CoCalc -- demo_cvxrPortfolioAnalytics.R

GitHub Repository: braverock/portfolioanalytics
Path: blob/master/demo/demo_cvxrPortfolioAnalytics.R
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## Running Times for the following code with an Intel(R)
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## Core(TM) i7-10750H Processor. Unless listed as follows, 
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## sections take less than 10 seconds:
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## Section  9.1:  3 min and 40 seconds
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## Section  9.2:  4 min and 50 seconds
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## Section 11.1:  1 min and 10 seconds
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## Section   12:  1 min and 16 seconds
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## Section 2
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library(PortfolioAnalytics)
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library(CVXR)
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library(data.table)
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library(xts)
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library(PCRA)
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## SECTION 2.3
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data(edhec)
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class(edhec)
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ret_edhec <- tail(edhec, 60) # Extract the last 5 years
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range(index(edhec)) # Start and end dates of `edhec`
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range(index(ret_edhec)) # Start and end dates of ret_edhec
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# names(edhec) # Names of `edhec` long, so use shorter names
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colnames(ret_edhec) <- c("CA", "CTAG", "DS", "EM", "EMN", "ED", "FIA", "GM", "LSE", "MA", "RV", "SS", "FF")
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print(head(ret_edhec, 5))
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tsPlotMP(ret_edhec, layout = c(2, 7))
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## SECTION 3.1
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# Create portfolio object
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fund_edhec <- colnames(ret_edhec)
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pspec_maxret <- portfolio.spec(assets = fund_edhec)
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# Add constraints to the portfolio object
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pspec_maxret <- add.constraint(pspec_maxret, type = "full_investment")
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pspec_maxret <- add.constraint(portfolio = pspec_maxret, type = "box",
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                               min = rep(0.02, 13),
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                               max = c(rep(0.15, 8), rep(0.1, 5)))
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# Add objective to the portfolio object
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pspec_maxret <- add.objective(portfolio = pspec_maxret, 
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                              type = "return", name = "mean")
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pspec_maxret
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## SECTION 3.2
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# Run the optimization with default solver
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opt_maxret <- optimize.portfolio(R = ret_edhec, portfolio = pspec_maxret, optimize_method = "CVXR")
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opt_maxret
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opt_maxret$solver
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# Run the optimization with a different solver
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opt_maxret_glpk <- optimize.portfolio(R = ret_edhec, portfolio = pspec_maxret, optimize_method = c("CVXR", "GLPK"))
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opt_maxret_glpk$solver
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class(opt_maxret)
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names(opt_maxret)
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opt_maxret$weights
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opt.outputMvo(opt_maxret, ret_edhec, digits =3)
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## SECTION 3.3
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bt_maxret <- optimize.portfolio.rebalancing(R = ret_edhec, portfolio = pspec_maxret,
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                                            optimize_method = "CVXR",
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                                            rebalance_on = "quarters", training_period = 36)
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names(bt_maxret)
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names(bt_maxret$opt_rebalancing)
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## SECTION 4.1
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# Create portfolio object
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pspec_gmv <- portfolio.spec(assets = fund_edhec)
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# Add full-investment constraint
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pspec_gmv <- add.constraint(pspec_gmv, type = "full_investment")
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# Add objective of minimizing variance
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pspec_gmv <- add.objective(portfolio = pspec_gmv, type = "risk", name = "var")
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opt_gmv <- optimize.portfolio(ret_edhec, pspec_gmv, optimize_method = "CVXR")
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opt.outputMvo(opt_gmv, ret_edhec, digits =3)
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## SECTION 4.2
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# portfolio object
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pspec_gmv <- add.constraint(pspec_gmv, type = "long_only")
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pspec_gmvGroup <- add.constraint(pspec_gmv, type = "group",
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                                 groups = list(groupA=1,
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                                               groupB=c(2:12),
