 3 47.2 2 46.7 5 46.3 8 46.1 Euro 51.4 3 52.0 2 52.0 6 51.7 2 54.6 2 54.8 5 52.9 4 51.4 4 51.4 GBP 77.9 7 77.5 1 75.9 2 74.7 1 76.1 5 77.6 2 75.2 8 73.2 4 73.3 JPY 41.1 8 40.8 6 41.0 1 40.0 9 40.5 4 40.0 6 39.5 6 39.2 3 40.1
Feb-03 Mar03 Apr-03 May03 Jun-03
47.81
47.73
47.43
47.12
46.79
Jul-03 Aug03 Sep-03
46.30
46.02 45.92
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
18
5 Oct-03 Nov03 Dec-03 45.4 0 45.5 4 45.5 9 45.4 6 45.2 7 45.0 5 43.9 6 45.2 2 45.5 1 46.0
6 53.1 1 53.2 6 56.0 2 57.3 3 57.5 2 55.3 1 52.6 5 54.3 6 55.2 5 56.5
3 76.1 1 76.8 7 79.7 4 82.7 3 84.7 1 82.3 3 79.0 9 80.8 8 83.1 8 84.8
1 41.4 8 41.6 7 42.2 9 42.7 1 42.7 7 41.3 7 40.7 6 40.4 2 41.5 7 42.1 45.42
8 53.0 0 53.1 0 55.9 8 57.3 1 57.5 0 55.3 0 52.7 1 54.2 9 55.2 6 56.5
1 76.0 0 76.7 4 79.6 5 82.6 5 84.6 2 82.2 7 78.9 9 80.6 8 83.1 3 84.8
7 41.5 0 41.6 7 42.3 1 42.7 4 42.8 0 41.4 1 40.7 8 40.4 0 41.6 2 42.2
6 45.4 1 45.5 4 45.5 7 45.5 2 45.3 3 45.1 2 43.9 4 45.0 9 45.6 3 46.3
7 52.9 3 53.0 4 55.8 6 57.2 8 57.4 8 55.2 9 52.6 0 54.1 0 55.2 5 56.7
7 75.7 0 76.4 8 79.3 0 82.4 1 84.3 8 82.0 0 78.6 0 80.1 7 82.9 1 84.7
6 41.5 6 41.7 4 42.3 4 42.8 3 42.8 9 41.4 9 40.8 0 40.3 7 41.7 6 42.4
0 45.4 0 45.6 0 45.6 1 45.5 5 45.3 9 45.1 7 43.9 5 45.0 8 45.6 9 46.4
1 52.8 9 52.9 9 55.8 0 57.2 1 57.4 4 55.9 0 52.5 3 54.0 3 55.3 3 56.9
9 75.4 2 76.1 2 78.8 9 81.9 7 83.9 5 81.5 4 78.0 9 79.6 3 82.4 7 84.5
8 41.7 1 41.9 0 42.4 8 42.9 7 43.0 6 41.6 4 40.9 3 40.5 0 41.9 9 42.7
45.53
45.60
Jan-04
45.49
Feb-04 Mar04 Apr-04 May04 Jun-04 Jul-04
45.30 445.0 9 43.98
45.20
45.57 46.15
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
19
6 Aug04 Sep-04 46.3 3 46.1 0 45.7 8 45.1 1 43.9 7 43.7 6 43.7 0 43.7 0 43.7 4 43.5
1 56.4 5 56.2 9 57.1 1 58.6 3 58.9 6 57.5 1 56.8 9 57.6 5 56.6 3 55.2
3 84.3 1 82.6 1 82.6 2 83.9 4 84.8 3 82.2 8 82.4 8 83.2 5 82.9 3 80.7
3 41.9 5 41.8 8 41.9 7 43.1 3 42.3 6 42.3 2 41.6 7 41.5 1 40.7 9 40.8 46.42
5 56.4 8 56.3 4 57.1 8 58.6 9 59.0 1 57.6 1 59.9 5 57.4 6 56.6 9 55.2
1 84.3 1 82.6 1 82.6 1 83.9 6 84.8 3 82.3 3 82.4 9 83.2 5 82.9 3 80.7
0 42.0 3 41.9 7 42.0 6 43.2 2 42.4 5 42.4 4 41.7 3 41.5 9 40.8 7 40.8
0 46.6 1 46.3 1 46.0 8 45.3 3 44.1 7 44.0 3 43.9 1 43.8 7 43.9 4 43.6
2 56.6 8 56.5 3 57.4 4 58.8 8 59.2 2 57.8 7 57.1 9 57.9 2 56.9 4 55.5
8 84.3 7 82.6 0 82.7 1 83.9 4 84.8 6 82.4 4 82.5 7 83.2 8 83.0 2 80.8
5 42.3 2 42.2 1 42.3 7 43.4 8 42.7 2 42.7 4 42.0 4 41.8 6 41.1 6 41.1
3 46.9 2 46.5 0 46.3 3 45.4 9 44.3 4 44.2 0 44.0 8 44.0 4 44.1 2 43.8
1 57.0 1 56.7 4 57.7 6 59.1 5 58.3 4 58.1 8 57.5 2 58.2 8 57.3 3 55.8
7 84.3 6 82.4 5 82.7 2 83.8 8 84.8 3 82.4 4 82.5 9 83.3 1 83.1 1 80.8
9 42.7 6 42.5 6 42.8 1 43.8 8 43.1 2 43.1 6 42.4 8 42.3 2 41.6 3 41.6
46.15
Oct-04 Nov04 Dec-04
45.86
45.19
44.03
Jan-05
43.85
Feb-05 Mar05 Apr-05 May-
43.77
43.75
43.80 43.55
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
20
05 Jun-05
0 43.5 8 43.5 4 43.6 2 43.9 2 44.8 1 45.7 6 45.8 2 44.4 1 44.3 3 44.5
3 53.0 3 52.4 4 53.7 6 53.9 1 53.8 5 53.9 1 54.3 5 53.7 6 52.9 6 53.4
9 79.2 4 76.2 3 78.2 5 79.5 9 79.0 3 79.3 0 80.2 2 78.3 1 77.5 0 77.5
0 40.0 9 38.8 8 39.4 2 39.6 2 39.0 2 38.6 2 38.5 0 38.4 7 37.6 2 37.9 43.62
9 53.0 7 52.4 9 53.6 9 53.9 8 53.9 0 53.9 6 54.4 2 53.8 7 52.9 8 53.5
6 79.2 3 76.2 3 78.2 4 79.5 9 79.0 4 79.3 2 80.2 7 78.4 1 77.5 4 77.6
8 40.1 7 38.9 7 39.4 9 39.7 2 39.1 3 38.7 0 38.6 1 38.5 8 37.7 0 38.0
6 43.7 2 43.6 9 43.7 3 43.9 9 44.8 9 45.8 4 45.5 9 44.6 7 44.5 8 44.8
1 53.2 8 52.7 2 53.8 6 54.1 1 54.1 0 54.1 5 54.6 5 54.2 2 53.4 1 54.0
1 79.2 8 76.3 3 78.2 6 79.5 7 79.1 0 79.3 8 80.4 0 78.7 3 76.1 7 78.1
