Relationship Between Commodities and Currency Pair Realized Variance Derrick Hang Econ 201FS April 28, 2010

Agenda Last time… “HAR-RV” Regressions Bayesian Analysis Conclusions

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 18 th : 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” Analysis Commodity Regressor: Gold * AUDUSDCHFUSDEURUSDGBPUSDJPYUSD β4β β 4 P-value NZDUSDCADUSDNOKUSDZARUSD β4β β 4 P-value

“HAR-RV” Analysis Commodity Regressor: Oil * AUDUSDCHFUSDEURUSDGBPUSDJPYUSD β4β β 4 P-value NZDUSDCADUSDNOKUSDZARUSDCADJPY β4β β 4 P-value

“HAR-RV” Analysis Commodity Regressor: Gold * Indicates significance at 0.05 level AUDUSD w/ RV com ZARUSDZARUSD w/ RV com α β1β *0.4011* β2β β3β β4β * * P-value of F-Test R2R

“HAR-RV” Analysis Commodity Regressor: Oil * Indicates significance at 0.05 level CADUSDCADUSD w/ RV com CADJPYCADJPY w/ RV com α β1β β2β β3β β4β * * P-value of F-Test R2R

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

RV Bayesian Analysis Model Specifications ◦ Prior distribution: ◦ We must specify m t-1 and C t-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)

RV Bayesian Analysis Overview of updating equations to determine the posterior distribution Let signal be the coefficient variance Let noise be the observational variance

Posterior Kernel Density: CADUSD

Posterior Kernel Density: CADJPY

Posterior Kernel Density: AUDUSD

Posterior Kernel Density: ZARUSD

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