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

[HamaNadia]

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 BFGS
Convergence in    72 Iterations. Final criterion was  0.0000076 <=  0.0000100

With Heteroscedasticity/Misspecification Adjusted Standard Errors
Irregular Data From 2019:01:04 To 2019:12:31
Usable Observations                       248
Log Likelihood                      1452.2309

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
Mean Model(R_CD)
1.  R_CD{1}                      -0.033481639  0.072957684     -0.45892  0.64629261
2.  R_WTI{1}                      0.022344460  0.025867675      0.86380  0.38769857
3.  Constant                      0.001052688  0.000421485      2.49757  0.01250488
Mean Model(R_WTI)
4.  R_CD{1}                       0.125284658  0.189327145      0.66174  0.50814019
5.  R_WTI{1}                     -0.016129370  0.062471479     -0.25819  0.79626202
6.  Constant                      0.001282165  0.001364289      0.93980  0.34731800

7.  C(1,1)                       -0.001501066  0.000619092     -2.42462  0.01532423
8.  C(2,1)                        0.000592884  0.003488902      0.16993  0.86506173
9.  C(2,2)                       -0.000000059  0.001107805 -5.36627e-05  0.99995718
10. A(1,1)                        0.237719648  0.067333822      3.53046  0.00041483
11. A(1,2)                        0.096203205  0.134880748      0.71325  0.47569331
12. A(2,1)                        0.049170309  0.026700697      1.84154  0.06554297
13. A(2,2)                       -0.134456462  0.133390725     -1.00799  0.31345946
14. B(1,1)                        0.954266921  0.030796329     30.98639  0.00000000
15. B(1,2)                        0.274165501  0.145133090      1.88906  0.05888343
16. B(2,1)                       -0.027665158  0.006309282     -4.38483  0.00001161
17. 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
        next
set hedges(i,j) = hdcc(t)(i,j)/hdcc(t)(j,j)
end do j
end do i
dec 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 j
end 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!!

[TomDoan]

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.