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research and data is needed to conclude that a higher index results in a larger USD premium, mostly because the index is only significant for the USDGBP model in the second period.
Finally, we find support for the BoE meetings in this period to send the USDGBP basis higher on the meeting days, as it has a coefficient of over 1bp. The effect likely stems from the meetings not resulting in the worst case scenario, which has been priced in to some extent ahead of the meetings, as the BoE only hikes 3 times during the period. This was highlighted in section 8.1.3, as almost all the meetings in this period resulted in a jump higher of over 1bp. We do not believe that this is sufficient evidence to say that the BoE meetings are supportive for the GBP, but we believe the meetings are important for the basis as they directly control the monetary policy.
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∆USDGBP chi2 63.95
Breusch-Pagan test for heteroscedasticity Prob > chi2 0.0000
∆GBPEUR chi2 3.48
Breusch-Pagan test for heteroscedasticity Prob > chi2 0.0623
Table 12: Breusch-Pagan test statistic, period 2
8.3.4 Autocorrelation of residuals
The Breusch-Godfrey test for autocorrelation is performed on both models, as mention in section 5.1.3.
The ΔUSDGBP model does not reject the null hypothesis, thus the model has zero autocorrelation in the residuals. This is indicated with p-value than the chi-square in Table 13. For the ΔGBPEUR model have a higher chi-square than p-value, thus the null hypothesis is rejected. The ΔGBPEUR are therefore assumed to have autocorrelation for the residuals. This rejection reveals that standard errors have to be modified. Following section 8.3.1, we are able to adjust the model for autocorrelation with the Newey-West modified standard errors.
∆USDGBP chi2 0.446
Breusch-Godfrey test for autocorrelation Prob > chi2 0.5043
∆GBPEUR chi2 35.957
Breusch- Godfrey test for autocorrelation Prob > chi2 0.0000
Table 13: Breusch-Godfrey test statistic, period 2
8.3.5 Multicollinearity
First, we investigate the correlation of the ΔUSDGBP model. As can be observed in Table 14, the correlation between all variables are low, with the highest correlation in absolute values being between the LIBOR-OIS spread for GBP and the dummy variable for BoE meetings. The VIF results are available in Table 15, and the results range from 1.02 to 1.00, with a mean of 1.01, which yields the same conclusion as in the previously, that our model does not contain multicollinearity. It is worth mentioning that no variables are excluded from the model, due to high correlation and/or VIF values.
CDS EPU Broad dollar LIBOR-OIS End-year BoE
UK US index GBP effect Meetings
CDS UK 1.0000
EPU US 0.0564 1.0000
Broad dollar index 0.0443 0.0756 1.0000
LIBOR-OIS GBP 0.0413 0.0181 0.0836 1.0000
End-year effect -0.0130 0.0103 -0.0012 0.0091 1.0000
BoE meetings 0.0278 -0.0090 -0.0278 -0.1085 -0.0172 1.0000
Table 14: Correlation matrix for ΔUSDGBP, period 2
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Variable VIF 1/VIF
LIBOR-OIS GBP 1.02 0.9804 Broad dollar index 1.01 0.9901 BoE meetings 1.01 0.9901
EPU US 1.01 0.9901
CDS UK 1.01 0.9901
End-year effect 1.00 1.0000
Mean VIF 1.01
Table 15: VIF test results for ΔUSDGBP, period 2
Continuing with the ΔGBPEUR model, the correlations can be observed in Table 16, where the highest correlation is between the LIBOR-OIS spread for EUR and the dummy variable for end of year effect of -0.1310, which is not to be considered as high. The VIF test results are displayed in Table 17, and ranging from 1.02 to 1.00 with a mean of 1.01, which is within the conclusion that our model does not contain multicollinearity. No variables are excluded because of high correlations and/or VIF values in the model.