6 40.4 3 39.2 5 39.7 3 39.9 2 39.3 5 38.9 5 38.8 9 38.9 6 38.0 9 38.5
2 43.8 6 43.8 3 43.8 3 44.0 6 44.9 5 45.8 9 46.0 2 44.8 1 44.7 5 45.0
7 55.6 3 53.0 9 54.2 1 54.4 2 54.4 1 54.4 4 54.9 6 54.6 3 53.8 7 54.5
9 79.3 6 76.5 0 78.3 8 79.6 7 79.1 9 79.4 8 80.5 5 79.0 3 78.3 1 78.5
1 40.8 7 39.7 0 40.1 6 40.3 2 39.7 6 39.3 6 39.3 2 39.4 7 38.6 3 39.0
Jul-05 Aug05 Sep-05
43.58
43.68
43.95
Oct-05 Nov05 Dec-05
44.84
45.80
45.87
Jan-06
44.49
Feb-06 Mar-
44.37 44.57
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
21
06 Apr-06 May06 Jun-06
0 45.0 6 45.4 3 46.0 7 46.4 8 46.5 3 46.1 9 45.4 8 44.8 6 44.6 4 44.3
8 55.3 7 58.0 5 58.3 4 58.9 7 59.6 1 58.8 1 57.3 7 57.8 1 58.9 8 57.7
7 79.8 9 84.9 3 84.9 4 85.7 4 88.1 1 87.0 2 85.2 8 85.7 7 87.6 7 86.8
3 38.5 9 40.6 7 40.1 9 40.1 9 40.1 9 39.4 5 38.3 6 38.2 5 38.0 9 36.9 45.09
8 55.4 4 58.1 2 58.4 0 59.0 4 59.6 9 58.8 7 57.4 9 57.8 9 59.0 7 57.8
6 79.9 2 84.9 9 84.9 9 85.8 0 88.1 7 87.0 6 85.1 4 85.8 4 87.7 6 86.8
5 36.6 8 40.7 8 40.2 9 40.2 9 40.3 0 39.5 2 38.5 0 38.3 6 38.2 1 37.0
2 45.1 8 45.5 3 46.1 4 46.5 7 46.6 6 46.3 3 45.6 5 45.0 8 44.9 3 44.7
3 55.7 0 58.3 6 58.6 2 59.2 8 60.0 1 59.1 8 57.7 7 58.2 4 59.4 9 58.3
4 80.1 2 85.1 6 85.1 4 85.9 8 88.3 9 87.3 2 85.6 6 86.1 9 88.2 3 87.5
0 39.0 0 41.0 9 40.5 8 40.6 0 40.6 3 39.8 7 38.8 4 38.7 4 38.6 3 37.5
2 45.3 2 45.6 5 46.2 7 46.7 2 47.2 8 46.4 9 45.8 1 45.2 8 45.2 3 45.1
2 56.1 3 58.7 8 59.0 6 59.7 5 61.0 7 59.6 0 58.4 6 58.6 8 60.0 7 59.0
8 80.4 8 85.4 8 85.5 3 86.4 0 89.6 7 87.6 7 86.0 0 86.5 9 88.8 2 88.2
7 39.5 3 41.6 3 41.1 4 41.1 6 41.6 0 40.4 2 39.3 7 39.3 0 39.2 7 38.2
45.47
46.10
Jul-06 Aug06 Sep-06
46.52
46.57
46.21
Oct-06 Nov06 Dec-06 Jan-07
45.53
44.92
44.70 44.41
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
22
5 Feb-07 Mar07 Apr-07 May07 Jun-07 44.1 7 43.9 9 42.1 5 40.8 2 40.8 1 40.5 2
7 57.7 3 58.2 3 56.9 6 55.1 6 54.8 4 55.1 3
0 86.4 1 85.6 6 83.8 2 80.9 5 80.9 9 81.5 8
2 36.6 3 37.5 0 35.4 4 33.8 1 33.3 4 33.0 3 44.29
5 57.8 8 58.3 6 58.0 1 55.3 2 54.9 2 55.2 9
8 86.6 0 85.8 1 85.1 7 81.1 6 81.1 7 81.7 6
2 36.7 8 37.6 6 36.1 1 33.9 6 33.4 9 33.1 8
3 44.6 4 44.4 3 43.0 4 41.3 8 41.3 7 41.0 8
8 58.4 6 58.9 2 58.3 1 56.0 1 55.6 0 55.9 8
1 87.2 7 86.4 7 85.5 6 82.0 0 82.0 1 82.6 0
2 37.2 9 38.1 7 36.4 6 34.5 4 34.0 5 33.7 4
1 44.9 8 44.7 5 43.5 6 40.9 3 41.8 5 41.5 6
5 59.0 8 59.5 0 59.1 3 56.7 6 56.3 7 56.7 5
2 87.9 0 87.0 3 86.5 1 82.8 7 82.8 7 83.4 5
0 37.9 5 38.8 1 37.2 5 35.2 7 34.7 7 34.4 6
44.09
42.98
40.93
40.92
Jul-07
40.63
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
23
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
24
doc_133137809.doc
The purpose of this study is to test the validity of the UFH (Unbiased Forward Rate Hypothesis). To test this hypothesis, the conventional method uses an Ordinary Least Squares (OLS) regression, with the spot rate as the dependent variable, while the one-period lagged forward rate as the independent variable.
Are Forward Rates An Efficient Indicator of Future Spot Rates
An Empirical Study
International Financial Management
Contents