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                                               groupC=13),
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                                 group_min = c(0, 0.05, 0.05),
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                                 group_max = c(0.4, 0.8, 0.5))
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pspec_gmvGroup <- add.constraint(pspec_gmvGroup, type = "return", return_target = 0.003)
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pspec_gmvGroup
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# optimization
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opt_gmvGroup <- optimize.portfolio(ret_edhec, pspec_gmvGroup,    optimize_method = "CVXR")
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opt.outputMvo(opt_gmvGroup, ret_edhec, digits =3)
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opt_gmvGroup_ecos <- optimize.portfolio(ret_edhec, pspec_gmvGroup, optimize_method = c("CVXR", "ECOS"))
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opt.outputMvo(opt_gmvGroup_ecos, ret_edhec, digits =3)
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opt_gmvGroup$solver
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opt_gmvGroup_ecos$solver
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## SECTION 5.1
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pspec_qu <- portfolio.spec(assets = fund_edhec)
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pspec_qu <- add.constraint(pspec_qu, type = "full_investment")
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pspec_qu <- add.constraint(pspec_qu, type = "long_only")
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# Add objectives
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pspec_qu <- add.objective(portfolio = pspec_qu, type = "return", name = "mean")
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pspec_qu <- add.objective(portfolio = pspec_qu, type = "risk", name = "var",
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                          risk_aversion = 20)
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## SECTION 5.2
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opt_qu <- optimize.portfolio(ret_edhec, pspec_qu, optimize_method = "CVXR")
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opt.outputMvo(opt_qu, ret_edhec, digits =3)
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## SECTION 6.1
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pspec_es <- portfolio.spec(assets = fund_edhec)
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pspec_es <- add.constraint(pspec_es, type = "full_investment")
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pspec_es <- add.constraint(pspec_es, type = "long_only")
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# Add objective of minimizing ES by using the default gamma
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pspec_gmes <- add.objective(portfolio = pspec_es, type = "risk", name = "ES") # Uses default tail probability 0.05
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# Add objective of minimizing ES by using the specific gamma=0.1
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pspec_gmes_1 <- add.objective(portfolio = pspec_es, type = "risk", name = "ES", arguments = list(p=0.1))
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## SECTION 6.2
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# GMES with default gamma=0.05
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opt_gmes <- optimize.portfolio(ret_edhec, pspec_gmes, optimize_method = "CVXR")
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opt_gmes
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# GMES with specific gamma=0.1
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opt_gmes_1 <- optimize.portfolio(ret_edhec, pspec_gmes_1, optimize_method = "CVXR")
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opt_gmes_1
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## SECTION 7.1
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pspec_csm <- portfolio.spec(assets = fund_edhec)
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pspec_csm <- add.constraint(pspec_csm, type = "full_investment")
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pspec_csm <- add.constraint(pspec_csm, type = "long_only")
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# Add objective of minimizing CSM
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pspec_mcsm <- add.objective(portfolio = pspec_csm, type = "risk", name = "CSM",
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                            arguments = list(p=0.05))
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## SECTION 7.2
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opt_mcsm <- optimize.portfolio(ret_edhec, pspec_mcsm, optimize_method = "CVXR")
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opt_mcsm
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## SECTION 8.1
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# Create portfolio object
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pspec_sr <- portfolio.spec(assets = fund_edhec)
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## Add constraints of maximizing Sharpe Ratio
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pspec_sr <- add.constraint(pspec_sr, type = "full_investment")
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pspec_sr <- add.constraint(pspec_sr, type = "long_only")
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## Add objectives of maximizing Sharpe Ratio
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pspec_sr <- add.objective(pspec_sr, type = "return", name = "mean")
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pspec_sr <- add.objective(pspec_sr, type = "risk", name = "var")
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# Optimization
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optimize.portfolio(ret_edhec, pspec_sr, optimize_method = "CVXR", maxSR = TRUE)
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## SECTION 8.2
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# Create portfolio object
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pspec_ESratio <- portfolio.spec(assets = fund_edhec)
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## Add constraints of maximizing return per unit ES
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pspec_ESratio <- add.constraint(pspec_ESratio, type = "full_investment")
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pspec_ESratio <- add.constraint(pspec_ESratio, type = "long_only")
