Function to compute Left risk measure.

Description

Function to compute Left risk measure.

Usage

LR_cp(data, FT, ov)

Arguments

Value

A (N x T) data.frame containing the LR_cp measure for the N time series over time windows

Examples

LR <- LR_cp(sample.data, FT= 1290, ov = 125)
df <- as.data.frame(matrix(unlist(LR), nrow = length(LR), ncol = ncol(sample.data)))
colnames(df) <- c(paste("tw", rep(1:16)))
plot(df[,1], pch=19, col=asset.label$label, ylab="LR_cp", xlab="ETFs")

Data for clustering and labeling ETFs

Description

Contains asset class of ETFs

Usage

asset.label

Format

A data frame with 44 observations (rows) on 3 variables (columns)

id

name of ETF

label

from 1 to 5 according to the specific asset class

class

specific asset class (5 categories)

Source

Created in-house to serve as an example

Examples

data(asset.label)

Function to create overlapping windows.

Description

Function to create overlapping windows.

Usage

create_overlapping_windows(data, FT = 1290, ov = 125)

Arguments

Value

a list containing the rolling windows

Function to compute gross returns.

Description

Calculate gross returns from prices.

Usage

g_ret(x)

Arguments

Value

An object of the same class as x with the gross returns

Procedure to find the most-left distribution set.

Description

Estimation of the vector of unknown parameters for the density functions associated with the two mixture components.

Usage

infoset(y, plot_cp)

Arguments

Value

An object of class "infoset" is a list containing the following components for the firse two iterations (k=2):

change.points

a vector of change points.

prior.probability

the a priori probabilities.

first.type.errors

the cumulative distribution functions associated with the leftmost component of the mixture.

second.type.errors

the cumulative distribution functions associated with the rightmost component of the mixture.

mean

the parameters (drift) of the left-hand component of the log-normal mixture.

sd

the parameters (volatility) of the left-hand component of the log-normal mixture.

References

Mariani, F., Polinesi, G., Recchioni, M. C. (2022). A tail-revisited Markowitz mean-variance approach and a portfolio network centrality. Computational Management Science, 19(3), 425-455.

Mariani, F., Ciommi, M., Chelli, F. M., Recchioni, M. C. (2020). An iterative approach to stratification: Poverty at regional level in Italy. Social Indicators Research, 1-31.

Examples

gross.ret<-as.data.frame(lapply(sample.data, g_ret))
infoset(gross.ret$ETF_1, plot_cp = "T")

############################################################
## EXAMPLE 1: Clustering ETFs
############################################################


gross.ret<-as.data.frame(lapply(sample.data, g_ret))
result<-NULL
for(i in 1:ncol(gross.ret)){
 result[[i]]<-infoset(gross.ret[,i], plot_cp = "F")
}
output<-matrix(unlist(result),12,ncol=ncol(gross.ret)) # output contains the information set
output<-t(output)
rownames(output)<-colnames(gross.ret)
colnames(output)<-c("ch_1","ch_2","priori_1","priori_2","first_1",
                   "first_2","second_1","second_2","mean_1","mean_2","dev_1", "dev_2")
output<- as.data.frame(output)
group_label <- as.factor(asset.label$label)
d <- dist(output, method = 'euclidean')
hc_SIMS <- hclust(d, method = 'complete')
library(dendextend)
library(colorspace)
dend_SIMS <- as.dendrogram(hc_SIMS)
dend_SIMS <- color_branches(dend_SIMS, k = 4, col = c(1:4))
labels_colors(dend_SIMS) <-
       rainbow_hcl(5)[sort_levels_values(as.numeric(group_label)[order.dendrogram(dend_SIMS)])]
labels(dend_SIMS) <- paste(as.character(group_label)[order.dendrogram(dend_SIMS)],
       '(', labels(dend_SIMS), ')', sep = '')
dend_SIMS <- hang.dendrogram(dend_SIMS, hang_height = 0.001)
dend_SIMS <- assign_values_to_leaves_nodePar(dend_SIMS, 0.5, 'lab.cex')
dev.new()
old_par <- par(no.readonly = TRUE)
on.exit(par(old_par))
par(mar = c(1.8, 1.8, 1.8, 1))
plot(dend_SIMS, main = 'Complete linkage (the labels give the true ETF class)',
     horiz = TRUE, nodePar = list(cex = 0.007))
legend('topleft', legend = c('emerging equity Asia', 'emerging equity America',
                           'corporate bond', 'commodities', 'aggregate bond'),
             fill = c('#BDAB66', '#65BC8C', '#C29DDE', '#E495A5', '#55B8D0'), border = 'white')

Plot methods for a LR_cp object

Description

Plot methods for a LR_cp object

Usage

plot_LR_cp(LR_cp_measure, asset_label)

Arguments

Value

plot of LR_cp measures by asset classes

Plot methods for a ptf_construction object

Description

Plot methods for a ptf_construction object

Usage

plot_ptf(ptf.oos.values)

Arguments

Value

plot oos portfolio values

Function to compute portfolio values

Description

Function to compute portfolio values

Usage

ptf_construction(
  data,
  FT,
  ov,
  LR_cp_measure,
  ptf = c("M", "C_M", "EDC", "C_EDC")
)

Arguments

Value

An object of class "ptf_construction" is a list containing the following components for all the time windows considered:

ptf oos value

a vector of out of sample returns.

weigths

portfolio weights.

Data for infoset function

Description

Contains daily prices of ETFs

Usage

sample.data

Format

A data frame with 3174 rows and 44 columns

Source

Created in-house to serve as an example

Examples

data(sample.data)

Data with time points for portfolio construction using the LR_cp measure

Description

Contains daily prices of ETFs

Usage

sample.data.ts

Format

A data frame with 3175 rows and 45 columns

Source

Created in-house to serve as an example

Examples

data(sample.data.ts)

Plot methods for a ptf_construction object

Description

Plot methods for a ptf_construction object

Usage

summary_ptf(ptf.oos.values)

Arguments

Value

summary of oos portfolio values

Function to find the most-left distribution set.

Description

An adaptive clustering algorithm identifies sub-groups of gross returns at each iteration by approximating their distribution with a sequence of two-component log-normal mixtures.

Usage

tail_mixture(y, shift, n_it, plot)

Arguments

Value

data object