参与约束下的投资组合优化 [英] Portfolio Optimisation under participation constraints
问题描述
我正在尝试通过优化投资组合以在资产参与约束下实现最小方差来找到套期保值比率。最终，我想针对其他风险度量（例如最小CVaR，VaR或最大收益/风险）优化资产权重。
I am trying to find a set of hedge ratios by optimising a portfolio for minimum variance under participation constraints of the assets. Ultimately I would like to optimise the assets weights for other measures of risk such as minimum CVaR, VaR or maximum return/risk.
我的投资组合包括9个系列。 1个国内资产和4个以0％货币对冲的国际资产：
My portfolio comprises 9 series. 1 domestic asset and 4 international assets which are 0% currency hedged:
"D_Asset1","F_Asset2","F_Asset3","F_Asset4","F_Asset5"
对于那些100％货币对冲的货币，我也有系列：
I have also series for those that are 100% currency hedged:
"H_F_Asset2","H_F_Asset3","H_F_Asset4","H_F_Asset5"
投资组合资产权重之和应等于1，且仅做多（即无杠杆/空头），国内资产权重为60％ 。另一资产将具有组约束，以便对冲资产和未对冲资产的总和等于固定目标权重（即我的基准中的权重）。组约束定义为：
The sum of the portfolio asset weights should be equal to one and long only (i.e no leverage / shorting), the domestic asset will have a weight of 60 %. The other asset will have group constraints so that the sum of the hedged and unhedged asset equal a fix target weight (i.e the weight in my benchmark). The group constraints are defined as:
("F_Asset2"+"H_F_Asset2") = 0.2 & ("F_Asset2"+"H_F_Asset2") >= 0
("F_Asset3"+"H_F_Asset3") = 0.1 & ("F_Asset3"+"H_F_Asset3") >= 0
("F_Asset4"+"H_F_Asset4") = 0.05 & ("F_Asset4"+"H_F_Asset4") >= 0
("F_Asset5"+"H_F_Asset5") = 0.05 & ("F_Asset5"+"H_F_Asset5") >= 0
因此，我应该能够得出权重通过查看每个未对冲/对冲组中优化权重的比例来优化我的每项资产的对冲比率。我尝试将其编码如下：
Therefore I should be able to derive through the weights optimisation the hedge ratio for each of my assets by looking at the proportionality of the optimised weights in each unhedged/hedged groups. I have tried to code this as follows:
opt_data <- as.timeSeries(Asset_returns[,c"D_Asset1","F_Asset2","F_Asset3","F_Asset4","F_Asset5","H_F_Asset2","H_F_Asset3","H_F_Asset4","H_F_Asset5")])
spec <- portfolioSpec()
setSolver(spec) <- "solveRquadprog"
cons <- c("eqsumW['D_Asset1']=0.6","eqsumW[c('F_Asset2','H_F_Asset2')]=0.2","eqsumW[c('F_Asset3','H_F_Asset3')]=0.1","eqsumW[c('F_Asset4','H_F_Asset4')]=0.05","eqsumW[c('F_Asset5','H_F_Asset5')]=0.05")
portfolioConstraints(list(mu=apply(opt_data,2,function(x) mean(x)),sigma=cov(opt_data)), spec,cons)
minriskPortfolio(list(mu=apply(opt_data,2,function(x) mean(x)),sigma=cov(opt_data),spec,constraints = cons)
这似乎不起作用，因为我的资产总和最终分配给了对冲资产4（0.3809 ）5（0.6191）只是不重视其他资产组的固定权重...所以我显然做错了事。以下是在运行以下数据示例的脚本时获得的打印结果。
This does not seem to work as the sum of my assets end up being allocated to the hedged asset 4 (0.3809) an 5 (0.6191) only an the fixed weight for the other group of assets is not respected...so I am obviously doing something wrong. Below is the print i get when running my script forr the below data sample.