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## Add objectives of maximizing return per unit ES
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pspec_ESratio <- add.objective(pspec_ESratio, type = "return", name = "mean")
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pspec_ESratio <- add.objective(pspec_ESratio, type = "risk", name = "ES", arguments = list(p=0.05))
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# Optimization
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optimize.portfolio(ret_edhec, pspec_ESratio, optimize_method = "CVXR", ESratio = TRUE)
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## SECTION 8.3
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# Create portfolio object
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pspec_CSMratio <- portfolio.spec(assets = fund_edhec)
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## Add constraints of maximizing return per unit CSM
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pspec_CSMratio <- add.constraint(pspec_CSMratio, type = "full_investment")
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pspec_CSMratio <- add.constraint(pspec_CSMratio, type = "long_only")
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## Add objectives of maximizing return per unit CSM
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pspec_CSMratio <- add.objective(pspec_CSMratio, type = "return", name = "mean")
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pspec_CSMratio <- add.objective(pspec_CSMratio, type = "risk", name = "CSM",
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                                arguments = list(p=0.05))
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# Optimization
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optimize.portfolio(ret_edhec, pspec_CSMratio, optimize_method = "CVXR", CSMratio = TRUE)
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## Section 9
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# Get daily returns of the 30 smallcap stocks
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library(PCRA)
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library(PortfolioAnalytics)
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library(xts)
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stocksCRSPdaily <- getPCRAData(dataset = "stocksCRSPdaily")
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smallcapTS <- selectCRSPandSPGMI(
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  periodicity = "daily",
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  stockItems = c("Date", "TickerLast", "CapGroupLast", "Return"),
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  factorItems = NULL,
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  subsetType = "CapGroupLast",
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  subsetValues = "SmallCap",
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  outputType = "xts")
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# find top 30 small cap stocks based on the market capitalization
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smallcapDT <- factorsSPGMI[CapGroupLast == "SmallCap"]
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scSize <- smallcapDT[, mean(LogMktCap), by = "TickerLast"]
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names(scSize)[2] <- "Size"
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scSize <- scSize[order(scSize$Size, decreasing = TRUE),]
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sc30largest <- scSize[,TickerLast][1:30]
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# daily return of top 30 stocks
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retD_CRSP <- smallcapTS[ , sc30largest]
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names(retD_CRSP)
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# monthly return of top 30 stocks needed for monthly rebalancing
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ep <- endpoints(retD_CRSP, on= "months", k=1)
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prod1 <- function(x){apply(x+1, 2, prod)}
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retM_CRSP <- period.apply(retD_CRSP, INDEX = ep, FUN = prod1) - 1
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## SECTION 9.1
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# Generate GMV, GMES and GMCSM portfolios
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pspec_sc <- portfolio.spec(assets = sc30largest)
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pspec_sc <- add.constraint(pspec_sc, type = "full_investment")
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pspec_sc <- add.constraint(pspec_sc, type = "long_only")
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pspec_GMV <- add.objective(pspec_sc, type = "risk", name = "var")
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pspec_GMES <- add.objective(pspec_sc, type = "risk", name = "ES")
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pspec_GMCSM <- add.objective(pspec_sc, type = "risk", name = "CSM")
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# Optimize Portfolio at Monthly Rebalancing and 500-Day Training
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bt.GMV <- optimize.portfolio.rebalancing(retD_CRSP, pspec_GMV,
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                                         optimize_method = "CVXR",
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                                         rebalance_on = "months",
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                                         rolling_window = 500)
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bt.ES <- optimize.portfolio.rebalancing(retD_CRSP, pspec_GMES,
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                                        optimize_method = "CVXR",
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                                        rebalance_on = "months",
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                                        rolling_window = 500)
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bt.CSM <- optimize.portfolio.rebalancing(retD_CRSP, pspec_GMCSM,
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                                         optimize_method = "CVXR",
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                                         rebalance_on = "months",
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                                         rolling_window = 500)
