demo/demo_cvxrPortfolioAnalytics.R
In braverock/PortfolioAnalytics: Portfolio Analysis, Including Numerical Methods for Optimization of Portfolios
#' ---
#' title: "CVXR for PortfolioAnalytics Demo"
#' date: "6/24/2023"
#' ---
#' This script demonstrates the examples and code chunk in
#' the vignette CVXR for PortfolioAnalytic
#' 2 GETTING STARTED
#' knitr setting
knitr::opts_chunk$set(
echo = TRUE,
collapse = TRUE,
comment = "#>"
)
Sys.setlocale("LC_TIME", "English")
#' load package
library(knitr)
library(PortfolioAnalytics)
library(CVXR)
library(data.table)
library(xts)
library(PCRA)
#' load data
data(edhec)
#' Use edhec for a returns object
ret_edhec <- tail(edhec, 60)
colnames(ret_edhec) <- c("CA", "CTAG", "DS", "EM", "EMN", "ED", "FIA",
"GM", "LSE", "MA", "RV", "SS", "FF")
print(head(ret_edhec, 5))
#' Get a character vector of the asset names
fund_edhec <- colnames(ret_edhec)
#' Time Series Plot of Edhec Return
tsPlotMP(ret_edhec, layout = c(2, 7), main = "Time Series Plot of Edhec Return")
#' 3 MAXIMIZING MEAN RETURN
#' Create portfolio object
pspec_maxret <- portfolio.spec(assets = fund_edhec)
#' Add constraints to the portfolio object
pspec_maxret <- add.constraint(pspec_maxret, type = "full_investment")
pspec_maxret <- add.constraint(portfolio = pspec_maxret, type = "box",
min = rep(0.02, 13),
max = c(rep(0.15, 8), rep(0.1, 5)))
#' Add objective to the portfolio object
pspec_maxret <- add.objective(portfolio = pspec_maxret,
type = "return", name = "mean")
pspec_maxret
#' Run the optimization with default solver
opt_maxret <- optimize.portfolio(R = ret_edhec, portfolio = pspec_maxret,
optimize_method = "CVXR", trace = TRUE)
opt_maxret
opt_maxret$solver
#' Run the optimization with specific solver
opt_maxret_glpk <- optimize.portfolio(R = ret_edhec, portfolio = pspec_maxret,
optimize_method = c("CVXR", "GLPK"), trace = TRUE)
opt_maxret_glpk$solver
#' Run back-testing
bt_maxret <- optimize.portfolio.rebalancing(R = ret_edhec, portfolio = pspec_maxret,
optimize_method = "CVXR",
rebalance_on = "quarters",
training_period = 36)
#' show results
class(bt_maxret)
names(bt_maxret)
#' 4 MINIMIZING VARIANCE
#' Create portfolio object
pspec_gmv <- portfolio.spec(assets = fund_edhec)
#' Add full-investment constraint
pspec_gmv <- add.constraint(pspec_gmv, type = "full_investment")
#' Add objective of minimizing variance
pspec_gmv <- add.objective(portfolio = pspec_gmv, type = "risk", name = "var")
#' Run the optimization with default CVXR solver
opt_gmv <- optimize.portfolio(ret_edhec, pspec_gmv, optimize_method = "CVXR")
opt_gmv
#' portfolio object
pspec_mv <- add.constraint(pspec_gmv, type = "long_only")
pspec_mv <- add.constraint(pspec_mv, type = "group",
groups = list(groupA=1,
groupB=c(2:12),
groupC=13),
group_min = c(0, 0.05, 0.05),
group_max = c(0.4, 0.8, 0.5))
pspec_mv <- add.constraint(pspec_mv, type = "return", return_target = 0.003)
pspec_mv
#' optimization
opt_mv <- optimize.portfolio(ret_edhec, pspec_mv, optimize_method = "CVXR")
opt_mv
#' Run the optimization with specific CVXR solver
opt_mv_ecos <- optimize.portfolio(ret_edhec, pspec_mv, optimize_method = c("CVXR", "ECOS"))
opt_mv_ecos
opt_mv$solver
opt_mv_ecos$solver
#' 5 MAXIMIZING QUADRATIC UTILITY
#' Generate MVO portfolio
pspec_mvo <- portfolio.spec(assets = fund_edhec)
pspec_mvo <- add.constraint(pspec_mvo, type = "full_investment")
pspec_mvo <- add.constraint(pspec_mvo, type = "long_only")
#' Add objectives
pspec_mvo <- add.objective(portfolio = pspec_mvo, type = "return", name = "mean")
pspec_mvo <- add.objective(portfolio = pspec_mvo, type = "risk", name = "var",
risk_aversion = 20)
#' Run optimization
opt_mvo <- optimize.portfolio(ret_edhec, pspec_mvo, optimize_method = "CVXR")
opt_mvo
#' 6 MINIMIZING EXPECTED SHORTFALL
#' Generate min-ES portfolio
pspec_es <- portfolio.spec(assets = fund_edhec)
pspec_es <- add.constraint(pspec_es, type = "full_investment")
pspec_es <- add.constraint(pspec_es, type = "long_only")
#' Add objective of minimizing ES by using the default gamma
pspec_es <- add.objective(portfolio = pspec_es, type = "risk", name = "ES")
#' Add objective of minimizing ES by using the specific gamma=0.1
pspec_es_1 <- add.objective(portfolio = pspec_es, type = "risk", name = "ES",
