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Queensland University of Technology EFN426

EFN426 Fisher Open Hypothesis

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EFN426
Assignment 2
Fisher Open Hypothesis
Due: DRAFT version Sunday 20. September 11:59pm, FINAL version Sunday 4. October 11:59pm

Data description:Monthly data on the following variables:
A2.dta
date
iUK
iAU
S
monthly date December 1998 – August 2015 (201 observations)
nominal 12-month interest rate (%pa) – UK
nominal 12-month interest rate (%pa) – Australia
Price of Australian dollars denoted in British pounds

NOTE: the data has already been declared as time series, using date as the time variable
This research problem examines spot GBP/AUD exchange rates and predictions of the exchange rates. This
task is based on an international parity condition called the Fisher open hypothesis. Under this hypothesis,
the expected movement in spot rates is a function of interest rate differentials. Suppose

𝑟𝑟𝑡𝑡,𝐴𝐴𝐴𝐴
𝑟𝑟𝑡𝑡,𝐴𝐴𝑈𝑈
𝑆𝑆𝑡𝑡
𝐸𝐸[𝑆𝑆𝑡𝑡+12]
represents the Australian interest rate at time 𝑡𝑡 for next 12 periods (months),
represents the UK interest rate at time 𝑡𝑡 for the next 12 periods (months),
represents the price of AUD denoted in GBP at time 𝑡𝑡,
represents the expected exchange rate at time 𝑡𝑡 + 12.

The Fisher open hypothesis takes the form
𝐸𝐸[𝑆𝑆𝑡𝑡+12] = 𝑆𝑆𝑡𝑡 × 1+𝑟𝑟𝑡𝑡,𝑈𝑈𝑈𝑈
1+𝑟𝑟𝑡𝑡,𝐴𝐴𝑈𝑈
. (1)
Optimally, the Fisher open hypothesis would provide an unbiased estimator for the spot exchange rate a
year in the future. In other words, any rate of return differential between similar bonds denoted in the two
currencies should be offset by the expected change in the exchange rate. In log- form, the above equation
becomes

𝐸𝐸[𝑠𝑠𝑡𝑡+12] = 𝑠𝑠𝑡𝑡 + 𝑟𝑟𝑡𝑡,𝐴𝐴𝑈𝑈 - 𝑟𝑟𝑡𝑡,𝐴𝐴𝐴𝐴(2)
For (2) to be an unbiased estimator for the future spot exchange rate,
𝑠𝑠𝑡𝑡+12 - 𝐸𝐸[𝑠𝑠𝑡𝑡+12] = 𝑢𝑢𝑡𝑡
where 𝑢𝑢𝑡𝑡 is White Noise. Rewriting (3),
(3)
(𝑠𝑠𝑡𝑡+12 - 𝑠𝑠𝑡𝑡) - 𝑟𝑟𝑡𝑡,𝐴𝐴𝑈𝑈 - 𝑟𝑟𝑡𝑡,𝐴𝐴𝐴𝐴 = 𝑢𝑢𝑡𝑡
provides the interpretation of the change in log exchange rate and the interest rate differential sharing a
(4)
long run equilibrium.
PART I
Test if the Fisher open hypothesis holds.
PART II
[5 marks]
[15 marks]

Looking at equation (4), note that the claimed equilibrium should exist between the rate differential (known
at time t) and the change in exchange rates (known a year later). For more contemporaneous relationship
analysis, consider the difference in expected and realized spot exchange rate 𝑠𝑠𝑡𝑡 - 𝐸𝐸[𝑠𝑠𝑡𝑡], and the rate
differential 𝑟𝑟𝑡𝑡,𝐴𝐴𝑈𝑈 - 𝑟𝑟𝑡𝑡,𝐴𝐴𝐴𝐴, both measured at time t. Carry out a full analysis on the short and long run
dynamics, looking at the two series individually, and examining the interaction between the two.
For all testing and inference, use 5% level of significance.

EFN426
Assignment 2 Submission Instructions
A2 DRAFT (do-file and word doc):
Name your files as YourGroupName_A2_DRAFT.
List the contributing group members’ names and student numbers at the top of the dofile and the report.
All analysis should be attempted.
Penalty clause: Maximum points possible for the A2 FINAL is 20 marks, 50% of which
is conditional on A2 DRAFT submission:

A2 DRAFT submittedVariable partFixed partMaximum marks for
A2 FINAL
Yes – both parts attempted101020
Yes – only one part attempted51015
No draft submitted01010
Unrelated / unoriginal
documents submitted
01010
After submission, the draft will be commented on and the code checked, to give you
feedback on where to improve, what is missing, where you go wrong, etc. The feedback
will not provide correct solutions or fix your answers, just point out where things go
wrong or things are missing. It is your task to improve the draft and seek further
feedback prior to submitting the final version. Feedback will be given for attempted tasks
only. If no attempt is made, no feedback is to be provided.
Drafts are not marked.
A2 FINAL (do-file and word doc):
Name your files as YourGroupName_A2_FINAL.
List the contributing group members’ names and student numbers at the top of the dofile and the report.
Complete analysis and a working do-file that matches up with the report. Maximum is 20
marks, unless a penalty clause is applied due to A2 DRAFT being not fully attempted /
not submitted / unoriginal / unrelated.
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