Contents......................................................................................................2 Introduction.................................................................................................3 Literature Review.........................................................................................4 Exchange Rate..........................................................................................4 Spot Rate..................................................................................................4 Forward Rate............................................................................................4 Significance Of The Forward Rate.............................................................5 Unbiased Forward Rate Hypothesis (UFH)...................................................6 Hypothesis Testing......................................................................................8 Null Hypothesis H0 : UFH Holds True........................................................8 Alternative Hypothesis H1 : UFH Does Not Hold True...............................8 Results Of Hypothesis Testing.....................................................................9 1-Month Forward Rate As A Predictor Of Future Spot Rate.......................9 3-Month Forward Rate As A Predictor Of Future Spot Rate.....................11 6-Month Forward Rate As A Predictor Of Future Spot Rate.....................12 Conclusion.................................................................................................14 References.................................................................................................15 Appendix: Data Used In Study...................................................................17
Are Future Rates An Efficient Indicator Of Future Spot Rates | 2 Appendix: Data Used In Study
Introduction
The purpose of this study is to test the validity of the UFH (Unbiased Forward Rate Hypothesis). To test this hypothesis, the conventional method uses an Ordinary Least Squares (OLS) regression, with the spot rate as the dependent variable, while the one-period lagged forward rate as the independent variable. To support the UFH, the constant term would not differ from zero, the coefficient of the oneperiod lagged forward rate would not significantly differ from one, and the error term would not exhibit any serial correlation. Monthly exchange rate data was used from January 2003 to July 2007. The equation is applied to exchange rate equations for the US Dollar, Euro, British Pound and Japanese Yen. Both the spot and forward exchange rates are measured as units of currency per INR. To run the regression, the Ordinary Least Squares Method (OLS) was used.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 3 Appendix: Data Used In Study
Literature Review
Exchange Rate
It is the price of one country's money in relation to another’s. Exchange rates may be fixed or flexible. An exchange rate is fixed when two countries agree to maintain a fixed rate through the use of monetary policy. Historically, the most famous fixed exchange-rate system was the gold standard; in the late 1850s, one ounce of gold was defined as being worth 20 U.S dollars and 4 pounds sterling, resulting in an exchange rate of 5 dollars per pound. An exchange rate is flexible, or "floating," when two countries agree to let international market forces determine the rate through supply and demand. The rate will fluctuate with a country's exports and imports. Most world trade currently takes place with flexible exchange rates that fluctuate within relatively fixed limits.
Spot Rate
The present conversion price of one currency into another, being the exchange rate for immediate delivery (ie. within two business days) of currencies to be exchanged. The spot rate is the exchange rate existing in the market at any given moment in time. It is the rate you would be able to buy foreign currency at "now".