arguments = list(p=0.1))
#' GMES with default gamma=0.05
opt_es <- optimize.portfolio(ret_edhec, pspec_es, optimize_method = "CVXR")
opt_es
#' GMES with specific gamma=0.1
opt_es_1 <- optimize.portfolio(ret_edhec, pspec_es_1, optimize_method = "CVXR")
opt_es_1
#' 7 MINIMIZING EXPECTED QUADRATIC SHORTFALL
#' Generate min-EQS portfolio
pspec_eqs <- portfolio.spec(assets = fund_edhec)
pspec_eqs <- add.constraint(pspec_eqs, type = "full_investment")
pspec_eqs <- add.constraint(pspec_eqs, type = "long_only")
#' Add objective of minimizing EQS
pspec_eqs <- add.objective(portfolio = pspec_eqs, type = "risk", name = "EQS",
arguments = list(p=0.05))
#' GMEQS with default gamma=0.05
opt_eqs <- optimize.portfolio(ret_edhec, pspec_eqs, optimize_method = "CVXR")
opt_eqs
#' 8 MAXIMIZING MEAN RETURN PER UNIT RISK
#' Create portfolio object
pspec_sr <- portfolio.spec(assets = fund_edhec)
#' Add constraints of maximizing Sharpe Ratio
pspec_sr <- add.constraint(pspec_sr, type = "full_investment")
pspec_sr <- add.constraint(pspec_sr, type = "long_only")
#' Add objectives of maximizing Sharpe Ratio
pspec_sr <- add.objective(pspec_sr, type = "return", name = "mean")
pspec_sr <- add.objective(pspec_sr, type = "risk", name = "var")
#' Optimization
optimize.portfolio(ret_edhec, pspec_sr, optimize_method = "CVXR", maxSR = TRUE)
#' Create portfolio object
pspec_ESratio <- portfolio.spec(assets = fund_edhec)
#' Add constraints of maximizing return per unit ES
pspec_ESratio <- add.constraint(pspec_ESratio, type = "full_investment")
pspec_ESratio <- add.constraint(pspec_ESratio, type = "long_only")
#' Add objectives of maximizing return per unit ES
pspec_ESratio <- add.objective(pspec_ESratio, type = "return", name = "mean")
pspec_ESratio <- add.objective(pspec_ESratio, type = "risk", name = "ES",
arguments = list(p=0.05))
#' Optimization
optimize.portfolio(ret_edhec, pspec_ESratio, optimize_method = "CVXR", ESratio = TRUE)
#' Create portfolio object
pspec_EQSratio <- portfolio.spec(assets = fund_edhec)
#' Add constraints of maximizing return per unit EQS
pspec_EQSratio <- add.constraint(pspec_EQSratio, type = "full_investment")
pspec_EQSratio <- add.constraint(pspec_EQSratio, type = "long_only")
#' Add objectives of maximizing return per unit EQS
pspec_EQSratio <- add.objective(pspec_EQSratio, type = "return", name = "mean")
pspec_EQSratio <- add.objective(pspec_EQSratio, type = "risk", name = "EQS",
arguments = list(p=0.05))
#' Optimization
optimize.portfolio(ret_edhec, pspec_EQSratio, optimize_method = "CVXR", EQSratio = TRUE)
#' 9 COMPARATIVE PERFORMANCE OF PORTFOLIOS
#' use CRSP daily data set
stocksCRSPdaily <- getPCRAData(dataset = "stocksCRSPdaily")
smallcapTS <- selectCRSPandSPGMI(
periodicity = "daily",
stockItems = c("Date", "TickerLast", "CapGroupLast", "Return"),
factorItems = NULL,
subsetType = "CapGroupLast",
subsetValues = "SmallCap",
outputType = "xts")
#' find top 30 small cap stocks based on the market capitalization
smallcapDT <- factorsSPGMI[CapGroupLast == "SmallCap"]
scSize <- smallcapDT[, mean(LogMktCap), by = "TickerLast"]
names(scSize)[2] <- "Size"
scSize <- scSize[order(scSize$Size, decreasing = TRUE),]
sc30largest <- scSize[,TickerLast][1:30]
#' daily return of top 30 stocks
retD_CRSP <- smallcapTS[ , sc30largest]
print(head(retD_CRSP, 3))
#' monthly return of top 30 stocks in last 5 years
ep <- endpoints(retD_CRSP, on= "months", k=1)
prod1 <- function(x){apply(x+1, 2, prod)}
retM_CRSP <- period.apply(retD_CRSP, INDEX = ep, FUN = prod1) - 1
retM_CRSP_5 <- tail(retM_CRSP, 60)
#' time series plot of 10 stocks
tsPlotMP(retM_CRSP_5[, 1:10])
#' Test run time for Backtesting with GMV, GMES, GMEQS portfolios
start_time1 <- Sys.time()
#' Generate GMV, GMES and GMEQS portfolios
pspec_sc <- portfolio.spec(assets = sc30largest)
pspec_sc <- add.constraint(pspec_sc, type = "full_investment")
pspec_sc <- add.constraint(pspec_sc, type = "long_only")
pspec_GMV <- add.objective(pspec_sc, type = "risk", name = "var")
pspec_GMES <- add.objective(pspec_sc, type = "risk", name = "ES")
pspec_GMEQS <- add.objective(pspec_sc, type = "risk", name = "EQS")
#' Optimize Portfolio at Monthly Rebalancing and 500-Day Training
