# [R-SIG-Finance] dynamic copula using rmgarch package (ignore previous question, don't know how to delete it)

Robert Iquiapaza rbali at ufmg.br
Thu Jun 23 21:02:23 CEST 2016

```Could you show how are you computing the return of an equally-weighted
portfolio and the VaR?
Robert

2016-06-22 16:36 GMT-03:00 Sachin Kuruvithadam <sacios at hotmail.it>:

> (there were some mistakes in the previous code, I've corrected it and I'm
> reposting)
>
>
> I'm trying to simulate 1-step ahead returns 5000 times for a portfolio of
> 9 variables. After specifying their GJR-GARCH specifications with SPD
> marginals, I use the following code (which was inspired by the examples in
> the 'rmgarch.tests' folder). I use the first 571x9 observations for fitting
> and the last 570 for out-of-sample analysis. Moreover, I use a
> moving-window approach, in the sense that I always use the last 571
> observations in the cgarchfilter rather than [1:(T+i)] as in the example.
> Once the simulated returns 'simx' are stored in 'simulatedreturns', I
> compute the return of an equally-weighted portfolio as a 570x5000 matrix,
> i.e. one series of return of each observation for each simulation. Last, I
> compute VaR (90%, 95%, 99%) as the respective quantile (0.10, 0.05, 0.01).
>
>
> My problem is that, contrary to the literature I've found on the topic,
> VaR is severely underestimated, I obtain a number of violations which is
> way more than expected (should be 57 for 90%VaR, 28 for 95%VaR, 6 for
> 99%VaR). Is there any error in the code I have below? I've followed the
> example by the letter and cannot understand what went wrong. Anyone can
> help? Any hint is GREATLY appreciated!
>
>
> library(rugarch)
> library(rmgarch)
>
> data(dji30retw)
> Dat = dji30retw[, 1:9, drop = FALSE]
>
> model <- ugarchspec(variance.model=list(model="gjrGARCH",
> garchOrder=c(1,1), variance.targeting=TRUE),
>                     mean.model=list(armaOrder=c(0,0), include.mean=F,
> archm=F, archpow=1),
>                     distribution.model="norm")
> spec = cgarchspec(uspec = multispec(replicate(9, model)), VAR = FALSE,
> robust = FALSE,
>                     lag.criterion = "AIC", external.regressors = NULL,
>                     dccOrder = c(1,1), asymmetric = TRUE,
> distribution.model = list(copula = "mvt",
>
>            method = "ML", time.varying = TRUE,
>
>            transformation = "spd"))
> fit = cgarchfit(spec, data = Dat, out.sample = 570, cluster = NULL,
> spd.control = list(lower = 0.1, upper = 0.9, type = "mle", kernel =
> "normal"),
>                   fit.control = list(eval.se=FALSE))
> T = dim(Dat)[1]-570
> simMu = simS = filtMu = filtS = matrix(NA, ncol = 9, nrow = 570)
> simCor = simC = filtC = filtCor = array(NA, dim = c(9,9,570))
> colSd = function(x) apply(x, 2, "sd")
> specx = spec
> for(i in 1:9) specx at umodel\$fixed.pars[[i]] = as.list(fit at model
> \$mpars[fit at model\$midx[,i]==1,i])
> setfixed(specx)<-as.list(fit at model\$mpars[fit at model\$midx[,10]==1,10])
>
> simulatedreturns <- array(dim=c(570,9,5000))
> for(i in 1:570){
>   if(i==1){
>     presigma = matrix(tail(sigma(fit), 1), ncol = 9)
>     prereturns = matrix(unlist(Dat[T, ]), ncol = 9, nrow = 1)
>     preresiduals = matrix(tail(residuals(fit),1), ncol = 9, nrow = 1)
>     preR = last(rcor(fit))[,,1]
>     diag(preR) = 1
>     preQ = fit at mfit\$Qt[[length(fit at mfit\$Qt)]]
>     preZ = tail(fit at mfit\$Z, 1)
>     tmp = cgarchfilter(specx, Dat[2:(T+1), ], filter.control = list(n.old
> = T))
>     filtMu[i,] = tail(fitted(tmp), 1)
>     filtS[i,] = tail(sigma(tmp), 1)
>     filtC[,,i] = last(rcov(tmp))[,,1]
>     filtCor[,,i] = last(rcor(tmp))[,,1]
>   } else{
>     presigma = matrix(tail(sigma(tmp), 1), ncol = 9)
>     prereturns = matrix(unlist(Dat[(T+i-1), ]), ncol = 9, nrow = 1)
>     preresiduals = matrix(tail(residuals(tmp),1), ncol = 9, nrow = 1)
>     preR = last(rcor(tmp))[,,1]
>     diag(preR) = 1
>     preQ = tmp at mfilter\$Qt[[length(tmp at mfilter\$Qt)]]
>     preZ = tail(tmp at mfilter\$Z, 1)
>
>     tmp = cgarchfilter(specx, Dat[(i+1):(T+i), ], filter.control =
> list(n.old = T))
>     filtMu[i,] = tail(fitted(tmp), 1)
>     filtS[i,] = tail(sigma(tmp), 1)
>     filtC[,,i] = last(rcov(tmp))[,,1]
>     filtCor[,,i] = last(rcor(tmp))[,,1]
>   }
>   sim = cgarchsim(fit, n.sim = 1, m.sim = 5000, startMethod = "sample",
> preR = preR, preQ = preQ, preZ = preZ,
>                     prereturns = prereturns, presigma = presigma,
> preresiduals = preresiduals, cluster = NULL)
>   simx = t(sapply(sim at msim\$simX, FUN = function(x) x[1,]))
>   simMu[i,] = colMeans(simx)
>   simC[,,i] = sim at msim\$simH[[1]][,,1]
>   simCor[,,i] = sim at msim\$simR[[1]][,,1]
>   simS[i,] = sqrt(diag(simC[,,i]))
>   simulatedreturns[i,,]=simx
> }
>
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>
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