Forward Rate
The N-day forward rate is the rate which appears in a contract to exchange a currency for another N days in the future. It is distinguished from the spot rate, which is the rate used in agreements to exchange one currency for another immediately. No currency changes hand between the parties in a forward contract at the time it is signed; the currency is exchanged at the maturity date of the contract N days in the future.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 4 Appendix: Data Used In Study
According to Eugene Fama (1984), a forward rate can be interpreted as the sum of a premium and the expected future spot rate. The forward exchange rate Ft-1 observed for an exchange at time 't' is the market determined certainty equivalent of the future spot exchange rate St.”
Significance Of The Forward Rate
Insurance against exchange rate risk can be obtained through contracts in the forward market. Such activity is called hedging. A hedge is the offset of a given position in a separate bu parallel market by an equal and opposite position in which the effect of the offset reduces or eliminates the effects of a value change in both positions. In simple terms, a hedge locks in the current value in a contract. The instrument for a hedge is often a currency swap in which a spot contract is offset by an equalamount forward contract.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 5 Appendix: Data Used In Study
Unbiased Forward Rate Hypothesis (UFH)
According to Cornell (1987) there is often the belief that the forward rate must be an unbiased predictor of the spot rate, otherwise speculators could profit from the bias by taking one position in the spot market and the opposite position in the forward market. For example, if the US dollar forward rate systematically under-predicted the future spot rate, speculators could buy US dollars while simultaneously taking a short forward position. On the day when the forward contract falls due, the position could, on average, be closed out at a profit because the spot rate would be above the rate specified by the forward contract. Therefore, the argument runs, the existence of such bias is inconsistent with the concept of an efficient market. The asset approach to exchange rate determination, explored by Fama (1984) and others, emphasizes the role of new information on exchange rate movements and poses two alternative hypotheses for the predictions of future spot rates. One popular hypothesis is the expectations theory of a forward rate model. In the “simple efficiency” specification of forward exchange markets, it is often argued that the forward rate “fully reflects” available information about the exchange rate expectations; consequently the forward rate is usually viewed as an unbiased predictor of the future spot rate. The expectations theory posits that the economic agents are able to process information rapidly. Through the arbitrage activities of the economic agents and market adjustments, the forward rates reflect the information that is expected to determine future exchange rates. In perfectly efficient markets the forward rate equates to the market’s expectation of the future spot exchange rate (with no-arbitrage, risk neutrality and market rationality). This relationship is known as the ‘Unbiased Forward Rate Hypothesis’ (UFH). Simply, the UFH states that
Are Future Rates An Efficient Indicator Of Future Spot Rates | 6 Appendix: Data Used In Study
the forward rate should provide an unbiased and efficient forecast of future spot exchange rates such that: St = Ft-1 + ?
Are Future Rates An Efficient Indicator Of Future Spot Rates | 7 Appendix: Data Used In Study
Hypothesis Testing
Monthly exchange rate data was used from January 2003 to July 2007. The data was taken from the ICRA bulltein. The equation is applied to exchange rate equations for the USD, EURO, GBP, JPY. Both the spot and forward exchange rates are measured as units of currency per INR. To run the regression, the Ordinary Least Squares Method (OLS) was used. The results of the OLS are contained in the tables given below.
Null Hypothesis H0 : UFH Holds True
• • The constant term would not differ from zero The coefficient of the one-period lagged forward rate would not significantly differ from one • The error term would not exhibit any serial correlation
Alternative Hypothesis H1 : UFH Does Not Hold True
This study examines the effectiveness of the forward exchange rate (lagged one period) in determining the spot exchange rate. The equation utilized is: St = ß0 + ß1*Ft-1 + ? Where St is the current spot exchange rate and Ft-1 is the one-period lagged forward rate. The linear form of the variables was used.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 8 Appendix: Data Used In Study
Results Of Hypothesis Testing
1-Month Forward Rate As A Predictor Of Future Spot Rate
COEFFICIENT CURRENCY ß0 ß1 OF CORRELATIO N USD EURO GBP JPY
45.05884 (-0.001787) 11.95574 (3.408828) 10.71917 (2.148151) 0.117735 (0.047060) -0.001787 (-0.438995) 0.784171 (12.39997) 0.868497 (14.12562) 0.992622 (15.82819)
DURBINWATSON COEFFICIENT D-W
0.110240
R2
0.003623
0.743663
1.245095
0.790127
1.332391
0.825389
1.623423
(the figures in parentheses represent calculated t-statistic values) ß0: At 5 percent significance level the t-statistic from table of normal
distribution is 1.645. For Euro and GBP, since the calculated t-statistic value of ?0 is greater than the t-statistic table value, the null hypothesis is rejected and the alternative hypothesis can be accepted, concluding that the constant term does not equal zero in case of USD and Euro. Thus, the UFH does not hold true. ß1: At the 5% level of significance, the calculated t-statistic value of ? 1 is greater than the tstatistic table value for Euro, GBP and JPY. Hence, currencies. This is done as ?1 the null hypothesis is rejected for these