bt.GMV <- optimize.portfolio.rebalancing(retD_CRSP, pspec_GMV,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
bt.ES <- optimize.portfolio.rebalancing(retD_CRSP, pspec_GMES,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
bt.EQS <- optimize.portfolio.rebalancing(retD_CRSP, pspec_GMEQS,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
#' Extract time series of portfolio weights
wts.GMV <- extractWeights(bt.GMV)
wts.GMV <- wts.GMV[complete.cases(wts.GMV),]
wts.ES <- extractWeights(bt.ES)
wts.ES <- wts.ES[complete.cases(wts.ES),]
wts.EQS <- extractWeights(bt.EQS)
wts.EQS <- wts.EQS[complete.cases(wts.EQS),]
#' Compute cumulative returns of three portfolios
GMV <- Return.rebalancing(retM_CRSP, wts.GMV)
ES <- Return.rebalancing(retM_CRSP, wts.ES)
EQS <- Return.rebalancing(retM_CRSP, wts.EQS)
#' Combine GMV, ES and EQS portfolio cumulative returns
ret.comb <- na.omit(merge(GMV, ES, EQS, all=F))
names(ret.comb) <- c("GMV", "GMES", "GMEQS")
backtest.plot(ret.comb, colorSet = c("black", "darkblue", "darkgreen"),
ltySet = c(3, 2, 1))
#' Return run-time for Backtesting with GMV, GMES, GMEQS portfolios
end_time1 <- Sys.time()
runningtime1 <- end_time1 - start_time1
cat("The run time for Figure 9.2 is", format(round(runningtime1, 2)))
#' Test run-time for Backtesting with SR, ESratio, EQSratio portfolios
start_time2 <- Sys.time()
#' Generate GMV, GMES and GMEQS portfolios
pspec_sc_ratio <- add.objective(pspec_sc, type = "return", name = "mean")
pspec_Sr <- add.objective(pspec_sc_ratio, type = "risk", name = "var")
pspec_ESr <- add.objective(pspec_sc_ratio, type = "risk", name = "ES")
pspec_EQSr <- add.objective(pspec_sc_ratio, type = "risk", name = "EQS")
#' Optimize Portfolio at Monthly Rebalancing and 500-Day Training
bt.Sr <- optimize.portfolio.rebalancing(retD_CRSP, pspec_Sr, maxSR = TRUE,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
bt.ESr <- optimize.portfolio.rebalancing(retD_CRSP, pspec_ESr,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
bt.EQSr <- optimize.portfolio.rebalancing(retD_CRSP, pspec_EQSr,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
#' Extract time series of portfolio weights
wts.Sr <- extractWeights(bt.Sr)
wts.Sr <- wts.Sr[complete.cases(wts.Sr),]
wts.ESr <- extractWeights(bt.ESr)
wts.ESr <- wts.ESr[complete.cases(wts.ESr),]
wts.EQSr <- extractWeights(bt.EQSr)
wts.EQSr <- wts.EQSr[complete.cases(wts.EQSr),]
#' Compute cumulative returns of three portfolios
Sr <- Return.rebalancing(retM_CRSP, wts.Sr, rebalance_on = "months")
ESr <- Return.rebalancing(retM_CRSP, wts.ESr, rebalance_on = "months")
EQSr <- Return.rebalancing(retM_CRSP, wts.EQSr, rebalance_on = "months")
#' Combine Sr, ESr and EQSr portfolio cumulative returns
ret.comb <- na.omit(merge(Sr, ESr, EQSr, all=F))
names(ret.comb) <- c("Sharpe ratio", "ES ratio", "EQS ratio")
backtest.plot(ret.comb, colorSet = c("black", "darkblue", "darkgreen"),
ltySet = c(3, 2, 1))
#' Return run-time for Backtesting with SR, ESratio, EQSratio portfolios
end_time2 <- Sys.time()
runningtime2 <- end_time2 - start_time2
cat("The run time for Figure 9.3 is", format(round(runningtime2, 2)))
#' mean-var efficient frontier
meanvar.ef <- create.EfficientFrontier(R = retM_CRSP_5, portfolio = pspec_sc,
type = "mean-StdDev")
meanvar.ef
chart.EfficientFrontier(meanvar.ef, match.col = "StdDev", type = "l",
chart.assets = FALSE, main = "Mean-StdDev Efficient Frontier",
RAR.text = "Sharpe ratio", pch = 1)
#' Show Efficient Frontier Data
meanvar.ef$frontier[, 1:2]
sr = meanvar.ef$frontier[, 1]/meanvar.ef$frontier[, 2]
cat("maximum Sharpe ratio:", max(sr))
cat("mean of the maximum SR portfolio:", meanvar.ef$frontier[, 1][sr == max(sr)])
cat("StdDev of the maximum SR portfolio:", meanvar.ef$frontier[, 2][sr == max(sr)])
#' Generate Mean-StdDev Efficient Frontier
pspec_MV <- add.objective(pspec_sc, type = "risk", name = "var")
pspec_MV <- add.objective(portfolio = pspec_MV, type = "return", name = "mean")
opt_MV <- optimize.portfolio(retM_CRSP_5, pspec_MV, optimize_method = "CVXR",
maxSR = TRUE, trace = TRUE)
opt_MV
#' Show Mean-StdDev Efficient Frontier
chart.EfficientFrontier(opt_MV, match.col = "StdDev", chart.assets = FALSE,
main = "Mean-StdDev Efficient Frontier",
RAR.text = "Sharpe Ratio", pch = 1, xlim = c(0, 0.1))
