Relationship Between Commodities and Currency

Pair Realized Variance

Derrick HangEcon 201FS

April 28, 2010

Agenda

Last time…“HAR-RV” RegressionsBayesian AnalysisConclusions

From last time….

Question: Does this relationship between “commodity currency-pairs” and its respective commodity hold when examining their realized variance?◦ Is the realized variance of the commodity a useful indicator for the

realized variance of the “commodity currency-pairs”?

March 18th: spike in gold RV; US central bank announced it will by long-term treasury bonds (surprise); which raised the appeal for gold; spike seen at same date for some currency-pairs as well

Combine analysis from last time and focus on one topic

Regress for currency-pair RV using the lagged RV of the commodity and HAR-RV regressors for the currency pair RV to control for trends

“HAR-RV” AnalysisCommodity Regressor: Gold

*

AUDUSD

CHFUSD EURUSD GBPUSD JPYUSD

β4 0.0647 0.0444 0.0283 0.0356 0.0178

β4

P-value0.0379 0.2854 0.0762 0.0933 0.0928

NZDUSD

CADUSD

NOKUSD

ZARUSD

β4 0.0560 0.2252 0.0763 0.0367

β4

P-value0.0628 0.2494 0.0687 0.0341

1:422:35:21:1: tComtPairtPairtPairtPair RVRVRVRVRV

“HAR-RV” AnalysisCommodity Regressor: Oil

*

AUDUSD

CHFUSD EURUSD GBPUSD JPYUSD

β4 0.0228 0.0165 0.0087 0.0124 0.0249

β4

P-value0.2560 0.4898 0.3459 0.3289 0.3751

NZDUSD

CADUSD

NOKUSD

ZARUSD CADJPY

β4 0.0177 0.3240 0.0341 0.0056 0.0560

β4

P-value0.3342 0.0027 0.1420 0.5788 0.0021

1:422:35:21:1: tComtPairtPairtPairtPair RVRVRVRVRV

“HAR-RV” AnalysisCommodity Regressor: Gold

* Indicates significance at 0.05 level

AUDUSD

AUDUSDw/ RVcom

ZARUSD ZARUSDw/ RVcom

α 0.0000 0.0000 0.0000 0.0000

β1 0.4137* 0.4011* 0.1867 0.1494

β2 -0.0537 -0.0421 -0.1108 -0.0877

β3 -0.0244 -0.0662 0.0769 0.0461

β4 - 0.0647* - 0.0367*

P-value of F-Test

0.0003 0.0001 0.1588 0.0442

R2 0.1754 0.2126 0.0523 0.0969

)( 1:422:35:21:1: tComtPairtPairtPairtPair RVRVRVRVRV

“HAR-RV” AnalysisCommodity Regressor: Oil

* Indicates significance at 0.05 level

CADUSD

CADUSD w/ RVcom

CADJPY CADJPY w/ RVcom

α 0.0002 0.0001 0.0000 0.0000

β1 0.0316 -0.0375 0.1298 0.1201

β2 0.0145 0.0122 0.0611 0.0742

β3 0.0038 -0.0044 -0.0312 -0.0499

β4 - 0.3240* - 0.0560*

P-value of F-Test

0.9896 0.0935 0.4674 0.0154

R2 0.0012 0.0935 0.0260 0.1201

)( 1:422:35:21:1: tComtPairtPairtPairtPair RVRVRVRVRV

Findings from “HAR-RV” regression

The HAR-RV regressors are not significant in most of the regressors and when it is, only the daily lag is significant◦ This can be attributed to the relatively small 6-months worth of data

NZDUSD, CHFUSD were expected to follow the gold but the regression was not significant

NOKUSD was expected to follow the oil but the regression was not significant

JPYUSD, EURUSD, GBPUSD were expected to not have significant regressions since the relationship of the pair to the commodity is not clear

Only AUDUSD, ZARUSD, CADUSD, CADJPY have significant regressions

RV Bayesian Analysis

Robustness check: Are findings from simple “HAR-RV”-like regression similar through those obtained from a different approach?

I chose to employ the univariate DLM framework ◦ outlined in Chapter 5 of Harrison and West◦ DLM models allow the regression coefficient to be

time-varying, a check on the adequacy of the previous approach with constant beta coefficients

◦ Easier to explain than multivariate DLM framework

RV Bayesian Analysis

Recall:

Main Model Assumptions◦ Observational variance is constant◦ Error terms all come from a normal distribution

whose parameters are updated◦ Posterior estimates of the coefficients come from a

t-distribution whose parameters are updated

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RV Bayesian AnalysisModel Specifications

◦ Prior distribution:

◦ We must specify mt-1 and Ct-1 initially; so there is a burn-in for the model to learn the “true” values

Focus on Posterior estimates: Model returns a series of the expected value of the coefficient for each day; we will look at the kernel density of these expected values

We expect the RV of the currency pair to be a random walk => beta in front of lagged RV is 1 and the beta in front of the commodity RV is 0 (zero predictive power)

),(~)|( 1111,1, ttntiti CmTDt

RV Bayesian AnalysisOverview of updating equations to

determine the posterior distributionLet signal be the coefficient varianceLet noise be the observational variance

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RVF

RVY

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Posterior Kernel Density: CADUSD

),0(~;1:,21:,1: VNvvRVRVRV tttOILttCADUSDtttCADUSD

Posterior Kernel Density: CADJPY

),0(~;1:,21:,1: VNvvRVRVRV tttOILttCADJPYtttCADJPY

Posterior Kernel Density: AUDUSD

),0(~;1:,21:,1: VNvvRVRVRV tttGOLDttAUDUSDtttAUDUSD

Posterior Kernel Density: ZARUSD

),0(~;1:,21:,1: VNvvRVRVRV tttGOLDttZARUSDtttZARUSD

Findings from Bayesian Approach

All chosen regressions seem to point toward the commodity variance as a significant positive indicator for the currency pair variance

These commodity variance coefficients seem to be significant from zero for the majority of the sample window; the distributions for all the commodity variance coefficients all are clearly non-zero centered

Thus, the constant coefficient from the previous non-time varying analysis seem to be sufficient

Conclusions

The “HAR-RV” and the Bayesian dynamic linear model approach seem to support each other’s results

Unfortunately, there were no across-the-board systematic patterns but initial hypothesis is upheld providing justification for further research in this topic

There seems to be some small evidence in favor a positive relationship between the RV of a currency-pair and the RV commodity although not a expected pair regressions turn out to be significant

Conclusions

The “HAR-RV” and the Bayesian dynamic linear model approach AUDUSD, ZARUSD are the strongest pairs in the dataset for the case of gold (AU, SA large producers of gold) and CADUSD (CADJPY) are relatively strong pairs for the oil commodity

Explanation: The relationship of RVs were captured for these selected currency pairs because of their stronger connection with the commodity during the data period; perhaps, redoing the analysis with a larger dataset will yield the RV relationships with other expected commodity currency-pairs