differs significantly from 1. Thus, the UFH does not hold true.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 9 Appendix: Data Used In Study
Durbin-Watson Method: In the Durbin-Watson method, the table indicates the value of dL as 1.50 and dU as 1.59. If the calculated D-W coefficient is less than the dL, there is evidence of serial correlation. In the observed results, for USD, EURO and GBP the D-W coefficient is between 0 and 1.50. Hence, the error term does exhibit serial correlation, so the null hypothesis is rejected. Thus, the UFH does not hold true.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 10 Appendix: Data Used In Study
3-Month Forward Rate As A Predictor Of Future Spot Rate
COEFFICIENT CURRENCY ß0 ß1 OF CORRELATIO N USD EURO GBP JPY
14.45822 (2.270781) 33.46007 (5.442149) 38.14741 (4.432297) -3.927117 (-0.714900) 0.668419 (4.767703) 0.398283 (3.610222) 0.532391 (5.029998) 1.078376 (7.936162)
DURBINWATSON COEFFICIENT D-W
0.315975
R2
0.312535
0.206774
0.538618
0.335997
0.521475
0.557454
0.538786
(the figures in parentheses represent calculated t-statistic values) ß0: At 5 percent significance level the t-statistic from table of normal
distribution is 1.645. For USD, Euro and GBP, since the calculated t-statistic value of ?0 is greater than the t-statistic table value, the null hypothesis is rejected and the alternative hypothesis can be accepted, concluding that the constant term does not equal zero in case of USD, Euro and GBP. Thus, the UFH does not hold true. ß1: At the 5% level of significance, the calculated t-statistic value of ? 1 is greater than the tstatistic table value for all four of USD, Euro, GBP and JPY. Hence, the null hypothesis is rejected for all the currencies. This is done as ?1 differs significantly from 1. Thus, the UHF does not hold true. Durbin-Watson Method: In the Durbin-Watson method, the table indicates the value of dL as 1.50 and dU as 1.59. If the calculated D-W Are Future Rates An Efficient Indicator Of Future Spot Rates | 11 Appendix: Data Used In Study
coefficient is less than the dL, there is evidence of serial correlation. In the observed results, for USD, Euro, GBP and JPY the D-W coefficient is between 0 and 1.50. Hence, the error term does exhibit serial correlation, so the null hypothesis is rejected. Thus, the UFH does not hold true.
6-Month Forward Rate As A Predictor Of Future Spot Rate
COEFFICIENT CURRENCY ß0 ß1 OF CORRELATIO N USD EURO GBP JPY
37.03276 (5.097000) 44.41145 (6.6561914) 57.30744 (5.818859) 13.40185 (1.420825) 0.167168 (1.050916) 0.203402 (1.679010) 0.301171 (2.480161) 0.640236 (2.782176)
DURBINWATSON COEFFICIENT D-W
0.176323
R2
0.022959
0.056586
0.343079
0.115730
0.296857
0.141404
0.204496
(the figures in parentheses represent calculated t-statistic values) ß0: At 5 percent significance level the t-statistic from table of normal
distribution is 1.645. For USD, Euro and GBP, since the calculated t-statistic value of ?0 is greater than the t-statistic table value, the null hypothesis is rejected and the alternative hypothesis can be accepted, concluding that the constant term does not equal zero in case of USD, Euro and GBP. Thus, the UFH does not hold true. ß1: At the 5% level of significance, the calculated t-statistic value of ? 1 is greater than the tstatistic table value for Euro, GBP and JPY. Hence, the null hypothesis is rejected for these currencies. This is done as ?1 differs significantly from 1. Thus, the UFH does not hold true. Are Future Rates An Efficient Indicator Of Future Spot Rates | 12 Appendix: Data Used In Study
Durbin-Watson Method: In the Durbin-Watson method, the table indicates the value of dL as 1.50 and dU as 1.59. If the calculated D-W coefficient is less than the dL, there is evidence of serial correlation. In the observed results, for USD, Euro, GBP and JPY the D-W coefficient is between 0 and 1.50. Hence, the error term does exhibit serial correlation, so the null hypothesis is rejected. Thus, the UFH does not hold true.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 13 Appendix: Data Used In Study
Conclusion
The study indicates that the 1-month forward rate, the 3-month forward rate and the 6-month forward rate are NOT unbiased indicators of the future spot rates. Furthermore, as the time to delivery or maturity of the forward contract increases, the ability of forward rates to predict the future spot rates decreases.
Are Future Rates An Efficient Indicator Of Future Spot Rates | 14 Appendix: Data Used In Study
References
• • • • http://www.dictionary.bnet.com/definition/spot+exchange+rate.html http://en.mimi.hu/business/spot_rate.html http://www.answers.com/topic/exchange-rate Fama, E. F. (1984), “Forward and Spot Exchange Rates,” Journal of Monetary Economics, 14, 319 – 338. • Meese, R.A. and Rogoff, K. 1983. Empirical exchange rate models of the seventies:do they fit out of sample? Journal of International Economics, vol. 14, pp. 3-24. • Mussa, M.L. 1979. Empirical regularities in the behaviour of exchange rates andtheories of the foreign exchange market. In Karl Brunner and Allan H. Meltzer (eds).Carnegie - Rochester Conference Series on Public Policy, vol. 11, pp. 9-57. • Ngama, Y. L., 1994. A re-examination of the forward exchange rate unbiasednesshypothesis, Weltwirtschaftliches Archive. vol. 130, no. 3, pp. 447-460. • Emily Polito, Trinity College “Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate?” • Spahn, Paul B. "The Tobin Tax and Exchange Rate Stability.” Finance and Development. 33.2, 1996, pp. 24-28. • Bakshi, G. S. and Naka, A. (1997), “Unbiasedness of the Forward Exchange Rates,” Financial Review, 32, 145-162.