#' Initialize Portfolio
pspec_sc_init <- portfolio.spec(assets = sc30largest)
pspec_sc_init <- add.constraint(pspec_sc_init, type = "full_investment")
#' Portfolio with long-only constraints
pspec_sc_lo <- add.constraint(portfolio = pspec_sc_init, type = "long_only")
#' Portfolio with long-only box constraints
pspec_sc_lobox <- add.constraint(portfolio = pspec_sc_init, type = "box",
min = 0.02, max = 0.1)
#' Portfolio with long-short box constraints
pspec_sc_lsbox <- add.constraint(portfolio = pspec_sc_init, type = "box",
min = -0.1, max = 0.1)
#' Combine the portfolios into a list
portf_list <- combine.portfolios(list(pspec_sc_lo, pspec_sc_lobox, pspec_sc_lsbox))
#' Plot the efficient frontier overlay of the portfolios with varying constraints
legend_labels <- c("Long Only", "Long Only Box", "Long Short Box")
chart.EfficientFrontierOverlay(R = retM_CRSP_5, portfolio_list = portf_list,
type = "mean-StdDev", match.col = "StdDev",
legend.loc = "bottomright", chart.assets = FALSE,
legend.labels = legend_labels, cex.legend = 1,
labels.assets = FALSE, lwd = c(3,3,3),
col = c("black", "dark red", "dark green"),
main = "Overlay Mean-StdDev Efficient Frontiers",
xlim = c(0.03, 0.11), ylim = c(0.005, 0.035))
#' Mean-ES Efficient Frontier
meanetl.ef <- create.EfficientFrontier(R = retM_CRSP_5, portfolio = pspec_sc,
type = "mean-ES")
chart.EfficientFrontier(meanetl.ef, match.col = "ES", type = "l",
chart.assets = FALSE, main = "Mean-ES Efficient Frontier",
RAR.text = "ES ratio", pch = 1)
#' Overlay Mean-ES Efficient Frontiers
legend_labels <- c("Long Only ES (p=0.05)",
"Long Only Box ES (p=0.05)", "Long Short Box ES (p=0.05)")
chart.EfficientFrontierOverlay(R = retM_CRSP_5, portfolio_list = portf_list,
type = "mean-ES", match.col = "ES",
legend.loc = "bottomright", chart.assets = FALSE,
legend.labels = legend_labels, cex.legend = 1,
labels.assets = FALSE, lwd = c(3,3,3),
col = c("black", "dark red", "dark green"),
main = "Overlay Mean-ES Efficient Frontiers",
xlim = c(0.03, 0.17), ylim = c(0.005, 0.035))
#' Create long-only ES portfolios with different tail probabilities
ES_05 <- add.objective(portfolio = pspec_sc_lo, type = "risk", name = "ES",
arguments = list(p=0.05))
ES_10 <- add.objective(portfolio = pspec_sc_lo, type = "risk", name = "ES",
arguments = list(p=0.1))
ES_15 <- add.objective(portfolio = pspec_sc_lo, type = "risk", name = "ES",
arguments = list(p=0.15))
#' Combine the portfolios into a list
portf_ES_list <- combine.portfolios(list(ES_05, ES_10, ES_15))
#' Plot the efficient frontier overlay of the portfolios with varying tail probabilities
legend_ES_labels <- c("ES (p=0.05)", "ES (p=0.1)", "ES (p=0.15)")
chart.EfficientFrontierOverlay(R = retM_CRSP_5, portfolio_list = portf_ES_list,
type = "mean-ES", match.col = "ES",
legend.loc = "bottomright", chart.assets = FALSE,
legend.labels = legend_ES_labels, cex.legend = 1,
labels.assets = FALSE, lwd = c(3,3,3),
col = c("black", "dark red", "dark green"),
main = "Overlay Mean-ES Efficient Frontiers",
xlim = c(0.035, 0.165), ylim = c(0.005, 0.03))
#' Mean-EQS Efficient Frontier
meaneqs.ef <- create.EfficientFrontier(R = retM_CRSP_5, portfolio = pspec_sc,
type = "mean-EQS")
chart.EfficientFrontier(meaneqs.ef, match.col = "EQS", type = "l",
chart.assets = FALSE, main = "Mean-EQS Efficient Frontier",
RAR.text = "EQS ratio", pch = 1)
#' usage example: minStd Portfolio
minstd_port <- add.objective(pspec_sc, type = "risk", name = "StdDev")
minstd_w <- optimize.portfolio(retM_CRSP_5, minstd_port, optimize_method = "CVXR")$weight
#' risk values with default alpha = 0.05
extract_risk(retM_CRSP_5, minstd_w)
#' risk values with specific alpha
extract_risk(retM_CRSP_5, minstd_w, ES_alpha = 0.1, EQS_alpha = 0.1)
#' example 1: Compare StdDev of minStd and minES portfolios with guideline
chart.EfficientFrontierCompare(R = retM_CRSP_5, portfolio = pspec_sc, risk_type = "StdDev",
match.col = c("StdDev", "ES"), lwd = c(2, 2))
#' example 2: Compare ES of minStd, minES and minEQS portfolios without guideline
chart.EfficientFrontierCompare(R = retM_CRSP_5, portfolio = pspec_sc, risk_type = "ES",
match.col = c("StdDev", "ES", "EQS"), guideline = FALSE,
col = c(1,2,4), lty = c(1, 2, 4), lwd = c(2, 2, 2))
