在我的一个previous questions on portfolio optimisation之后，我现在尝试解决权重问题，这些权重在一组限制条件下最小化我的投资组合的方差。这似乎在大多数时间都有效，但在某些情况下不会返回任何重量。我隔离了一些这些案例并尝试在excel上解决它们。使用完全相同的数据我得到了excel的解决方案。所以我对此感到困惑。无论如何，我已经发布了一小部分数据样本，其中我的脚本在R中返回零权重向量，但我在excel中得到了一个解决方案。
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
我的脚本如下：
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)
在上述数据上运行此操作会得到以下结果：
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
使用excel解算器运行相同约束和数据的优化时，我得到以下解决方案：
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
我知道哪里弄错了？我假设它可能与spec＆lt; - portfolioSpec（）中的求解器的一些初始设置相关联，但我的想法已经用完......
答案 0 :(得分：0)
好的我觉得我已经部分解决了这个问题。似乎国内资产的约束率是60％。当我把它取下时，我得到的结果与在excel中运行优化时的结果完全相同。我认为在oprtimiser中有一些向上/向下触发这个...如果有人作为更好的答案，请让论坛知道，因为这可能是其他人感兴趣的。以下是有和没有60％约束的截图。
cons <- c("eqsumW[c('USDU','USDH')]=0.20","eqsumW[c('EURU','EURH')]=0.10","eqsumW[c('JPYU','JPYH')]=0.05","eqsumW[c('CHFU','CHFH')]=0.05")
> minvariancePortfolio(list(mu=apply(mydata,2,function(x) mean(x)),sigma=cov(mydata)), spec = portfolioSpec() , constraints = cons)
Title:
MV Minimum Variance Portfolio
Estimator: covEstimator
Solver: solveRquadprog
Optimize: minRisk
Constraints:
Portfolio Weights:
GBPU USDU EURU JPYU CHFU USDH EURH JPYH CHFH
0.6000 0.0000 0.0000 0.0423 0.0000 0.2000 0.1000 0.0077 0.0500
Covariance Risk Budgets:
GBPU USDU EURU JPYU CHFU USDH EURH JPYH CHFH
0.6927 0.0000 0.0000 0.0454 0.0000 0.1098 0.0970 0.0082 0.0470
Target Return and Risk:
[1] 0.0042
Description:
Tue Nov 01 16:34:52 2016 by user: 43951663
>
> cons <- c("eqsumW['GBPU']=0.6" ,"eqsumW[c('USDU','USDH')]=0.20","eqsumW[c('EURU','EURH')]=0.10","eqsumW[c('JPYU','JPYH')]=0.05","eqsumW[c('CHFU','CHFH')]=0.05")
> minvariancePortfolio(list(mu=apply(mydata,2,function(x) mean(x)),sigma=cov(mydata)), spec = portfolioSpec() , constraints = cons)
Title:
MV Minimum Variance Portfolio
Estimator: covEstimator
Solver: solveRquadprog
Optimize: minRisk
Constraints:
Portfolio Weights:
GBPU USDU EURU JPYU CHFU USDH EURH JPYH CHFH
0 0 0 0 0 0 0 0 0
Covariance Risk Budgets:
GBPU USDU EURU JPYU CHFU USDH EURH JPYH CHFH
Target Return and Risk:
[1] 0
Description:
Tue Nov 01 16:35:57 2016 by user: 43951663
>
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