GOLD & NYSE – Volatility & Market Return relationship Vishal Jagtap ESG1012057

Problem Definition To find out the relationship between gold price returns & NYSE returns To find whether the relationship between GOLD & NYSE volatility patterns. Is there any spill over of volatility from either markets to each other?

Data Source Gold World Council Yahoo Finance

Univariate Analysis - NYSE First check ACF on NYSE past returns If there is ACF then GARCH can be used! acfnyse=acf(NyseGold[["NYSE"]]^2,50)

GARCH on NYSE Formulate the AR(1) + GARCH(1,1) model on NYSE nyse.fit=garch(NyseGold[["NYSE"]]~-1+ar(1),~garch(1,1)) Result – Univariate model built !

GARCH on NYSE- Rt, Sigma.t Volatility Returns

Univariate Analysis - GOLD First check ACF on GOLD past returns If there is ACF then GARCH can be used! acfgold=acf(NyseGold[[“GOLD"]]^2,50)

GARCH on GOLD Formulate the AR(1) + GARCH(1,1) model on GOLD gold.fit=garch(NyseGold[[“GOLD"]]~-1+ar(1),~garch(1,1)) Result – Univariate model built !

GARCH on GOLD- Rt, Sigma.t Volatility Returns

Multivariate Model Estimate Multivariate GARCH model for GOLD/USD and NYSE/USD long term returns Model type: BEKK nyse.gold=cbind(NyseGold[["NYSE"]],NyseGold[["GOLD"]]) nyse.gold.mgarch=mgarch(nyse.gold~-1+ar(1),~bekk(1,1))

Multivariate Model Summary

Series & Sigma Predictions-1Day predict(nyse.gold.mgarch,1) $series.pred: [,1] [,2] [1,] -0.0002945477 -0.00002440113 $sigma.pred: [,1] [,2] [1,] 0.01980845 0.01667906 $R.pred: , , 1 [,1] [,2] [1,] 1 -0.020587 , , 2 [,1] [,2] [1,] -0.020587 1 Predict(nyse.fit,1)

Model Summary ARCH The previous shocks/news affect current market returns for both market Both markets have memory The shock in NYSE & Gold are negatively correlated. NYSE shock can affect GOLD market by -4.7% while GOLD news shock can affect NYSE market by -4 % GARCH Volatility in NYSE will spill over to GOLD market by 1.5% Volatility in GOLD will spill over to NYSE market by 1.1% Past volatility affects the present day volatility in both the markets Clearly, from volatility & returns chart the NYSE & GOLD are no more cross correlated. Need to find out more regimes to fine tune model Estimated Coefficients: -------------------------------------------------------------- Value Std.Error t value Pr(>|t|) AR(1; 1, 1) -0.0449175 0.0197992 -2.26865 2.336e-002  Insignificant AR(1; 2, 2) 0.0012733 0.0175224 0.07267 9.421e-001 A(1, 1) 0.0011962 0.0001234 9.69262 0.000e+000 A(2, 1) -0.0004793 0.0002440 -1.96383 4.964e-002  Insignificant A(2, 2) 0.0012385 0.0001175 10.54447 0.000e+000 ARCH(1; 1, 1) 0.2979970 0.0120898 24.64872 0.000e+000 ARCH(1; 2, 1) -0.0478967 0.0075150 -6.37352 2.137e-010 ARCH(1; 1, 2) -0.0409351 0.0131554 -3.11165 1.878e-003 ARCH(1; 2, 2) 0.2097110 0.0101576 20.64578 0.000e+000 GARCH(1; 1, 1) 0.9503682 0.0040171 236.58184 0.000e+000 GARCH(1; 2, 1) 0.0154081 0.0029255 5.26676 1.489e-007 GARCH(1; 1, 2) 0.0113266 0.0041957 2.69956 6.983e-003 GARCH(1; 2, 2) 0.9697143 0.0031189 310.91736 0.000e+000

Model - Volatility

Further Work Find regimes in both NYSE & GOLD data to formulate better model