•
ICRA Bulletin, February 2007
Are Future Rates An Efficient Indicator Of Future Spot Rates | 15 Appendix: Data Used In Study
•
Kohlhagen, S.W. (1979), “The Forward Rate as an Unbiased Predictor of the Future Spot Rate,” Columbia Journal of World Business, 14, 77 – 85
Are Future Rates An Efficient Indicator Of Future Spot Rates | 16 Appendix: Data Used In Study
Appendix: Data Used In Study
Spot and Future Rates of USD, Euro, GBP and JPY in terms of INR for the period of Jan ‘03 to July ’07
Are Future Rates An Efficient Indicator Of Future Spot Rates | 17 Appendix: Data Used In Study
Exchange Movement Of The Rupee Spot Month Jan-03 USD 47.9 3 47.7 4 47.6 4 47.3 8 47.0 8 46.7 1 46.2 2 45.9 4 45.8 Euro 50.9 3 51.4 4 51.5 1 51.4 4 54.6 0 54.5 1 52.5 8 51.1 8 51.3 GBP 77.5 0 76.9 3 75.3 7 74.5 7 76.4 4 77.5 4 75.1 2 73.2 3 73.7 JPY 40.3 5 40.0 0 40.1 8 39.4 9 40.1 5 39.4 8 38.9 5 38.7 0 39.8 1-Month Forward USD 48.02 Euro 50.9 5 51.4 5 51.5 4 51.4 3 54.5 9 54.5 5 52.6 1 51.2 2 51.3 GBP 77.5 2 76.9 4 75.3 8 74.5 5 76.4 1 77.5 5 75.1 4 73.2 5 73.7 JPY 40.4 3 40.0 7 40.2 5 39.5 4 40.2 9 39.5 6 39.0 3 38.7 7 39.8 3-Month Forward USD 48.2 7 48.1 2 48.0 2 47.6 0 47.2 1 47.0 1 46.5 2 46.2 1 45.9 Euro 51.1 3 51.6 9 51.7 4 51.5 3 54.6 1 54.7 3 52.7 9 51.3 5 51.3 GBP 77.6 9 77.1 9 75.6 4 74.6 0 76.3 2 77.6 8 75.2 8 73.3 2 73.5 JPY 40.7 1 40.3 9 40.5 6 39.7 4 40.3 4 39.8 0 39.2 7 39.9 8 39.9 6-Month Forward USD 48.6 9 48.5 5 48.4 3 47.9 0 47.3 3 47.2 2 46.7 5 46.3 8 46.1 Euro 51.4 3 52.0 2 52.0 6 51.7 2 54.6 2 54.8 5 52.9 4 51.4 4 51.4 GBP 77.9 7 77.5 1 75.9 2 74.7 1 76.1 5 77.6 2 75.2 8 73.2 4 73.3 JPY 41.1 8 40.8 6 41.0 1 40.0 9 40.5 4 40.0 6 39.5 6 39.2 3 40.1
Feb-03 Mar03 Apr-03 May03 Jun-03
47.81
47.73
47.43
47.12
46.79
Jul-03 Aug03 Sep-03
46.30
46.02 45.92
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
18
5 Oct-03 Nov03 Dec-03 45.4 0 45.5 4 45.5 9 45.4 6 45.2 7 45.0 5 43.9 6 45.2 2 45.5 1 46.0
6 53.1 1 53.2 6 56.0 2 57.3 3 57.5 2 55.3 1 52.6 5 54.3 6 55.2 5 56.5
3 76.1 1 76.8 7 79.7 4 82.7 3 84.7 1 82.3 3 79.0 9 80.8 8 83.1 8 84.8
1 41.4 8 41.6 7 42.2 9 42.7 1 42.7 7 41.3 7 40.7 6 40.4 2 41.5 7 42.1 45.42
8 53.0 0 53.1 0 55.9 8 57.3 1 57.5 0 55.3 0 52.7 1 54.2 9 55.2 6 56.5
1 76.0 0 76.7 4 79.6 5 82.6 5 84.6 2 82.2 7 78.9 9 80.6 8 83.1 3 84.8
7 41.5 0 41.6 7 42.3 1 42.7 4 42.8 0 41.4 1 40.7 8 40.4 0 41.6 2 42.2
6 45.4 1 45.5 4 45.5 7 45.5 2 45.3 3 45.1 2 43.9 4 45.0 9 45.6 3 46.3
7 52.9 3 53.0 4 55.8 6 57.2 8 57.4 8 55.2 9 52.6 0 54.1 0 55.2 5 56.7
7 75.7 0 76.4 8 79.3 0 82.4 1 84.3 8 82.0 0 78.6 0 80.1 7 82.9 1 84.7