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#' ---
#' title: "CVXR for PortfolioAnalytics Demo"
#' date: "6/24/2023"
#' ---
#' This script demonstrates the examples and code chunk in
#' the vignette CVXR for PortfolioAnalytic
#' 2 GETTING STARTED
#' knitr setting
knitr::opts_chunk$set(
echo = TRUE,
collapse = TRUE,
comment = "#>"
)
Sys.setlocale("LC_TIME", "English")
#' load package
library(knitr)
library(PortfolioAnalytics)
library(CVXR)
library(data.table)
library(xts)
library(PCRA)
#' load data
data(edhec)
#' Use edhec for a returns object
ret_edhec <- tail(edhec, 60)
colnames(ret_edhec) <- c("CA", "CTAG", "DS", "EM", "EMN", "ED", "FIA",
"GM", "LSE", "MA", "RV", "SS", "FF")
print(head(ret_edhec, 5))
#' Get a character vector of the asset names
fund_edhec <- colnames(ret_edhec)
#' Time Series Plot of Edhec Return
tsPlotMP(ret_edhec, layout = c(2, 7), main = "Time Series Plot of Edhec Return")
#' 3 MAXIMIZING MEAN RETURN
#' Create portfolio object
pspec_maxret <- portfolio.spec(assets = fund_edhec)
#' Add constraints to the portfolio object
pspec_maxret <- add.constraint(pspec_maxret, type = "full_investment")
pspec_maxret <- add.constraint(portfolio = pspec_maxret, type = "box",
min = rep(0.02, 13),
max = c(rep(0.15, 8), rep(0.1, 5)))
#' Add objective to the portfolio object
pspec_maxret <- add.objective(portfolio = pspec_maxret,
type = "return", name = "mean")
pspec_maxret
#' Run the optimization with default solver
opt_maxret <- optimize.portfolio(R = ret_edhec, portfolio = pspec_maxret,
optimize_method = "CVXR", trace = TRUE)
opt_maxret
opt_maxret$solver
#' Run the optimization with specific solver
opt_maxret_glpk <- optimize.portfolio(R = ret_edhec, portfolio = pspec_maxret,
optimize_method = c("CVXR", "GLPK"), trace = TRUE)
opt_maxret_glpk$solver
#' Run back-testing
bt_maxret <- optimize.portfolio.rebalancing(R = ret_edhec, portfolio = pspec_maxret,
optimize_method = "CVXR",
rebalance_on = "quarters",
training_period = 36)
#' show results
class(bt_maxret)
names(bt_maxret)
#' 4 MINIMIZING VARIANCE
#' Create portfolio object
pspec_gmv <- portfolio.spec(assets = fund_edhec)
#' Add full-investment constraint
pspec_gmv <- add.constraint(pspec_gmv, type = "full_investment")
#' Add objective of minimizing variance
pspec_gmv <- add.objective(portfolio = pspec_gmv, type = "risk", name = "var")
#' Run the optimization with default CVXR solver
opt_gmv <- optimize.portfolio(ret_edhec, pspec_gmv, optimize_method = "CVXR")
opt_gmv
#' portfolio object
pspec_mv <- add.constraint(pspec_gmv, type = "long_only")
pspec_mv <- add.constraint(pspec_mv, type = "group",
groups = list(groupA=1,
groupB=c(2:12),
groupC=13),
group_min = c(0, 0.05, 0.05),
group_max = c(0.4, 0.8, 0.5))
pspec_mv <- add.constraint(pspec_mv, type = "return", return_target = 0.003)
pspec_mv
#' optimization
opt_mv <- optimize.portfolio(ret_edhec, pspec_mv, optimize_method = "CVXR")
opt_mv
#' Run the optimization with specific CVXR solver
opt_mv_ecos <- optimize.portfolio(ret_edhec, pspec_mv, optimize_method = c("CVXR", "ECOS"))
opt_mv_ecos
opt_mv$solver
opt_mv_ecos$solver
#' 5 MAXIMIZING QUADRATIC UTILITY
#' Generate MVO portfolio
pspec_mvo <- portfolio.spec(assets = fund_edhec)
pspec_mvo <- add.constraint(pspec_mvo, type = "full_investment")
pspec_mvo <- add.constraint(pspec_mvo, type = "long_only")
#' Add objectives
pspec_mvo <- add.objective(portfolio = pspec_mvo, type = "return", name = "mean")
pspec_mvo <- add.objective(portfolio = pspec_mvo, type = "risk", name = "var",
risk_aversion = 20)
#' Run optimization
opt_mvo <- optimize.portfolio(ret_edhec, pspec_mvo, optimize_method = "CVXR")
opt_mvo
#' 6 MINIMIZING EXPECTED SHORTFALL
#' Generate min-ES portfolio
pspec_es <- portfolio.spec(assets = fund_edhec)
pspec_es <- add.constraint(pspec_es, type = "full_investment")
pspec_es <- add.constraint(pspec_es, type = "long_only")
#' Add objective of minimizing ES by using the default gamma
pspec_es <- add.objective(portfolio = pspec_es, type = "risk", name = "ES")
#' Add objective of minimizing ES by using the specific gamma=0.1
pspec_es_1 <- add.objective(portfolio = pspec_es, type = "risk", name = "ES",
arguments = list(p=0.1))
#' GMES with default gamma=0.05
