# R returns numeric(0) when putting p=0.995 for calculating VaR

My code actually works just fine. What I don't understand is, if I put p=0.995 instead of 0.95, the console gives me numeric(0). What can cause this error? However, when I use "gaussian" method, it works just fine.

The function tries to calculate the Value at Risk at the probability level of 99.5%. At 95% the function works as it should. You can reconstruct using the following code.

Thanks!

VaR(bonds.returns,p=0.995, weights= weights,portfolio_method = "component", method="historical")


bonds.returns

   structure(c(0.0075452479085516, -0.000430602750240983, -0.000618087487474384,
0.00222086866888427, 0.0106496372204352, 0.00136921667853951,
0.00423968343697001, 0.0024904263575809, -0.000195676402276579,
0.000280808046426939, 0.00478090360779571, 0.0034797185745854,
0.00730203951222119, -0.000343622174203362, -0.00819027347184287,
-0.00430557592076686, 0.0121157759451644, 0.00511236623854172,
0.00632861635220117, 0.00281239014100998, -0.000272659992988644,
0.00102275383776207, 0.00580914478101358, 0.00408258034556819,
0.00683299709040042, 0.00444050627813075, 0.00112276199450645,
-0.00105140888790989, 0.00547308066278407, 0.00292103243043851,
0.000354539209820759, 0.000498394063572771, 0.000774893452150316,
0.00578507825894592, 0.00786336442020064, 0.00264068177602228,
0.0044426685809873, 0.00123386036476414, 0.000437716332879923,
0.00273957849531858, 0.00459152849567035, 0.00344127119889892,
0.00372234677044103, 0.00235998145728855, -0.000988017658188123,
0.000196396130996312, 0.00448116019271083, 0.00288335334692413,
0.00421227034351057, 0.00228605784355529, -0.00052312928966014,
0.00158416670737593, 0.00452201783723516, 0.0028924387350957,
0.00519960504742145, 0.00304595059792567, 0.00181483311621222,
0.00192813007255133, 0.00722328637152936, 0.00474544339681326,
0.00443227606157648, 0.00133718717534648, -5.13615959075731e-05,
-0.00041091387245229, 0.00307284387075546, 0.00220280114340743,
0.00575621301775153, 0.00313461918612856, -0.000187677120282226,
0.000272182906913443, 0.00450387051372281, 0.00321330157395727,
0.0056956454201833, 0.00323328013180268, 0.000923749602274482,
0.00117925737548585, 0.00519286314193823, 0.00386179068890669,
0.00449726636750203, 0.00136557388242409, 6.81855816717647e-05,
-9.74013324506195e-06, 0.00322401550644313, 0.00166993533855031,
0.00521548174581388, 0.0035394698147293, -0.000146521679975864,
0.000879258910347014, 0.00566832951610041, 0.00377491914601547,
0.00289058379650298, -0.00118324046075591, 8.10011745171479e-05,
-0.000577086623739564, 0.0027756673251278, 0.00217195850043939,
0.00844551759115331, 0.00488711529000163, 0.000326399164418012,
0.0021100258858846, 0.00678345055135887, 0.00597233751253223,
0, -0.00294687131050764, -0.0124380701571574, -0.00119904076738608,
0.00780792316926782, -0.00107682631649164, 0.00416801143436785,
0.00224983241044274, -5.49742537244713e-05, 0.000394003811757804,
0.00469870579507048, 0.00247967034970653, 0.00207520724910104,
0.00483573674509374, 0.000787690448444067, 0.00624265490733067,
0.00121078347334125, -0.00618572147130281, 0.00466954738246472,
0.00228923662382208, -0.00131503490280616, -0.000811840997970381,
0.00319055121231049, 0.00204454540964982, 0.000172922203210746,
0.0043951044178534, 0.00170323796408711, -0.000533617929562413,
0.000841575646791437, 0.0009493670886076, 0.00477505036185932,
0.00240800263076935, 0.00104766339315954, 0.000909138960833111,
0.00509077850888784, 0.00328909345018547, 0.00160412259506937,
0.00107103890774041, 0.00254974502549743, 0.000578467062284815,
0.00337908555366173, -0.00140072718602857, 0.00422467406148375,
0.00172189447526239, -0.000234400179706773, -0.000341913740047883,
0.00276556239616932, 0.00202703361172563), .indexCLASS = "Date", tclass = "Date", .indexTZ = "UTC", tzone = "UTC", class = c("xts",
"zoo"), index = structure(c(1491177600, 1491264000, 1491350400,
1491436800, 1491523200, 1491782400), tzone = "UTC", tclass = "Date"), .Dim = c(6L, 25L), .Dimnames = list(NULL, c("BE0000343526", "BE6248644013",
"FR0010171975", "FR0013152907", "IE00BV8C9186", "SI0002103677",
"XS0162513211", "XS0162869076", "XS0162990229", "XS0908570459",
"XS1117298247", "XS1146286205", "XS1196380031", "XS1196817586",
"XS1200679667", "XS1202849086", "XS1203860934", "XS1313004928",
"XS1362373224", "XS1388864503", "XS1405784015", "XS1418788599",
"XS1463101680", "XS1538284230", "XS1570260460")))