LIBOR-OIS LIBOR-OIS CDS Broad dollar End-year
GBP EUR UK index effect
LIBOR-OIS GBP 1.0000
LIBOR-OIS EUR 0.0905 1.0000
CDS UK 0.0413 0.0047 1.0000
Broad dollar index 0.0836 0.0091 0.0443 1.0000
End-year effect 0.0091 -0.1310 -0.0130 -0.0012 1.0000
Table 16: Correlation matrix for ΔGBPEUR, period 2
Variable VIF 1/VIF
LIBOR-OIS GBP 1.02 0.9804 Broad dollar index 1.01 0.9901 LIBOR-OIS EUR 1.01 0.9901
CDS UK 1.00 1.0000
End-year effect 1.00 1.0000
Mean VIF 1.01
Table 17: VIF test results for ΔGBPEUR, period 2
8.3.6 Exogeneity
We assume that the exogenity of the independent variables has not changed for the new sample period, therefore we refer to the discussion in section 7.2.6.
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9 Conclusion
This thesis aimed to uncover why the covered interest parity, CIP, has deviated from zero, and what have been the main drivers for the basis against the GBP. The deviations were investigated through the USDGBP and GBPEUR bases on the 3-month tenor primarily. We used the findings from existing research, which presented several different theories to why the basis had opened up in the first place, and why it continued to violate CIP over the past decade. The key variables that were tested, were carefully selected from the post-crisis papers by Borio et al. (2018), Du et al. (2017), Avdjiev et al. (2017) and Borio et al. (2016). This was done to challenge their theories and to see if the data still supported their claims. By looking at the variables separately and creating a set of regression models for 2010-2014 and 2015-2019, we presented an overview of what drives the basis, and were able to find supporting evidence for several of the theories presented in the literature review.
The basis widens significantly during periods of distress in the markets, evident by the basis movements during both the GFC and European sovereign debt crisis, which occurred across all maturities. The period from mid-2016 and onwards has exercised significantly higher volatility for the GBP-basis, compared to the relatively calm years between 2013 and 2015, which we identified to likely stem from the uncertainty brought by Brexit. Once Brexit reaches a clarification, we expect the basis to act less volatile and probably in the direction of a higher premium on the GBP, though there might be a period of prolonged deviations in absolute terms. The pricing of relative risk will continue to be accounted for, and the regulations are more likely to become stricter than the other way around, which could put the CIP even more out of line, as arbitrage activities would become even harder.
Through the regression analysis, some of the variables were found to be significant in both models and periods. The first variable was the LIBOR-OIS spread, a proxy used by Borio et al. (2016) for counterparty credit risk, which had the largest coefficient in both periods. Although not all LIBOR-OIS spreads were significant, at least one was for each basis model in both samples, pointing towards that the spread has been important over the last decade. For the USDGBP model, the LIBOR-OIS for GBP was significant in both samples and reflected a large drive towards a premium on USD. For the GBPEUR model, both LIBOR-OIS spreads for GBP and EUR were significant in both periods, with a larger spread difference between the two in the newest sample. The UK CDS spread were significant in both samples, supporting the findings of Borio et al. (2016). The coefficient changed drastically in the GBPEUR model
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from period 1 to 2, as it turned positive. We argue that the negative coefficient from period 1 was impacted by the European sovereign debt crisis, which dragged on the Eurozone. For the second period, the variable showed significance for both models where an increase in the UK CDS spread would be expected to yield an unfavorable move in the basis for GBP. The broad dollar index presented by Avdjiev et al. (2017) as a proxy for the dollar strength had significant results in both periods, supporting the theory that a stronger dollar widens the basis against USD.
We found evidence supporting the end-of-the-year effect from Du et al. (2017) and Borio et al. (2018) from 2015 and onwards, which lines up well with the stricter regulatory framework and likely the cause for a wider basis after this point. This could reflect the cost of carrying the position onto the Q4 balance sheet report. For the 3-month basis in both the models, the end of year effect had a negative relationship with the dependable variable, which reflects a drive for a larger premium for USD in the USDGBP basis and GBP in the GBPEUR basis.
Borio et al. (2018) investigated the relationship between FX hedging demand and CIP deviations through the funding gap, but it did not show any sign of significance for any of the periods. One reason for this might be that it suffers from the low frequency of data. Another possible explanation might be that there is no relationship to the GBP funding gap. As the authors do not include GBP in their otherwise major-focused paper, it might be reasonable to believe that they did not find any supporting evidence for the GBP. Therefore, we do not find sufficient evidence to support the theory that the hedging demand for FX impacts the CIP violations.