opt_es <- optimize.portfolio(ret_edhec, pspec_es, optimize_method = "CVXR")
opt_es
#' GMES with specific gamma=0.1
opt_es_1 <- optimize.portfolio(ret_edhec, pspec_es_1, optimize_method = "CVXR")
opt_es_1
#' 7 MINIMIZING EXPECTED QUADRATIC SHORTFALL
#' Generate min-EQS portfolio
pspec_eqs <- portfolio.spec(assets = fund_edhec)
pspec_eqs <- add.constraint(pspec_eqs, type = "full_investment")
pspec_eqs <- add.constraint(pspec_eqs, type = "long_only")
#' Add objective of minimizing EQS
pspec_eqs <- add.objective(portfolio = pspec_eqs, type = "risk", name = "EQS",
arguments = list(p=0.05))
#' GMEQS with default gamma=0.05
opt_eqs <- optimize.portfolio(ret_edhec, pspec_eqs, optimize_method = "CVXR")
opt_eqs
#' 8 MAXIMIZING MEAN RETURN PER UNIT RISK
#' Create portfolio object
pspec_sr <- portfolio.spec(assets = fund_edhec)
#' Add constraints of maximizing Sharpe Ratio
pspec_sr <- add.constraint(pspec_sr, type = "full_investment")
pspec_sr <- add.constraint(pspec_sr, type = "long_only")
#' Add objectives of maximizing Sharpe Ratio
pspec_sr <- add.objective(pspec_sr, type = "return", name = "mean")
pspec_sr <- add.objective(pspec_sr, type = "risk", name = "var")
#' Optimization
optimize.portfolio(ret_edhec, pspec_sr, optimize_method = "CVXR", maxSR = TRUE)
#' Create portfolio object
pspec_ESratio <- portfolio.spec(assets = fund_edhec)
#' Add constraints of maximizing return per unit ES
pspec_ESratio <- add.constraint(pspec_ESratio, type = "full_investment")
pspec_ESratio <- add.constraint(pspec_ESratio, type = "long_only")
#' Add objectives of maximizing return per unit ES
pspec_ESratio <- add.objective(pspec_ESratio, type = "return", name = "mean")
pspec_ESratio <- add.objective(pspec_ESratio, type = "risk", name = "ES",
arguments = list(p=0.05))
#' Optimization
optimize.portfolio(ret_edhec, pspec_ESratio, optimize_method = "CVXR", ESratio = TRUE)
#' Create portfolio object
pspec_EQSratio <- portfolio.spec(assets = fund_edhec)
#' Add constraints of maximizing return per unit EQS
pspec_EQSratio <- add.constraint(pspec_EQSratio, type = "full_investment")
pspec_EQSratio <- add.constraint(pspec_EQSratio, type = "long_only")
#' Add objectives of maximizing return per unit EQS
pspec_EQSratio <- add.objective(pspec_EQSratio, type = "return", name = "mean")
pspec_EQSratio <- add.objective(pspec_EQSratio, type = "risk", name = "EQS",
arguments = list(p=0.05))
#' Optimization
optimize.portfolio(ret_edhec, pspec_EQSratio, optimize_method = "CVXR", EQSratio = TRUE)
#' 9 COMPARATIVE PERFORMANCE OF PORTFOLIOS
#' use CRSP daily data set
stocksCRSPdaily <- getPCRAData(dataset = "stocksCRSPdaily")
smallcapTS <- selectCRSPandSPGMI(
periodicity = "daily",
stockItems = c("Date", "TickerLast", "CapGroupLast", "Return"),
factorItems = NULL,
subsetType = "CapGroupLast",
subsetValues = "SmallCap",
outputType = "xts")
#' find top 30 small cap stocks based on the market capitalization
smallcapDT <- factorsSPGMI[CapGroupLast == "SmallCap"]
scSize <- smallcapDT[, mean(LogMktCap), by = "TickerLast"]
names(scSize)[2] <- "Size"
scSize <- scSize[order(scSize$Size, decreasing = TRUE),]
sc30largest <- scSize[,TickerLast][1:30]
#' daily return of top 30 stocks
retD_CRSP <- smallcapTS[ , sc30largest]
print(head(retD_CRSP, 3))
#' monthly return of top 30 stocks in last 5 years
ep <- endpoints(retD_CRSP, on= "months", k=1)
prod1 <- function(x){apply(x+1, 2, prod)}
retM_CRSP <- period.apply(retD_CRSP, INDEX = ep, FUN = prod1) - 1
retM_CRSP_5 <- tail(retM_CRSP, 60)
#' time series plot of 10 stocks
tsPlotMP(retM_CRSP_5[, 1:10])
#' Test run time for Backtesting with GMV, GMES, GMEQS portfolios
start_time1 <- Sys.time()
#' Generate GMV, GMES and GMEQS portfolios
pspec_sc <- portfolio.spec(assets = sc30largest)
pspec_sc <- add.constraint(pspec_sc, type = "full_investment")
pspec_sc <- add.constraint(pspec_sc, type = "long_only")
pspec_GMV <- add.objective(pspec_sc, type = "risk", name = "var")
pspec_GMES <- add.objective(pspec_sc, type = "risk", name = "ES")
pspec_GMEQS <- add.objective(pspec_sc, type = "risk", name = "EQS")
#' Optimize Portfolio at Monthly Rebalancing and 500-Day Training
bt.GMV <- optimize.portfolio.rebalancing(retD_CRSP, pspec_GMV,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
