Package 'FRAPO'

Title: Financial Risk Modelling and Portfolio Optimisation with R
Description: Accompanying package of the book 'Financial Risk Modelling and Portfolio Optimisation with R', second edition. The data sets used in the book are contained in this package.
Authors: Bernhard Pfaff [aut, cre]
Maintainer: Bernhard Pfaff <[email protected]>
License: GPL (>= 3)
Version: 0.4-1
Built: 2025-01-29 02:36:35 UTC
Source: https://github.com/bpfaff/frapo

Help Index

Utility functions for handling book examples

Description

Utility functions for returning a list of the included examples and displaying, executing, saving and editing the example codes are provided.

Usage

listEx()
showEx(Example)
saveEx(Example)
editEx(Example, ...)
runEx(Example, ...)

Arguments

Example

Characater, the name of the example as contained in listEx().

...

Ellipsis argument. See details.

Details

The ellipsis arguments in the function editEx() are passed down to the function file.edit(). If the option editor is unset and/or a different editor shall be employed for openening the example code, then the ellipsis argument can be utilised by editor = "foo", wherey foo is the name of the editor to be used.
The ellipsis arguments in the function runEx() are passed down to the function source().

Value

listEx
Returns a character vector of the examples' names.
showEx
Returns the example of of Example to the console.
saveEx
Returns a logical whether the saving of the R code example into the working directory was successful.
editEx
Opens a copy of the example code in an editor.
runEx
Executes the example code.

Author(s)

Bernhard Pfaff

See Also

file.edit, source

Examples

## Not run: 
listEx()
showEx(Example = "Part1Chapter3Ex2")
saveEx(Example = "Part1Chapter3Ex2")
runEx(Example = "Part1Chapter3Ex2", echo = TRUE)
editEx(Example = listEx()[1], editor = "emacs")

## End(Not run)

Capping a series to bounds

Description

The values of a series that are absolute greater than min and/or max are capped to these specified values.

Usage

capser(y, min, max)

Arguments

y

Objects of classes: numeric, matrix, data.frame, ts, mts, and timeSeries are supported.
min

Numeric, minimum value for the series.
max

Numeric, maximim value for the series.

Value

An object of the same class as y, containing the truncated series.

Methods

y = "data.frame"

The calculation is applied per column of the data.frame and only if all columns are numeric.

y = "matrix"

The calculation is applied per column of the matrix.

y = "mts"

The calculation is applied per column of the mts object. The attributes are preserved and an object of the same class is returned.

y = "numeric"

Calculation of the es trend.

y = "timeSeries"

The calculation is applied per column of the timeSeries object and an object of the same class is returned.

y = "ts"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

y = "xts"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

y = "zoo"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

Author(s)

Bernhard Pfaff

See Also

trdbilson, trdbinary, trdes, trdhp, trdsma, trdwma

Examples

data(StockIndex)
y <- StockIndex[, "SP500"]
cs <- capser(y, min = 100, max = 200)
head(cs)

Diversification Measures

Description

These functions compute the diversification ratio, the volatility weighted average correlation and concentration ratio of a portfolio.

Usage

dr(weights, Sigma)
cr(weights, Sigma)
rhow(weights, Sigma)

Arguments

weights

Vector: portfolio weights.
Sigma

Matrix: Variance-covariance matrix of portfolio assets.

Details

The diversification ratio of a portfolio is defined as:

DR(ω)=∑i=1Nωiσiω′ΣωDR(\omega) = \frac{\sum_{i = 1}^N \omega_i \sigma_i}{\sqrt{\omega' \Sigma \omega}}

for a portfolio of NN assets and ωi\omega_i signify the weight of the i-th asset and σi\sigma_i its standard deviation and Σ\Sigma the variance-covariance matrix of asset returns. The diversification ratio is therefore the weighted average of the assets' volatilities divided by the portfolio volatility.