The regression models had an explanatory power measured through R2 of 10.37% and 12.85% for the USDGBP and GBPEUR models respectively for the second period, down from 20.14% and 29.06% in the first period. Although the R2 is significantly lower compared to the 2010-2014 period, it is still reasonable for the problem presented, especially with regards to the data being on a daily basis, which could introduce a large portion of noise. In addition, the role that the uncertainty caused by the political situation in the UK from 2016 and onwards, cannot be excluded. Although we did not find a direct ‘Brexit premium’ in our research, we believe that the event is interesting for further research.
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10 Further research
As our focus has been primarily on the 3M tenor and the GBP basis, testing the relationship between the key variables presented in this thesis on bases against other currencies and longer/shorter tenors is of high interest, and could end with conclusive evidence for the broader characteristics of the basis and CIP violations. Research on Brexit and the bases could also be of interest, but probably not until more data is available, and an agreement has been reached.
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11 Source
Al Jazeera News. (2019, January 15). Brexit: A timeline. Retrieved 14 March 2019, from https://www.aljazeera.com/news/2019/01/brexit-timeline-190115164043103.html
Alin, A. (2010). Multicollinearity. Wiley Interdisciplinary Reviews: Computational Statistics, 2(3), 370–374. https://doi.org/10.1002/wics.84, ISSN: 1939-0068
Avdjiev, S., Du, W., Koch, C., & Shin, H. S. (2017). The dollar, bank leverage and the deviation from covered interest parity. Retrieved 25 January 2019, from
https://www.bis.org/publ/work592.htm
Baker, S. R., Bloom, N., & Davis, S. J. (2012). Economic Policy Uncertainty Index. Retrieved 3 April 2019, from http://www.policyuncertainty.com/methodology.html
Baker, S. R., Bloom, N., & Davis, S. J. (2015). Measuring Economic Policy Uncertainty (Working Paper, National Bureau of Economic Research). https://doi.org/10.3386/w21633
BIS. (2011). Basel III: A global regulatory framework for more resilient banks and banking systems - revised version June 2011. Retrieved 13 February 2019, from
https://www.bis.org/publ/bcbs189.htm
BIS. (2014). Basel III leverage ratio framework and disclosure requirements. Retrieved 13 February 2019, from https://www.bis.org/publ/bcbs270.htm
BIS. (2016, December 11). Triennial Central Bank Survey of foreign exchange and OTC derivatives markets in 2016. Retrieved 6 February 2019, from https://www.bis.org/publ/rpfx16.htm BIS. (2017). Basel III: Finalising post-crisis reforms. Retrieved 13 February 2019, from
https://www.bis.org/bcbs/publ/d424.htm
Page 80 of 86
BoE. (2017). Bank Rate maintained at 0.50%. Retrieved 6 May 2019, from
https://www.bankofengland.co.uk/monetary-policy-summary-and-minutes/2017/december-2017
BoE. (2019). Official Bank Rate history. Retrieved 6 May 2019, from https://www.bankofengland.co.uk/boeapps/database/Bank-Rate.asp
Borio, C. E. V., Iqbal, M., McCauley, R. N., McGuire, P., & Sushko, V. (2018). The Failure of Covered Interest Parity: FX Hedging Demand and Costly Balance Sheets (SSRN Scholarly Paper No. ID 2910319). Retrieved 3 March 2019, from Social Science Research Network website: https://papers.ssrn.com/abstract=2910319
Borio, C., McCauley, R., McGuire, P., & Sushko, V. (2016). Covered interest parity lost:
understanding the cross-currency basis. Retrieved 7 February 2019, from https://www.bis.org/publ/qtrpdf/r_qt1609e.pdf
Brøgger, S. B. (2018). Foreign Exchange products, CBS
Brooks, C. (2014). Introductory Econometrics for Finance (Third). United States of America, New York: Cambridge university press. ISBN: 978-1-107-03466-2
Casella, G., Fienberg, S., & Olkin, I. (2013). An Introduction to Statistical Learning.