Title:
MV Minimum Risk Portfolio
Estimator: covEstimator
Solver: solveRquadprog
Optimize: minRisk
Constraints: LongOnly
Portfolio Weights:
D_Asset1 F_Asset2 F_Asset3 F_Asset4 F_Asset5 H_F_Asset2 H_F_Asset3
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
H_F_Asset4 H_F_Asset5
0.3809 0.6191
Covariance Risk Budgets:
D_Asset1 F_Asset2 F_Asset3 F_Asset4 F_Asset5 H_F_Asset2 H_F_Asset3
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
H_F_Asset4 H_F_Asset5
0.3809 0.6191
Target Return and Risk:
[1] -0.0052
Description:
Thu Oct 27 13:53:36 2016 by user: 43951663
我的系列如下：
GMT
D_Asset1 F_Asset2 F_Asset3 F_Asset4 F_Asset5 H_F_Asset2 H_F_Asset3 H_F_Asset4 H_F_Asset5
2002-07-05 0.0060728958 -0.013756357 -0.011423593 0.0134417810 -0.0003016946 -0.0009105038 -0.0018985396 0.014808963 -0.003882658
2002-07-12 -0.0897779000 -0.085188382 -0.089815019 -0.0138095353 -0.0762572363 -0.0685047064 -0.0832575916 -0.022109799 -0.047944944
2002-07-19 -0.0943660524 -0.046920616 -0.030421831 -0.0382901308 -0.0624865993 -0.0794080445 -0.0524289818 -0.031577514 -0.041396426
2002-07-26 0.0133063390 -0.057651106 -0.020437497 -0.0728233620 -0.0456981099 0.0064529146 -0.0396719802 -0.054443226 -0.024872592
2002-08-02 0.0112493491 0.009167815 0.016499805 0.0103302726 0.0252948946 0.0143938534 0.0118099642 0.014237543 0.026552984
2002-08-09 0.0802254120 0.067077593 0.057022734 0.0469759343 0.0558895137 0.0513020851 0.0548215098 0.029355000 0.019311812
2002-08-16 0.0121210802 0.004739185 0.002730157 -0.0071254354 -0.0147625074 0.0220800644 -0.0005414763 -0.017939892 -0.013482516
2002-08-23 0.0254279436 0.028461524 0.013045475 0.0007546919 0.0223311149 0.0133616906 0.0279480422 0.005884930 0.008278473
2002-08-30 -0.0478436889 -0.049203575 -0.039813657 -0.0356601715 -0.0256056009 -0.0276201640 -0.0386866322 -0.025089402 -0.004296057
2002-09-06 -0.0320257540 -0.038044390 -0.028008660 -0.0577045132 -0.0281928317 -0.0252990267 -0.0312053440 -0.049959243 -0.021289249
2002-09-13 -0.0005754118 -0.031013743 -0.024805745 -0.0045048220 -0.0035485481 -0.0055489175 -0.0259398560 0.017170857 0.004670684
2002-09-20 -0.0544596063 -0.049806038 -0.037835532 0.0040695629 -0.0467206777 -0.0523013152 -0.0589901499 0.020442551 -0.049443302
2002-09-27 -0.0264640157 0.003081610 0.011115685 0.0119000112 -0.0229705875 -0.0220045767 0.0091850943 0.009544600 -0.014769134
2002-10-04 -0.0350683237 -0.044400596 -0.026363396 -0.0591064104 -0.0404089273 -0.0317751096 -0.0394601664 -0.049204737 -0.028352867
2002-10-11 0.0455968470 0.047623114 0.034835901 -0.0516194024 0.0202454036 0.0435196284 0.0364044803 -0.047211423 0.013827130
2002-10-18 0.0682138514 0.050215807 0.044584318 0.0531850741 0.0789798029 0.0584691831 0.0566157920 0.055481410 0.060939407
2002-10-25 0.0112759198 -0.016565486 -0.019723747 -0.0234843100 0.0107604217 0.0149227748 -0.0177273307 -0.028938189 0.010213889
2002-11-01 -0.0040060015 0.012830724 -0.013284706 0.0043773949 -0.0193135586 0.0053397013 0.0007975884 -0.003459391 -0.015845981
2002-11-08 -0.0235192733 -0.004405182 0.008119140 -0.0033849145 -0.0101840271 -0.0059125661 -0.0036278513 -0.004716045 0.011824785
2002-11-15 0.0227169708 0.027997661 0.013501476 -0.0219131086 0.0096590849 0.0160309555 0.0242988333 -0.022932122 0.014512210
2002-11-22 0.0237869242 0.018522337 0.020965808 0.0062667869 0.0233331986 0.0242851881 0.0316120790 0.026096681 0.019139845
我很乐意使用另一个优化器，只要它位于R中并允许我处理其他风险度量，例如CVaR，VaR等...任何解决此问题的想法都会对我和这个论坛上的其他人。
I would be quite happy to use another optimiser as long it is in R and allows me to handle other measure of risk such as CVaR, VaR etc...Any idea on how to solve for this problem would be really helpful to me and probably others on this forum.
推荐答案
您的代码中有错别字。查看以下几行？
There are typos in your code. Review the following lines?
opt_data <- as.timeSeries(Asset_returns[,c("D_Asset1","F_Asset2","F_Asset3","F_Asset4","F_Asset5","H_F_Asset2","H_F_Asset3","H_F_Asset4","H_F_Asset5")])
上等缺点：
cons <- c("eqsumW['D_Asset1']=0.6","maxsumW[c('F_Asset2','H_F_Asset2')]=0.2","maxsumW[c('F_Asset3','H_F_Asset3')]=0.1","maxsumW[c('F_Asset4','H_F_Asset4')]=0.05","maxsumW[c('F_Asset5','H_F_Asset5')]=0.05")
我得到了：
minriskPortfolio(list(mu=apply(opt_data,2,function(x) mean(x)),sigma=cov(opt_data)),spec,constraints = cons)
Title:
MV Minimum Risk Portfolio
Estimator: covEstimator
Solver: solveRquadprog
Optimize: minRisk
Constraints:
Portfolio Weights:
D_Asset1 F_Asset2 F_Asset3 F_Asset4 F_Asset5 H_F_Asset2 H_F_Asset3
0.6000 0.0308 0.1000 0.0000 0.0000 0.1692 0.0000
H_F_Asset4 H_F_Asset5
0.0500 0.0500
Covariance Risk Budgets:
D_Asset1 F_Asset2 F_Asset3 F_Asset4 F_Asset5 H_F_Asset2 H_F_Asset3
0.6932 0.0283 0.0762 0.0000 0.0000 0.1557 0.0000
H_F_Asset4 H_F_Asset5
0.0172 0.0294
Target Return and Risk:
[1] -0.0043
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