bt.ES <- optimize.portfolio.rebalancing(retD_CRSP, pspec_GMES,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
bt.EQS <- optimize.portfolio.rebalancing(retD_CRSP, pspec_GMEQS,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
#' Extract time series of portfolio weights
wts.GMV <- extractWeights(bt.GMV)
wts.GMV <- wts.GMV[complete.cases(wts.GMV),]
wts.ES <- extractWeights(bt.ES)
wts.ES <- wts.ES[complete.cases(wts.ES),]
wts.EQS <- extractWeights(bt.EQS)
wts.EQS <- wts.EQS[complete.cases(wts.EQS),]
#' Compute cumulative returns of three portfolios
GMV <- Return.rebalancing(retM_CRSP, wts.GMV)
ES <- Return.rebalancing(retM_CRSP, wts.ES)
EQS <- Return.rebalancing(retM_CRSP, wts.EQS)
#' Combine GMV, ES and EQS portfolio cumulative returns
ret.comb <- na.omit(merge(GMV, ES, EQS, all=F))
names(ret.comb) <- c("GMV", "GMES", "GMEQS")
backtest.plot(ret.comb, colorSet = c("black", "darkblue", "darkgreen"),
ltySet = c(3, 2, 1))
#' Return run-time for Backtesting with GMV, GMES, GMEQS portfolios
end_time1 <- Sys.time()
runningtime1 <- end_time1 - start_time1
cat("The run time for Figure 9.2 is", format(round(runningtime1, 2)))
#' Test run-time for Backtesting with SR, ESratio, EQSratio portfolios
start_time2 <- Sys.time()
#' Generate GMV, GMES and GMEQS portfolios
pspec_sc_ratio <- add.objective(pspec_sc, type = "return", name = "mean")
pspec_Sr <- add.objective(pspec_sc_ratio, type = "risk", name = "var")
pspec_ESr <- add.objective(pspec_sc_ratio, type = "risk", name = "ES")
pspec_EQSr <- add.objective(pspec_sc_ratio, type = "risk", name = "EQS")
#' Optimize Portfolio at Monthly Rebalancing and 500-Day Training
bt.Sr <- optimize.portfolio.rebalancing(retD_CRSP, pspec_Sr, maxSR = TRUE,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
bt.ESr <- optimize.portfolio.rebalancing(retD_CRSP, pspec_ESr,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
bt.EQSr <- optimize.portfolio.rebalancing(retD_CRSP, pspec_EQSr,
optimize_method = "CVXR",
rebalance_on = "months",
training_period = 30,
rolling_window = 500)
#' Extract time series of portfolio weights
wts.Sr <- extractWeights(bt.Sr)
wts.Sr <- wts.Sr[complete.cases(wts.Sr),]
wts.ESr <- extractWeights(bt.ESr)
wts.ESr <- wts.ESr[complete.cases(wts.ESr),]
wts.EQSr <- extractWeights(bt.EQSr)
wts.EQSr <- wts.EQSr[complete.cases(wts.EQSr),]
#' Compute cumulative returns of three portfolios
Sr <- Return.rebalancing(retM_CRSP, wts.Sr, rebalance_on = "months")
ESr <- Return.rebalancing(retM_CRSP, wts.ESr, rebalance_on = "months")
EQSr <- Return.rebalancing(retM_CRSP, wts.EQSr, rebalance_on = "months")
#' Combine Sr, ESr and EQSr portfolio cumulative returns
ret.comb <- na.omit(merge(Sr, ESr, EQSr, all=F))
names(ret.comb) <- c("Sharpe ratio", "ES ratio", "EQS ratio")
backtest.plot(ret.comb, colorSet = c("black", "darkblue", "darkgreen"),
ltySet = c(3, 2, 1))
#' Return run-time for Backtesting with SR, ESratio, EQSratio portfolios
end_time2 <- Sys.time()
runningtime2 <- end_time2 - start_time2
cat("The run time for Figure 9.3 is", format(round(runningtime2, 2)))
#' mean-var efficient frontier
meanvar.ef <- create.EfficientFrontier(R = retM_CRSP_5, portfolio = pspec_sc,
type = "mean-StdDev")
meanvar.ef
chart.EfficientFrontier(meanvar.ef, match.col = "StdDev", type = "l",
chart.assets = FALSE, main = "Mean-StdDev Efficient Frontier",
RAR.text = "Sharpe ratio", pch = 1)
#' Show Efficient Frontier Data
meanvar.ef$frontier[, 1:2]
sr = meanvar.ef$frontier[, 1]/meanvar.ef$frontier[, 2]
cat("maximum Sharpe ratio:", max(sr))
cat("mean of the maximum SR portfolio:", meanvar.ef$frontier[, 1][sr == max(sr)])
cat("StdDev of the maximum SR portfolio:", meanvar.ef$frontier[, 2][sr == max(sr)])
#' Generate Mean-StdDev Efficient Frontier
pspec_MV <- add.objective(pspec_sc, type = "risk", name = "var")
pspec_MV <- add.objective(portfolio = pspec_MV, type = "return", name = "mean")
opt_MV <- optimize.portfolio(retM_CRSP_5, pspec_MV, optimize_method = "CVXR",
maxSR = TRUE, trace = TRUE)
opt_MV
#' Show Mean-StdDev Efficient Frontier
chart.EfficientFrontier(opt_MV, match.col = "StdDev", chart.assets = FALSE,
main = "Mean-StdDev Efficient Frontier",
RAR.text = "Sharpe Ratio", pch = 1, xlim = c(0, 0.1))
#' Initialize Portfolio
