Following one of my previous questions on portfolio optimisation I have now tried to solve for the weights which minimise the variance of my portfolio under a set of constraints on a rolling basis. This seems to works most of the time but on some occasions no weights are being returned. I isolated some of those cases and tried to solve them on excel. Using the exact same data I do get a solution in excel. So I am a bit confused by all this. Anyhow I have posted a small sample of data where my script returns a zero weights vector in R but for which I get a solution in excel.
GBP-U USD-U EUR-U JPY-U CHF-U USD-H EUR-H JPY-H CHF-H 2016-05-13 0.0013866228 -0.0004015032 0.0023176509 0.004868271 0.0230163636 -0.0046939993 0.0065432710 0.0146679154 0.022040377 2016-05-20 0.0027094242 -0.0063831791 -0.0126106089 -0.006146676 -0.0158351590 0.0031237903 0.0045931268 0.0173505502 0.008964457 2016-05-27 0.0181190929 0.0140661262 0.0099806390 -0.005023782 0.0206840583 0.0223892121 0.0282165690 0.0048453909 0.033676661 2016-06-03 -0.0102711128 0.0081653966 0.0133194563 0.031814348 0.0092257881 0.0009701383 -0.0161380212 -0.0101505102 -0.016812484 2016-06-10 -0.0144639135 0.0160062120 -0.0152727781 0.008429249 0.0015983898 -0.0021260494 -0.0229890046 -0.0054785155 -0.027628141 2016-06-17 -0.0152295990 -0.0183599416 -0.0266861641 -0.039472434 -0.0286395252 -0.0112888146 -0.0217678087 -0.0589147494 -0.026415992 2016-06-24 0.0200253356 0.0317549413 0.0346147227 0.029164922 0.0401491058 -0.0166789670 0.0006268938 -0.0379679346 0.004386684 2016-07-01 0.0696777854 0.0620232077 0.0754752233 0.065465564 0.0704656764 0.0314514909 0.0433540129 0.0379248977 0.041482495 2016-07-08 0.0016753950 0.0369097752 0.0076117981 0.007834512 0.0070165833 0.0130392554 -0.0084350439 -0.0354380321 -0.006380199 2016-07-15 0.0118593292 -0.0037643046 0.0058939005 0.028278185 -0.0020681743 0.0144418213 0.0257127861 0.0888542585 0.015778875 2016-07-22 0.0092918745 0.0130552307 0.0086318585 0.001398931 0.0062780458 0.0067460116 0.0077586182 0.0070486894 0.004685162 2016-07-29 -0.0004646661 -0.0094042916 0.0124831676 0.025141288 0.0018086154 -0.0002180359 0.0040494413 -0.0046691781 -0.006745367 2016-08-05 0.0101311910 0.0160368778 0.0045395343 -0.014712256 0.0081973627 0.0040861320 0.0006639525 -0.0289135714 0.007984259 2016-08-12 0.0177313054 0.0125451367 0.0377475690 0.050109303 0.0322171465 0.0007342288 0.0192744848 0.0332886266 0.014216897 2016-08-19 -0.0086591802 -0.0121869847 -0.0131592756 -0.018946998 -0.0182591489 -0.0003056645 -0.0156054036 -0.0176744155 -0.020491089 2016-08-26 -0.0032629188 -0.0112907806 -0.0099742141 -0.028672792 -0.0178773544 -0.0066076557 0.0061594585 -0.0078421386 0.005324054 2016-09-02 0.0082322936 -0.0063800658 -0.0012434593 0.010783580 0.0006709931 0.0054516933 0.0145201246 0.0429479722 0.015518353 2016-09-09 -0.0172703615 -0.0222186855 -0.0031692051 0.014054238 0.0031503483 -0.0243009678 -0.0119551411 0.0001827415 -0.004089906 2016-09-16 -0.0105444978 0.0257113060 -0.0072348498 -0.002332981 -0.0002596633 0.0054847746 -0.0203191336 -0.0263452760 -0.015320125 2016-09-23 0.0294827487 0.0150126367 0.0358026791 0.041563858 0.0298489405 0.0121889694 0.0268098637 0.0263689159 0.017033142 2016-09-30 -0.0010620124 0.0010033756 -0.0058345738 -0.025319672 -0.0159143301 0.0014163678 -0.0060494835 -0.0215285310 -0.014212323 2016-10-07 0.0213392520 0.0351900327 0.0426486765 0.047394294 0.0333505051 -0.0072195144 0.0034453853 0.0210516899 -0.002539864 2016-10-14 -0.0050982217 0.0095672058 0.0009866843 0.004577971 0.0035956430 -0.0102205657 0.0020303997 -0.0035136735 -0.002926098 2016-10-21 0.0002873986 0.0004041448 -0.0029951394 0.012861688 -0.0135120432 0.0038727554 0.0087025204 0.0127856995 -0.006358163 2016-10-28 -0.0039917961 -0.0029823347 0.0078312950 0.013806532 -0.0053670019 -0.0070482290 -0.0052953175 0.0188646173 -0.014826428 My script is as per the below:
require(fPortfolio) spec <- portfolioSpec() mydata <- as.timeSeries(mydata) cons <- c("eqsumW=1","eqsumW['GBP-U']=0.6" ,"eqsumW[c('USD-U','USD-H')]=0.20","eqsumW[c('EUR-U','EUR-H')]=0.10","eqsumW[c('JPY-U','JPY-H')]=0.05","eqsumW[c('CHF-U','CHF-H')]=0.05","LongOnly") minvariancePortfolio(list(mu=apply(mydata,2,function(x) mean(x)),sigma=cov(mydata)), spec = spec, constraints = cons) Running this on the above data gets me the following:
Title: MV Minimum Variance Portfolio Estimator: covEstimator Solver: solveRquadprog Optimize: minRisk Constraints: LongOnly Portfolio Weights: GBP-U USD-U EUR-U JPY-U CHF-U USD-H EUR-H JPY-H CHF-H 0 0 0 0 0 0 0 0 0 Covariance Risk Budgets: GBP-U USD-U EUR-U JPY-U CHF-U USD-H EUR-H JPY-H CHF-H Target Return and Risk: [1] 0 Description: Mon Oct 31 11:26:35 2016 by user: 43951663 When running the optimisation for the same constraints and data with the excel solver I get the following solution:
Constraints GBP 0.6000 USD 0.2000 EUR 0.1000 JPY 0.0500 CHF 0.0500 Portfolio 1.0000 Weights GBP-U USD-U EUR-U JPY-U CHF-U USD-H EUR-H JPY-H CHF-H 0.6000 0.0000 0.0000 0.0423 0.0000 0.2000 0.1000 0.0077 0.0500 Portfolio Stdev 0.01562 Portfolio Mean 0.00424 Any idea on where I get it wrong ? I assume it maybe linked to some of the initial settings of the the solver in spec <- portfolioSpec(), but I am running out of ideas...