ISBN: 978-1-4614-7137-0
CBOE. (2019, March 4). VIX Index Volatility. Retrieved 3 April 2019, from http://www.cboe.com/products/vix-index-volatility
Clarke, H. D., Goodwin, M., & Whiteley, P. (2017). Brexit: Why Britain Voted to Leave the European Union. Cambridge: Cambridge University Press. ISBN: 978-1-316-58440-8
Page 81 of 86
Danske Bank. (2018). Brexit monitor: Get ready for the end-game. Retrieved 5 May 2019 from https://research.danskebank.com/research/#/Research/article/2cf45289-da96-412c-8a8c-4d05ee111f73/EN
Du, W., Tepper, A., & Verdelhan, A. (2017). Deviations from Covered Interest Rate Parity.
https://doi.org/10.3386/w23170, Retrieved 13 February 2019, from National Bureau of Economic Research website http://www.nber.org/papers/w23170
Eurostat. (2017). Share of Member States in EU GDP. Retrieved 5 May 2019 from https://ec.europa.eu/eurostat/web/products-eurostat-news/-/DDN-20170410-1
Federal Reserve. (2017). Federal Reserve Board - Federal Reserve issues FOMC statement. Retrieved 6 May 2019, from
https://www.federalreserve.gov/newsevents/pressreleases/monetary20171213a.htm
Federal Reserve. (2019). The Fed - Foreign Exchange Rates - H.10 - Nominal/Real Indexes. Retrieved 2 May 2019, from from https://www.federalreserve.gov/releases/h10/summary/
FXCM. (2015). How Do Currency Swaps Work? Retrieved 18 February 2019, from FXCM website:
https://www.fxcm.com/uk/insights/how-do-currency-swaps-work/
Hull, J. C. (2018). Options, Futures and Other Derivatives.(9th), Pearson Education Limited. Harlow, United Kingdom. ISBN: 978-1-292-21289-0
ISDA. (2009). ISDA 24th Annual General Meeting. Retrieved 12 February 2019, from
https://www.isda.org/2009/04/28/remarks-at-isdas-24th-annual-general-meeting-beijing-china/
ISDA. (2018a). ISDA Future of Derivatives Survey. Retrieved 12 February 2019, from https://www.isda.org/2018/04/24/isda-future-of-derivatives-survey/
Page 82 of 86
ISDA. (2018b). Key Trends in the Size and Composition of OTC Derivatives Markets. Retrieved 12 February 2019, from https://www.isda.org/2018/12/10/key-trends-in-the-size-and-composition-of-otc-derivatives-markets/
Lane, P. R. (2012). The European Sovereign Debt Crisis. Journal of Economic Perspectives, 26(3), 49–
68. https://doi.org/10.1257/jep.26.3.49
Linderstrøm, M. D. (2013). Fixed Income Derivatives Lecture Notes. CBS
McGuire, P., & Peter, G. von. (2012). The Dollar Shortage in Global Banking and the International Policy Response. International Finance, 15(2), 155–178. https://doi.org/10.1111/j.1468-2362.2012.01300.x
Overdahl, J. A., & Kolb, R. W. (2009). Financial Derivatives. Wiley, ISBN: 978-0-470-54172-2 Retrieved 20 February 2019
https://www-dawsonera-com.esc-web.lib.cbs.dk:8443/abstract/9780470541722
StataCorp. 2017. Regress postestimation diagnostic plots. TX: Stata Press. Retrieved 4 April 2019, from https://www.stata.com/manuals13/rregresspostestimationdiagnosticplots.pdf
Williams, R. (2015). Heteroskedasticity. Retrieved 8 April 2019 https://www3.nd.edu/~rwilliam/stats2/l25.pdf
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12 Appendix
Appendix 1: Basis calculations for different tenors
Appendix 2: Dickey-Fuller test results and test statistics.
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APPENDIX 3: Descriptive statistics for G5 for different time periods
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Date
13 – Jan - 16 04 – Feb - 16 17 – Mar - 16 14 – Apr - 16 12 – May - 16 16 – Jun - 16 14 – Jul - 16 04 – Aug - 16 15 – Sept - 16 13 – Oct - 16 03 – Nov - 16 15 – Dec - 16 02 – Feb - 17 15 – Mar - 17 11 – May - 17 15 – Jun - 17 03 – Aug - 17 14 – Sept - 17 02 – Nov - 17 14 – Dec - 17 08 – Feb - 18 22 – Mar - 18 10 – May - 18 21 – Jun - 18 02 – Aug - 18 13 – Sept - 18 08 – Nov - 18 20 – Dec - 18 Source: (BoE, 2019)