pspec_sc_init <- portfolio.spec(assets = sc30largest)
pspec_sc_init <- add.constraint(pspec_sc_init, type = "full_investment")
#' Portfolio with long-only constraints
pspec_sc_lo <- add.constraint(portfolio = pspec_sc_init, type = "long_only")
#' Portfolio with long-only box constraints
pspec_sc_lobox <- add.constraint(portfolio = pspec_sc_init, type = "box",
min = 0.02, max = 0.1)
#' Portfolio with long-short box constraints
pspec_sc_lsbox <- add.constraint(portfolio = pspec_sc_init, type = "box",
min = -0.1, max = 0.1)
#' Combine the portfolios into a list
portf_list <- combine.portfolios(list(pspec_sc_lo, pspec_sc_lobox, pspec_sc_lsbox))
#' Plot the efficient frontier overlay of the portfolios with varying constraints
legend_labels <- c("Long Only", "Long Only Box", "Long Short Box")
chart.EfficientFrontierOverlay(R = retM_CRSP_5, portfolio_list = portf_list,
type = "mean-StdDev", match.col = "StdDev",
legend.loc = "bottomright", chart.assets = FALSE,
legend.labels = legend_labels, cex.legend = 1,
labels.assets = FALSE, lwd = c(3,3,3),
col = c("black", "dark red", "dark green"),
main = "Overlay Mean-StdDev Efficient Frontiers",
xlim = c(0.03, 0.11), ylim = c(0.005, 0.035))
#' Mean-ES Efficient Frontier
meanetl.ef <- create.EfficientFrontier(R = retM_CRSP_5, portfolio = pspec_sc,
type = "mean-ES")
chart.EfficientFrontier(meanetl.ef, match.col = "ES", type = "l",
chart.assets = FALSE, main = "Mean-ES Efficient Frontier",
RAR.text = "ES ratio", pch = 1)
#' Overlay Mean-ES Efficient Frontiers
legend_labels <- c("Long Only ES (p=0.05)",
"Long Only Box ES (p=0.05)", "Long Short Box ES (p=0.05)")
chart.EfficientFrontierOverlay(R = retM_CRSP_5, portfolio_list = portf_list,
type = "mean-ES", match.col = "ES",
legend.loc = "bottomright", chart.assets = FALSE,
legend.labels = legend_labels, cex.legend = 1,
labels.assets = FALSE, lwd = c(3,3,3),
col = c("black", "dark red", "dark green"),
main = "Overlay Mean-ES Efficient Frontiers",
xlim = c(0.03, 0.17), ylim = c(0.005, 0.035))
#' Create long-only ES portfolios with different tail probabilities
ES_05 <- add.objective(portfolio = pspec_sc_lo, type = "risk", name = "ES",
arguments = list(p=0.05))
ES_10 <- add.objective(portfolio = pspec_sc_lo, type = "risk", name = "ES",
arguments = list(p=0.1))
ES_15 <- add.objective(portfolio = pspec_sc_lo, type = "risk", name = "ES",
arguments = list(p=0.15))
#' Combine the portfolios into a list
portf_ES_list <- combine.portfolios(list(ES_05, ES_10, ES_15))
#' Plot the efficient frontier overlay of the portfolios with varying tail probabilities
legend_ES_labels <- c("ES (p=0.05)", "ES (p=0.1)", "ES (p=0.15)")
chart.EfficientFrontierOverlay(R = retM_CRSP_5, portfolio_list = portf_ES_list,
type = "mean-ES", match.col = "ES",
legend.loc = "bottomright", chart.assets = FALSE,
legend.labels = legend_ES_labels, cex.legend = 1,
labels.assets = FALSE, lwd = c(3,3,3),
col = c("black", "dark red", "dark green"),
main = "Overlay Mean-ES Efficient Frontiers",
xlim = c(0.035, 0.165), ylim = c(0.005, 0.03))
#' Mean-EQS Efficient Frontier
meaneqs.ef <- create.EfficientFrontier(R = retM_CRSP_5, portfolio = pspec_sc,
type = "mean-EQS")
chart.EfficientFrontier(meaneqs.ef, match.col = "EQS", type = "l",
chart.assets = FALSE, main = "Mean-EQS Efficient Frontier",
RAR.text = "EQS ratio", pch = 1)
#' usage example: minStd Portfolio
minstd_port <- add.objective(pspec_sc, type = "risk", name = "StdDev")
minstd_w <- optimize.portfolio(retM_CRSP_5, minstd_port, optimize_method = "CVXR")$weight
#' risk values with default alpha = 0.05
extract_risk(retM_CRSP_5, minstd_w)
#' risk values with specific alpha
extract_risk(retM_CRSP_5, minstd_w, ES_alpha = 0.1, EQS_alpha = 0.1)
#' example 1: Compare StdDev of minStd and minES portfolios with guideline
chart.EfficientFrontierCompare(R = retM_CRSP_5, portfolio = pspec_sc, risk_type = "StdDev",
match.col = c("StdDev", "ES"), lwd = c(2, 2))
#' example 2: Compare ES of minStd, minES and minEQS portfolios without guideline
chart.EfficientFrontierCompare(R = retM_CRSP_5, portfolio = pspec_sc, risk_type = "ES",
match.col = c("StdDev", "ES", "EQS"), guideline = FALSE,
col = c(1,2,4), lty = c(1, 2, 4), lwd = c(2, 2, 2))
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