I've been demonstrating how Wolfram Finance Platform could be used for Value at Risk (VaR) for a while now, but have only been showing single asset calculations like the following and then show EmpiricalDistribution, CombinedDistribution, etc..
InverseSurvivalFunction[EstimatedDistribution[FinancialData["AAPL", "Return", DatePlus[-365], "Value"],NormalDistribution[a, b]],0.95]
But that's quite boring, so I've looked around for a guide to portfolio VaR measurements and found this
http://www.math.nus.edu.sg/~urops/Projects/valueatrisk.pdf amongst other resources and built the following function:
multiAssetVaR[stocks_List, weights_List, buyDate_List,
estDist_: NormalDistribution[](*If no other distribution specified,
normal assumed*), conf_: 0.95(*risk level, default 0.95*)] :=
Module[{initialPrices, currentPrices, ratesOfReturn, rateWeights,
portRateOfReturn, stockReturns, varPortRateOfReturn, multiAssetVaR},
initialPrices =
Transpose[{Flatten[
ParallelMap[
FinancialData[#[[1]], "Price", {#[[2]]}, "Value"] &, {stocks,
buyDate} // Transpose]], weights}];
currentPrices =
Transpose[{ParallelMap[FinancialData[#, "Price"] &, stocks],
weights}];
ratesOfReturn =
Map[(Times @@ #[[2]] - Times @@ #[[1]])/Times @@ #[[1]] &,
Transpose[{initialPrices, currentPrices}]];
rateWeights =
Map[Times @@ #/Total[Times @@@ currentPrices] &, currentPrices];
portRateOfReturn = Total[Times @@@ {rateWeights, ratesOfReturn}];
stockReturns =
ParallelMap[
FinancialData[#[[1]], "Return", {#[[2]], Date[]}, "Value"] &,
Transpose[{stocks, buyDate}]];
varPortRateOfReturn =
rateWeights.Covariance[
Transpose[stockReturns]].Transpose[{rateWeights}];
multiAssetVaR = (InverseSurvivalFunction[estDist, conf]*(-1))*
Sqrt[varPortRateOfReturn]
]
Usage:
multiAssetVaR[{"LLOY.L", "BARC.L", "RBS.L"}, {2000, 1423, 1000}, {{2012, 11, 1}, {2012, 11, 1}, {2012, 11, 1}}]
I've only limited experience with actually applying financial models, could anyone advise whether what I've done is appropiate?
Comments on the code would also be appreciated, I used ParallelMap for FinancialData calls to reduce the lag in collecting data (my birthday was chosen for the purchase dates at DayOfWeek told me it was a Thursday) but have assumed parallelisation is not beneficial for the rest of the maps. Note that if I had a Bloomberg subscription myself then I'd use BloombergLink, but at the moment I just have FinancialData.