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# Extract time series of portfolio weights
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wts.GMV <- extractWeights(bt.GMV)
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wts.GMV <- wts.GMV[complete.cases(wts.GMV),]
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wts.ES <- extractWeights(bt.ES)
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wts.ES <- wts.ES[complete.cases(wts.ES),]
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wts.CSM <- extractWeights(bt.CSM)
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wts.CSM <- wts.CSM[complete.cases(wts.CSM),]
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# Compute cumulative returns of three portfolios
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GMV <- Return.rebalancing(retM_CRSP, wts.GMV)
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ES <- Return.rebalancing(retM_CRSP, wts.ES)
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CSM <- Return.rebalancing(retM_CRSP, wts.CSM)
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# Combine GMV, ES and CSM portfolio cumulative returns
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ret.comb <- na.omit(merge(GMV, ES, CSM, all=F))
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names(ret.comb) <- c("GMV", "GMES", "GMCSM")
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backtest.plot(ret.comb, colorSet = c("black", "darkblue", "darkgreen"), ltySet = c(3, 2, 1))
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## SECTION 9.2
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# Generate Sr, ESr and CSMr portfolios
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pspec_sc_ratio <- add.objective(pspec_sc, type = "return", name = "mean")
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pspec_Sr <- add.objective(pspec_sc_ratio, type = "risk", name = "var")
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pspec_ESr <- add.objective(pspec_sc_ratio, type = "risk", name = "ES")
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pspec_CSMr <- add.objective(pspec_sc_ratio, type = "risk", name = "CSM")
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# Optimize Portfolio at Monthly Rebalancing and 500-Day Training
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bt.Sr <- optimize.portfolio.rebalancing(retD_CRSP, pspec_Sr, maxSR = TRUE,
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                                        optimize_method = "CVXR",
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                                        rebalance_on = "months",
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                                        rolling_window = 500)
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bt.ESr <- optimize.portfolio.rebalancing(retD_CRSP, pspec_ESr,
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                                         optimize_method = "CVXR",
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                                         rebalance_on = "months",
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                                         rolling_window = 500)
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bt.CSMr <- optimize.portfolio.rebalancing(retD_CRSP, pspec_CSMr,
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                                          optimize_method = "CVXR",
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                                          rebalance_on = "months",
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                                          rolling_window = 500)
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# Extract time series of portfolio weights
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wts.Sr <- extractWeights(bt.Sr)
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wts.Sr <- wts.Sr[complete.cases(wts.Sr),]
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wts.ESr <- extractWeights(bt.ESr)
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wts.ESr <- wts.ESr[complete.cases(wts.ESr),]
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wts.CSMr <- extractWeights(bt.CSMr)
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wts.CSMr <- wts.CSMr[complete.cases(wts.CSMr),]
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# Compute cumulative returns of three portfolios
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Sr <- Return.rebalancing(retM_CRSP, wts.Sr, rebalance_on = "months")
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ESr <- Return.rebalancing(retM_CRSP, wts.ESr, rebalance_on = "months")
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CSMr <- Return.rebalancing(retM_CRSP, wts.CSMr, rebalance_on = "months")
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# Combine Sr, ESr and CSMr portfolio cumulative returns
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ret.comb.ratios <- na.omit(merge(Sr, ESr, CSMr, all=F))
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names(ret.comb.ratios) <- c("Sharpe ratio", "ES ratio", "CSM ratio")
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backtest.plot(ret.comb.ratios, colorSet = c("black", "darkblue", "darkgreen"), ltySet = c(3, 2, 1))
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## SECTION 10
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# monthly return of top 30 stocks in last 5 years
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ep <- endpoints(retD_CRSP, on= "months", k=1)
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prod1 <- function(x){apply(x+1, 2, prod)}
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retM_CRSP <- period.apply(retD_CRSP, INDEX = ep, FUN = prod1) - 1
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retM_CRSP_5 <- tail(retM_CRSP, 60)
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tsPlotMP(retM_CRSP_5, layout = c(2,15), yname = "RETURNS", 
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         stripText.cex = 0.7, axis.cex = 0.7)
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## SECTION 10.1
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# mean-var efficient frontier
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pspec_sc <- portfolio.spec(names(retM_CRSP_5))
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pspec_sc <- add.constraint(pspec_sc, type = "full_investment")
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pspec_sc <- add.constraint(pspec_sc, type = "long_only")
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meanvar.ef <- create.EfficientFrontier(R = retM_CRSP_5, 
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                                       portfolio = pspec_sc, type = "mean-StdDev")