6 41.5 6 41.7 4 42.3 4 42.8 3 42.8 9 41.4 9 40.8 0 40.3 7 41.7 6 42.4
0 45.4 0 45.6 0 45.6 1 45.5 5 45.3 9 45.1 7 43.9 5 45.0 8 45.6 9 46.4
1 52.8 9 52.9 9 55.8 0 57.2 1 57.4 4 55.9 0 52.5 3 54.0 3 55.3 3 56.9
9 75.4 2 76.1 2 78.8 9 81.9 7 83.9 5 81.5 4 78.0 9 79.6 3 82.4 7 84.5
8 41.7 1 41.9 0 42.4 8 42.9 7 43.0 6 41.6 4 40.9 3 40.5 0 41.9 9 42.7
45.53
45.60
Jan-04
45.49
Feb-04 Mar04 Apr-04 May04 Jun-04 Jul-04
45.30 445.0 9 43.98
45.20
45.57 46.15
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
19
6 Aug04 Sep-04 46.3 3 46.1 0 45.7 8 45.1 1 43.9 7 43.7 6 43.7 0 43.7 0 43.7 4 43.5
1 56.4 5 56.2 9 57.1 1 58.6 3 58.9 6 57.5 1 56.8 9 57.6 5 56.6 3 55.2
3 84.3 1 82.6 1 82.6 2 83.9 4 84.8 3 82.2 8 82.4 8 83.2 5 82.9 3 80.7
3 41.9 5 41.8 8 41.9 7 43.1 3 42.3 6 42.3 2 41.6 7 41.5 1 40.7 9 40.8 46.42
5 56.4 8 56.3 4 57.1 8 58.6 9 59.0 1 57.6 1 59.9 5 57.4 6 56.6 9 55.2
1 84.3 1 82.6 1 82.6 1 83.9 6 84.8 3 82.3 3 82.4 9 83.2 5 82.9 3 80.7
0 42.0 3 41.9 7 42.0 6 43.2 2 42.4 5 42.4 4 41.7 3 41.5 9 40.8 7 40.8
0 46.6 1 46.3 1 46.0 8 45.3 3 44.1 7 44.0 3 43.9 1 43.8 7 43.9 4 43.6
2 56.6 8 56.5 3 57.4 4 58.8 8 59.2 2 57.8 7 57.1 9 57.9 2 56.9 4 55.5
8 84.3 7 82.6 0 82.7 1 83.9 4 84.8 6 82.4 4 82.5 7 83.2 8 83.0 2 80.8
5 42.3 2 42.2 1 42.3 7 43.4 8 42.7 2 42.7 4 42.0 4 41.8 6 41.1 6 41.1
3 46.9 2 46.5 0 46.3 3 45.4 9 44.3 4 44.2 0 44.0 8 44.0 4 44.1 2 43.8
1 57.0 1 56.7 4 57.7 6 59.1 5 58.3 4 58.1 8 57.5 2 58.2 8 57.3 3 55.8
7 84.3 6 82.4 5 82.7 2 83.8 8 84.8 3 82.4 4 82.5 9 83.3 1 83.1 1 80.8
9 42.7 6 42.5 6 42.8 1 43.8 8 43.1 2 43.1 6 42.4 8 42.3 2 41.6 3 41.6
46.15
Oct-04 Nov04 Dec-04
45.86
45.19
44.03
Jan-05
43.85
Feb-05 Mar05 Apr-05 May-
43.77
43.75
43.80 43.55
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
20
05 Jun-05
0 43.5 8 43.5 4 43.6 2 43.9 2 44.8 1 45.7 6 45.8 2 44.4 1 44.3 3 44.5
3 53.0 3 52.4 4 53.7 6 53.9 1 53.8 5 53.9 1 54.3 5 53.7 6 52.9 6 53.4
9 79.2 4 76.2 3 78.2 5 79.5 9 79.0 3 79.3 0 80.2 2 78.3 1 77.5 0 77.5
0 40.0 9 38.8 8 39.4 2 39.6 2 39.0 2 38.6 2 38.5 0 38.4 7 37.6 2 37.9 43.62
9 53.0 7 52.4 9 53.6 9 53.9 8 53.9 0 53.9 6 54.4 2 53.8 7 52.9 8 53.5
6 79.2 3 76.2 3 78.2 4 79.5 9 79.0 4 79.3 2 80.2 7 78.4 1 77.5 4 77.6
8 40.1 7 38.9 7 39.4 9 39.7 2 39.1 3 38.7 0 38.6 1 38.5 8 37.7 0 38.0
6 43.7 2 43.6 9 43.7 3 43.9 9 44.8 9 45.8 4 45.5 9 44.6 7 44.5 8 44.8
1 53.2 8 52.7 2 53.8 6 54.1 1 54.1 0 54.1 5 54.6 5 54.2 2 53.4 1 54.0
1 79.2 8 76.3 3 78.2 6 79.5 7 79.1 0 79.3 8 80.4 0 78.7 3 76.1 7 78.1
6 40.4 3 39.2 5 39.7 3 39.9 2 39.3 5 38.9 5 38.8 9 38.9 6 38.0 9 38.5
