In kecoli/PCRM: Companion to Portfolio Construction and Risk Management

Start up

inslib <- function(x){
    x <-as.character(substitute(x))
    if(!x %in% rownames(installed.packages())) 
    {install.packages(x,repos="http://cran.stat.ucla.edu")}
    eval(parse(text=paste("library(",x,")",sep="")))}

inslib("mpo")
inslib("quadprog")
inslib("xts")
inslib("Rglpk")
inslib("corpcor")
load("crsp.short.Rdata")

n.stocks <- 5
names(midcap.ts)
names(smallcap.ts)
names(largecap.ts)
returns.ts = midcap.ts[,1:n.stocks]
returns = coredata(midcap.ts[,1:n.stocks])
sum=0.5
mu.target=0.02 
w.initial=rep(1/n.stocks,n.stocks) 
toc=0.3
upper=rep(0.3,n.stocks)
lower=rep(0,n.stocks)

set.seed(1234)
group=c(sample(1:2,n.stocks,replace=T))
upper.group=c(0.8,0.8)
lower.group=c(-0.5,-0.5)
ptc=0.001
digits=4
wts.only=T
mu.min = NULL 
mu.max = NULL 
rf = .003
npoints = 20
wts.plot = T 
printout = F
bar.ylim = c(-1,4)

Intial parameter values on constraints:

list.arg <- list(
        sum=sum,
        mu.target=mu.target, 
        group=group, 
        upper.group=upper.group,
        lower.group=lower.group, 
        upper=upper, 
        lower=lower, 
        toc=toc, 
        w.initial=w.initial,
        ptc=ptc)    
list.arg

Partial investment constraint

clist <- c("sum")
cset <- NULL
cset <-combine.cset(clist=clist,returns=returns,list.arg=list.arg)
(res  <- gmv(returns, cset=cset, wts.only=T,digits=4))
all.equal(sum(res$WTS),list.arg$sum,tolerance=0.01)
efrontPlot(returns, cset, rf = .003, npoints = 20,wts.plot = T, 
           bar.ylim = c(-1,4),list.arg=list.arg)

mtext(paste(clist,collapse="_"),side=1,line=5)

Note, the full investment is assumed (sum=1) for the following.

Long only constraints

clist <- c("lo")
cset <- NULL
cset <-combine.cset(clist=clist,returns=returns,list.arg=list.arg)
gmv(returns, cset=cset, wts.only=T,digits=4)
efrontPlot(returns, cset, rf = .003, npoints = 20,wts.plot = T,
        bar.ylim = c(-1,4),list.arg=list.arg)
mtext(paste(clist,collapse="_"),side=1,line=5)  

We will assume full investment as a default constraint in the next few scenarios.

Box constraints

clist <- c("box")
cset <- NULL
cset <-combine.cset(clist=clist,returns=returns,list.arg=list.arg)
gmv(returns, cset=cset, wts.only=T,digits=4)
efrontPlot(returns, cset, rf = .003, npoints = 20,wts.plot = T,
        bar.ylim = c(-1,4),list.arg=list.arg)
mtext(paste(clist,collapse="_"),side=1,line=5)

Long only and group constraints

clist <- c("lo","groups")
cset <- NULL
cset <-combine.cset(clist=clist,returns=returns,list.arg=list.arg)
gmv(returns, cset=cset, wts.only=T,digits=4)
efrontPlot(returns, cset, rf = .003, npoints = 20,wts.plot = T,
        bar.ylim = c(-1,4),list.arg=list.arg)
mtext(paste(clist,collapse="_"),side=1,line=5)

Long only and mean return constraints

clist <- c("lo","mu.target")
cset <-combine.cset(clist=clist,returns=returns,list.arg=list.arg)
gmv(returns, cset=cset, wts.only=T,digits=4)

Box and group constraints

clist <- c("box","groups")
cset <- NULL
cset <-combine.cset(clist=clist,returns=returns,list.arg=list.arg)
gmv(returns, cset=cset, wts.only=T,digits=4)
efrontPlot(returns, cset, rf = .003, npoints = 20,wts.plot = T,
        bar.ylim = c(-1,4),list.arg=list.arg)
mtext(paste(clist,collapse="_"),side=1,line=5)

Full investment, long only and turnover (2 versions) constraints

clist <- c("lo","turnover")
cset <- NULL
cset <-combine.cset(clist=clist,returns=returns,list.arg=list.arg)
gmv(returns, cset=cset, wts.only=T,digits=4)
efrontPlot(returns, cset, rf = .003, npoints = 20,wts.plot = T,
        bar.ylim = c(-1,4),list.arg=list.arg)
mtext(paste(clist,collapse="_"),side=1,line=5)
# 1+4+1+4+4+2+2+1+4+4+4  
# sum+lo+mu.target+box+box+group+group+turnover+w.sell+w.buy+w.initial

clist <- c("lo","turnover.hobbs")
cset <- NULL
cset <-combine.cset(clist=clist,returns=returns,list.arg=list.arg)
gmv(returns, cset=cset, wts.only=T,digits=4)
efrontPlot(returns, cset, rf = .003, npoints = 20,wts.plot = T,
        bar.ylim = c(-1,4),list.arg=list.arg)
mtext(paste(clist,collapse="_"),side=1,line=5)
# 1+4+1+4+4+2+2+1+4+4+4  
# sum+lo+mu.target+box+box+group+group+turnover+w.sell+w.buy+w.initial

Propcost constraints

clist <- c("propcost")
cset <- NULL
cset <-combine.cset(clist=clist,returns=returns,list.arg)
gmv(returns, cset=cset, wts.only=T,digits=4)
# global minum variance portfolio can always be achieved if all the initial weights are consumed by proportional cost, hence the new weights all equals to zero. 

efrontPlot(returns, cset, rf = .003, npoints = 20,wts.plot = T,
        bar.ylim = c(-1,4),list.arg=list.arg)
mtext(paste(clist,collapse="_"),side=1,line=5)

Long only and propcost constraints

clist <- c("lo","propcost")
cset <- NULL
cset <-combine.cset(clist=clist,returns=returns,list.arg)

try(efrontPlot(returns, cset, rf = .003, npoints = 20,wts.plot = T,
        bar.ylim = c(-1,4),list.arg=list.arg))

Box and propcost constraints

clist <- c("box","propcost")
cset <- NULL
cset <-combine.cset(clist=clist,returns=returns,list.arg)

efrontPlot(returns, cset, rf = .003, npoints = 20,wts.plot = T,
        bar.ylim = c(-1,4),list.arg=list.arg)
mtext(paste(clist,collapse="_"),side=1,line=5)

Full investment, box and propcost constraints (Bad example, expect errors)

clist <- c("sum","box","propcost")
list.arg <- list( sum=sum,
                  upper=upper,
                  lower=lower,
                  ptc=ptc,
                  w.initial=w.initial)
print(list.arg)
cset <- NULL
cset <-try(combine.cset(clist=clist,returns=returns,list.arg))
# Expected error msg: Error in propcost.modify(cset.i) : 
# sum constraint are not combinable with propcost constraint

kecoli/PCRM documentation built on May 7, 2022, 9:33 a.m.