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chart.EfficientFrontier(meanvar.ef, match.col = "StdDev", type = "l",
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                        chart.assets = FALSE, main = NULL,
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                        RAR.text = "Max Sharpe ratio", pch = 1)
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meanvar.ef$frontier[, 1:2]
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sr <- meanvar.ef$frontier[, 1]/meanvar.ef$frontier[, 2]
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maximumSR <- max(sr)
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meanMaxSR <-  meanvar.ef$frontier[, 1][sr == max(sr)]
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stdevMaxSR <- meanvar.ef$frontier[, 2][sr == max(sr)]
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dat <- (round(c(maximumSR, meanMaxSR, stdevMaxSR), 3))
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dat <- data.frame(dat)
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names(dat) <- NULL
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row.names(dat) <- c("maximum SR", "maxSRport Mean", "maxSRport Stdev")
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dat
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# Mean-StdDev Efficient Frontier
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pspec_MV <- add.objective(pspec_sc, type = "risk", name = "var")
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pspec_MV <- add.objective(portfolio = pspec_MV, type = "return", name = "mean")
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opt_MV <- optimize.portfolio(retM_CRSP_5, pspec_MV, optimize_method = "CVXR", maxSR = TRUE)
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opt.outputMvo(opt_MV, retM_CRSP_5, annualize = FALSE, digits = 3)
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pspec_sc_init <- portfolio.spec(assets = sc30largest)
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pspec_sc_init <- add.constraint(pspec_sc_init, type = "full_investment")
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# Portfolio with long-only constraints
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pspec_sc_lo <- add.constraint(portfolio = pspec_sc_init, type = "long_only")
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# Portfolio with long-only box constraints
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pspec_sc_lobox <- add.constraint(portfolio = pspec_sc_init, type = "box", 
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                                 min = 0.02, max = 0.1)
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# Portfolio with long-short box constraints
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pspec_sc_lsbox <- add.constraint(portfolio = pspec_sc_init, type = "box", 
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                                 min = -0.1, max = 0.1)
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# Combine the portfolios into a list
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portf_list <- combine.portfolios(list(pspec_sc_lo, pspec_sc_lobox, pspec_sc_lsbox))
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# Plot the efficient frontier overlay of the portfolios with varying constraints
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legend_labels <- c("Long Only", "Long Only Box (0.02,0.1)", "Long Short Box (-0.01,0.1)")
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chart.EfficientFrontierOverlay(R = retM_CRSP_5, portfolio_list = portf_list, 
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                               type = "mean-StdDev", match.col = "StdDev", 
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                               legend.loc = "bottomright", chart.assets = FALSE,
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                               legend.labels = legend_labels, cex.legend = 1,
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                               labels.assets = FALSE, lwd = c(3,3,3),
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                               col = c("black", "dark red", "dark green"),
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                               main = NULL,
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                               xlim = c(0.03, 0.11), ylim = c(0.005, 0.035))
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## SECTION 10.2
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# Mean-ES Efficient Frontier
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meanes.ef <- create.EfficientFrontier(R = retM_CRSP_5, portfolio = pspec_sc, type = "mean-ES")
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chart.EfficientFrontier(meanes.ef, match.col = "ES", type = "l",
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                        chart.assets = FALSE, main = NULL,
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                        RAR.text = "Max ES ratio", pch = 1)
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legend_labels <- c("Long Only ES (p=0.05)", 
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                   "Long Only Box ES (p=0.05)", "Long Short Box ES (p=0.05)")
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chart.EfficientFrontierOverlay(R = retM_CRSP_5, portfolio_list = portf_list, 
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                               type = "mean-ES", match.col = "ES",
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                               legend.loc = "bottomright", chart.assets = FALSE,
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                               legend.labels = legend_labels, cex.legend = 1,
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                               labels.assets = FALSE, lwd = c(3,3,3),
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                               col = c("black", "dark red", "dark green"),
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                               main = NULL,
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                               xlim = c(0.03, 0.17), ylim = c(0.005, 0.035))
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# Create long-only ES portfolios with different tail probabilities
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ES_05 <- add.objective(portfolio = pspec_sc_lo, type = "risk", name = "ES", 
