## VAR BEKK GARCH (optimal weight, hedge ratio, and hedging)

Discussions of ARCH, GARCH, and related models

### VAR BEKK GARCH (optimal weight, hedge ratio, and hedging)

I have estimated a bivariate VAR BEKK GARCH model using two series: Return on CD (R_CD) and Return on CS (R_CS). Then, I am tried to compute the optimal weight, hedge ratio and hedging effectivness (as mentioned in this link: (as mentioned in the link: https://www.emerald.com/insight/content ... /full/html) for these two series in RATS 10. The output of our estimation is given bellow:
system(model=var1)
variables R_CD R_WTI
lags 1
det constant
end(system)
*
garch(p=1,q=1,model=var1,mv=bekk,pmethod=simplex,piters=10,robusterrors,rvectors=rdcc,hmatrices=hdcc)

Code: Select all
`MV-GARCH, BEKK - Estimation by BFGSConvergence in    72 Iterations. Final criterion was  0.0000076 <=  0.0000100With Heteroscedasticity/Misspecification Adjusted Standard ErrorsIrregular Data From 2019:01:04 To 2019:12:31Usable Observations                       248Log Likelihood                      1452.2309    Variable                        Coeff      Std Error      T-Stat      Signif************************************************************************************Mean Model(R_CD)1.  R_CD{1}                      -0.033481639  0.072957684     -0.45892  0.646292612.  R_WTI{1}                      0.022344460  0.025867675      0.86380  0.387698573.  Constant                      0.001052688  0.000421485      2.49757  0.01250488Mean Model(R_WTI)4.  R_CD{1}                       0.125284658  0.189327145      0.66174  0.508140195.  R_WTI{1}                     -0.016129370  0.062471479     -0.25819  0.796262026.  Constant                      0.001282165  0.001364289      0.93980  0.347318007.  C(1,1)                       -0.001501066  0.000619092     -2.42462  0.015324238.  C(2,1)                        0.000592884  0.003488902      0.16993  0.865061739.  C(2,2)                       -0.000000059  0.001107805 -5.36627e-05  0.9999571810. A(1,1)                        0.237719648  0.067333822      3.53046  0.0004148311. A(1,2)                        0.096203205  0.134880748      0.71325  0.4756933112. A(2,1)                        0.049170309  0.026700697      1.84154  0.0655429713. A(2,2)                       -0.134456462  0.133390725     -1.00799  0.3134594614. B(1,1)                        0.954266921  0.030796329     30.98639  0.0000000015. B(1,2)                        0.274165501  0.145133090      1.88906  0.0588834316. B(2,1)                       -0.027665158  0.006309282     -4.38483  0.0000116117. B(2,2)                        0.954812538  0.041762870     22.86271  0.00000000`

Code: Select all
`*Optimal weight and hedge ratio: dec rect[series] hedges(%nvar,%nvar)do i=1,%nvar   do j=1,%nvar     if i==j        nextset hedges(i,j) = hdcc(t)(i,j)/hdcc(t)(j,j)end do jend do idec rect[series] weights(%nvar,%nvar)do i=1,%nvar   do j=1,%nvar      if i==j         next      set weights(i,j) = \$(hdcc(t)(j,j)-hdcc(t)(i,j))/(hdcc(t)(i,i)-2*hdcc(t)(i,j)+hdcc(t)(j,j))*     * This constrains the positions to the range[0,1]*     set weights(i,j) = %min(1.0,%max(0.0,weights(i,j)))*  end do jend do i`

The problem is that when I wrote the code of the hedge ratios and the optimal weight, the software didn't show any output. what I should do after writing the code to obtain the output. kindly, help me!!

Posts: 10
Joined: Sat Jul 10, 2021 6:53 am

### Re: VAR BEKK GARCH (optimal weight, hedge ratio, and hedging

What output do you want? The hedge ratios and portfolio weights are full time series. The Sadorsky paper (which was probably used as a base for the paper you cited) does graphs of the hedge ratios and a table of the average (over time) of the portfolio weights and hedge ratios. Now the Sadorsky paper is doing a three-variable system, so it has six hedge ratios (each asset hedged with each other asset) while you would just have the two directions in the bivariate model, but otherwise the presentation would be similar.
TomDoan

Posts: 7147
Joined: Wed Nov 01, 2006 5:36 pm