2 43.8 6 43.8 3 43.8 3 44.0 6 44.9 5 45.8 9 46.0 2 44.8 1 44.7 5 45.0
7 55.6 3 53.0 9 54.2 1 54.4 2 54.4 1 54.4 4 54.9 6 54.6 3 53.8 7 54.5
9 79.3 6 76.5 0 78.3 8 79.6 7 79.1 9 79.4 8 80.5 5 79.0 3 78.3 1 78.5
1 40.8 7 39.7 0 40.1 6 40.3 2 39.7 6 39.3 6 39.3 2 39.4 7 38.6 3 39.0
Jul-05 Aug05 Sep-05
43.58
43.68
43.95
Oct-05 Nov05 Dec-05
44.84
45.80
45.87
Jan-06
44.49
Feb-06 Mar-
44.37 44.57
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
21
06 Apr-06 May06 Jun-06
0 45.0 6 45.4 3 46.0 7 46.4 8 46.5 3 46.1 9 45.4 8 44.8 6 44.6 4 44.3
8 55.3 7 58.0 5 58.3 4 58.9 7 59.6 1 58.8 1 57.3 7 57.8 1 58.9 8 57.7
7 79.8 9 84.9 3 84.9 4 85.7 4 88.1 1 87.0 2 85.2 8 85.7 7 87.6 7 86.8
3 38.5 9 40.6 7 40.1 9 40.1 9 40.1 9 39.4 5 38.3 6 38.2 5 38.0 9 36.9 45.09
8 55.4 4 58.1 2 58.4 0 59.0 4 59.6 9 58.8 7 57.4 9 57.8 9 59.0 7 57.8
6 79.9 2 84.9 9 84.9 9 85.8 0 88.1 7 87.0 6 85.1 4 85.8 4 87.7 6 86.8
5 36.6 8 40.7 8 40.2 9 40.2 9 40.3 0 39.5 2 38.5 0 38.3 6 38.2 1 37.0
2 45.1 8 45.5 3 46.1 4 46.5 7 46.6 6 46.3 3 45.6 5 45.0 8 44.9 3 44.7
3 55.7 0 58.3 6 58.6 2 59.2 8 60.0 1 59.1 8 57.7 7 58.2 4 59.4 9 58.3
4 80.1 2 85.1 6 85.1 4 85.9 8 88.3 9 87.3 2 85.6 6 86.1 9 88.2 3 87.5
0 39.0 0 41.0 9 40.5 8 40.6 0 40.6 3 39.8 7 38.8 4 38.7 4 38.6 3 37.5
2 45.3 2 45.6 5 46.2 7 46.7 2 47.2 8 46.4 9 45.8 1 45.2 8 45.2 3 45.1
2 56.1 3 58.7 8 59.0 6 59.7 5 61.0 7 59.6 0 58.4 6 58.6 8 60.0 7 59.0
8 80.4 8 85.4 8 85.5 3 86.4 0 89.6 7 87.6 7 86.0 0 86.5 9 88.8 2 88.2
7 39.5 3 41.6 3 41.1 4 41.1 6 41.6 0 40.4 2 39.3 7 39.3 0 39.2 7 38.2
45.47
46.10
Jul-06 Aug06 Sep-06
46.52
46.57
46.21
Oct-06 Nov06 Dec-06 Jan-07
45.53
44.92
44.70 44.41
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
22
5 Feb-07 Mar07 Apr-07 May07 Jun-07 44.1 7 43.9 9 42.1 5 40.8 2 40.8 1 40.5 2
7 57.7 3 58.2 3 56.9 6 55.1 6 54.8 4 55.1 3
0 86.4 1 85.6 6 83.8 2 80.9 5 80.9 9 81.5 8
2 36.6 3 37.5 0 35.4 4 33.8 1 33.3 4 33.0 3 44.29
5 57.8 8 58.3 6 58.0 1 55.3 2 54.9 2 55.2 9
8 86.6 0 85.8 1 85.1 7 81.1 6 81.1 7 81.7 6
2 36.7 8 37.6 6 36.1 1 33.9 6 33.4 9 33.1 8
3 44.6 4 44.4 3 43.0 4 41.3 8 41.3 7 41.0 8
8 58.4 6 58.9 2 58.3 1 56.0 1 55.6 0 55.9 8
1 87.2 7 86.4 7 85.5 6 82.0 0 82.0 1 82.6 0
2 37.2 9 38.1 7 36.4 6 34.5 4 34.0 5 33.7 4
1 44.9 8 44.7 5 43.5 6 40.9 3 41.8 5 41.5 6
5 59.0 8 59.5 0 59.1 3 56.7 6 56.3 7 56.7 5
2 87.9 0 87.0 3 86.5 1 82.8 7 82.8 7 83.4 5
0 37.9 5 38.8 1 37.2 5 35.2 7 34.7 7 34.4 6
44.09
42.98
40.93
40.92
Jul-07
40.63
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
23
Are Future Rates An Efficient Indicator Of Future Spot Rates | Appendix: Data Used In Study
24
doc_133137809.doc