1. GOLD & NYSE – Volatility & Market Return relationship
Vishal Jagtap
ESG

2. 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?

3. Data Source
Gold World Council
Yahoo Finance

4. 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)

5. 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 !

6. GARCH on NYSE- Rt, Sigma.t
Volatility
Returns

7. 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)

8. 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 !

9. GARCH on GOLD- Rt, Sigma.t
Volatility
Returns

10. 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))

11. Multivariate Model Summary

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

13. 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) e-002  Insignificant
AR(1; 2, 2) e-001
A(1, 1) e+000
A(2, 1) e-002  Insignificant
A(2, 2) e+000
ARCH(1; 1, 1) e+000
ARCH(1; 2, 1) e-010
ARCH(1; 1, 2) e-003
ARCH(1; 2, 2) e+000
GARCH(1; 1, 1) e+000
GARCH(1; 2, 1) e-007
GARCH(1; 1, 2) e-003
GARCH(1; 2, 2) e+000

14. Model - Volatility

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