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                       arguments = list(p=0.05))
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ES_10 <- add.objective(portfolio = pspec_sc_lo, type = "risk", name = "ES", 
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                       arguments = list(p=0.1))
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ES_15 <- add.objective(portfolio = pspec_sc_lo, type = "risk", name = "ES", 
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                       arguments = list(p=0.15))
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# Combine the portfolios into a list
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portf_ES_list <- combine.portfolios(list(ES_05, ES_10, ES_15))
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# Plot the efficient frontier overlay of the portfolios with varying tail probabilities
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legend_ES_labels <- c("ES (p=0.05)", "ES (p=0.1)", "ES (p=0.15)")
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chart.EfficientFrontierOverlay(R = retM_CRSP_5, portfolio_list = portf_ES_list, 
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                               type = "mean-ES", match.col = "ES", 
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                               legend.loc = "bottomright", chart.assets = FALSE,
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                               legend.labels = legend_ES_labels, cex.legend = 1,
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                               labels.assets = FALSE, lwd = c(3,3,3),
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                               col = c("black", "dark red", "dark green"),
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                               main = NULL,
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                               xlim = c(0.035, 0.165), ylim = c(0.005, 0.03))
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## SECTION 10.3
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# Mean-CSM Efficient Frontier
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meancsm.ef <- create.EfficientFrontier(R = retM_CRSP_5, portfolio = pspec_sc, 
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                                       type = "mean-CSM")
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chart.EfficientFrontier(meancsm.ef, match.col = "CSM", type = "l",
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                        chart.assets = FALSE, main = NULL,
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                        RAR.text = "Max CSM ratio", pch = 1)
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## SECTION 11.1
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args(chart.EfficientFrontierCompare)
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# Compare StdDev of minStd and minES portfolios with guideline
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chart.EfficientFrontierCompare(R = retM_CRSP_5, portfolio = pspec_sc, risk_type = "StdDev", match.col = c("StdDev", "ES"), lwd = c(2, 2), xlim = c(0.0,0.14), ylim = c(0.005,0.032))
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# Compare ES of minStd and minES portfolios with guideline
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chart.EfficientFrontierCompare(R = retM_CRSP_5, portfolio = pspec_sc, 
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                               risk_type = "ES", match.col = c("ES", "StdDev"), lwd = c(2, 2), 
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                               xlim = c(0.0,0.14), ylim = c(0.005,0.032))
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# Compare ES of minStd, minES and minCSM portfolios without guideline
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chart.EfficientFrontierCompare(R = retM_CRSP_5, portfolio = pspec_sc, 
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                               risk_type = "ES",match.col = c("StdDev", "ES", "CSM"), 
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                               guideline = FALSE, col = c("darkred","darkgreen","blue"), 
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                               lty = c("dotted", "solid", "dashed"), lwd = c(1, 1.5, 1.5))
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## SECTION 11.2
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minStdDev_port <- add.objective(pspec_sc, type = "risk", name = "StdDev")
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minStdDev_opt <- optimize.portfolio(retM_CRSP_5, minStdDev_port,
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                                    optimize_method = "CVXR")
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minStdDev_w <- minStdDev_opt$weight
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minES_port <- add.objective(pspec_sc, type = "risk", name = "ES")
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minES_opt <- optimize.portfolio(retM_CRSP_5, minES_port, 
498
                                optimize_method = "CVXR")
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minES_w <- minES_opt$weight
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# Extract risk StdDev portfolio
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extract_risk(retM_CRSP_5, minStdDev_w)
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# Extract risk ES portfolio
505
extract_risk(retM_CRSP_5, minES_w)
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508
minStdDev_opt_covRob <-optimize.portfolio(retM_CRSP_5,minStdDev_port,
509
                                          optimize_method =
510
                                            "CVXR", momentFUN = 'custom.covRob.Mcd')
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extract_risk(retM_CRSP_5, minStdDev_w, moment_setting =
512
               minStdDev_opt_covRob$moment_values)
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## SECTION 12
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517
# Compare mean-var frontiers with classic and robust
518
# covariance matrix estimators.
519
sampleCov = meanvar.efficient.frontier(pspec_sc, retM_CRSP_5, optimize_method = 'CVXR')
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robustCov = meanvar.efficient.frontier(pspec_sc, retM_CRSP_5, optimize_method = 'CVXR', momentFUN = 'custom.covRob.TSGS')
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plotFrontiers(retM_CRSP_5, frontiers=list(sampleCov, robustCov), risk='StdDev')
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