weights

c(0.039728041, 0.040869022, 0.042067239, 0.039212564, 0.039765805,
0.040603312, 0.041035065, 0.04158508, 0.039500351, 0.042032909,
0.040638835, 0.040266658, 0.040995045, 0.04002851, 0.040191534,
0.039809092, 0.039765018, 0.041233473, 0.04085667, 0.027147317,
0.041430642, 0.040688867, 0.040016652, 0.040498212, 0.040034086
)

• Where is the VaR function defined? – Bob Jansen Jul 26 '17 at 15:09
• I also get numeric(0) for 0.95... there must be sth else wrong... – vonjd Jul 26 '17 at 15:18

The problem arises due to your data. Some of your columns do not have a negative value in that percentile (check for example XS1463101680 and XS1203860934 -- all positives), thus historical VaR is meaningless (your losses cannot be a positive value, loss is always negative). Therefore, you will get an error.

Also, your code for p = 0.95 returns the same error.

EDIT

Unfortunately, this particular function will not work if you have less than 200 data observations (returns). Why? Well, having investigated the code, I found the following:

On the bottom of this page you can see the formula that is used to compute historical component VaR:

component = {
# @todo need to add another loop here for subsetting, I think, when weights is a timeseries
#if (mu=NULL or sigma=NULL) {
#     pfolioret = Return.portfolio(R, weights, wealth.index = FALSE, contribution=FALSE, method = c("simple"))
#}
# for now, use as.vector
weights=as.vector(weights)
names(weights)<-colnames(R)

switch(method,
modified = { return(VaR.CornishFisher.portfolio(p,weights,mu,sigma,m3,m4))},
gaussian = { return(VaR.Gaussian.portfolio(p,weights,mu,sigma)) },
historical = { return(VaR.historical.portfolio(R, p,weights)) },
kernel = { return(VaR.kernel.portfolio(R, p,weights)) }
)

}, # end component portfolio switch


Tracing back the function VaR.historical.portfolio, on the bottom of this page we observe:

VaR.historical.portfolio = function(R,p,w)
{
alpha = .setalphaprob(p)
portret = c();
T = dim(R)[1]
N = dim(R)[2]
for( t in c(1:T) ){
portret = c(portret,sum(w*as.numeric(R[t,])))
}
hVaR = -1* sort(portret)[floor(alpha*T)]
return(hVaR)
}


T = dim(R)[1] piece gives you the number of rows of your data. Your alpha is 1 - 0.995 or 0.005. Then you have this code floor(alpha*T) which is basically destroying everything as alpha*T is 0.76 and floor(0.76) is 0. And sort(portret)[0] returns numeric(0).

The function works for p = 0.95 because your alpha is 0.05 and 102 * 0.05 = 5.1 and floor(5.1) = 5 so you're getting the fifth element as your historical component VaR.

• hey AK88, this is due to subsetting my data so I can post it in here. My original dataset is a lot longer and it sure has negative returns in them. Do you think maybe 99.5% doesn't have any negative values, but 95% does. Therefore the output can't calculate? But this still doesn't make sense. Historical VaR sorts all returns and calculates where that 5% is at. Can't VaR also measure all positive returns? – purpleblau Jul 27 '17 at 6:24
• I have another observation here. I calculated individual VaR using this: VaR(bonds.returns,p=0.995, weights= NULL,portfolio_method = "single", method="historical"), it worked fine! The output gave me a VaR of each single data column. This means my data shouldn't have any problems. Only when calculating the portfolio VaR it throws this error. – purpleblau Jul 27 '17 at 6:28
• Can you post your full data? – AK88 Jul 27 '17 at 6:55
• It's too big to paste in here. It doesn't allow me to. XS1463101680 sure has negative values. Every data column contains negative values. It's all real market data. All other methods worked except for historical in portfolio mode. – purpleblau Jul 27 '17 at 7:05
• Also very odd, if you do ?VaR, the explanation about the methods is missing. But I found it in here: link, if you look at that quantile function. VaR=quantile(-R,p) – purpleblau Jul 27 '17 at 7:07