The concentration ration is defined as:

CR=∑i=1N(ωiσi)2(∑i=1Nωiσi)2CR = \frac{\sum_{i = 1}^N (\omega_i \sigma_i)^2}{(\sum_{i = 1}^N \omega_i \sigma_i)^2}

and the volatility-weighted average correlation of the assets as:

ρ(ω)=∑i>jN(ωiσiωjσj)ρij∑i>jN(ωiσiωjσj)\rho(\omega) = \frac{\sum_{i > j}^N (\omega_i \sigma_i \omega_j \sigma_j)\rho_{ij}}{\sum_{i > j}^N (\omega_i \sigma_i \omega_j \sigma_j)}

The following equation between these measures does exist:

DR(ω)=1ρ(ω)(1−CR(ω))+CR(ω)DR(\omega) = \frac{1}{\sqrt{\rho(\omega) (1 - CR(\omega)) + CR(\omega)}}

Value

numeric, the value of the diversification measure.

Author(s)

Bernhard Pfaff

References

Choueifaty, Y. and Coignard, Y. (2008): Toward Maximum Diversification, Journal of Portfolio Management, Vol. 34, No. 4, 40–51.

Choueifaty, Y. and Coignard, Y. and Reynier, J. (2011): Properties of the Most Diversified Portfolio, Working Paper, http://papers.ssrn.com

See Also

PMD

Examples

data(MultiAsset)
Rets <- returnseries(MultiAsset, method = "discrete", trim = TRUE)
w <- Weights(PMD(Rets))
V <- cov(Rets)
DR <- dr(w, V)
CR <- cr(w, V)
RhoW <- rhow(w, V)
test <- 1 / sqrt(RhoW * (1 - CR) + CR)
all.equal(DR, test)

ESCB FX Reference Rates

Description

Daily spot rates of major currencies against the EUR.

Usage

data(ESCBFX)

Format

A data frame with 3,427 daily observations of the spot currency rates rates AUD, CAD, CHF, GBP, HKD, JPY and USD against EUR. The sample starts in 1999-01-04 and ends in 2012-04-04.

Details

The data has been retrieved from the Statistical Data Warehouse (SDW) Internet-Site of the ECB. In case of missing data entries due to holidays, the last observed data point has been carried forward.

Source

http://sdw.ecb.europa.eu

Examples

data(ESCBFX)

EURO STOXX 50

Description

Weekly price data of 48 EURO STOXX 50 constituents.

Usage

data(EuroStoxx50)

Format

A data frame with 265 weekly observations of 48 members of the EURO STOXX 50 index. The sample starts at 2003-03-03 and ends in 2008-03-24.

Details

The data set was used in the reference below. The authors adjusted the price data for dividends and have removed stocks if two or more consecutive missing values were found. In the remaining cases the NA entries have been replaced by interpolated values.

Source

http://host.uniroma3.it/docenti/cesarone/DataSets.htm
http://finance.yahoo.com/

References

Cesarone, F. and Scozzari, A. and Tardella, F.: Portfolio selection problems in practice: a comparison between linear and quadratic optimization models, Working Paper, Universita degli Studi Roma Tre, Universita Telematica delle Scienze Umane and Universita di Roma, July 2010.
http://arxiv.org/ftp/arxiv/papers/1105/1105.3594.pdf

Examples

data(EuroStoxx50)

FTSE 100

Description

Weekly price data of 79 FTSE 100 constituents.

Usage

data(FTSE100)

Format

A data frame with 265 weekly observations of 79 members of the FTSE 100 index. The sample starts at 2003-03-03 and ends in 2008-03-24.

Details

The data set was used in the reference below. The authors adjusted the price data for dividends and have removed stocks if two or more consecutive missing values were found. In the remaining cases the NA entries have been replaced by interpolated values.

Source

http://host.uniroma3.it/docenti/cesarone/DataSets.htm
http://finance.yahoo.com/

References

Cesarone, F. and Scozzari, A. and Tardella, F.: Portfolio selection problems in practice: a comparison between linear and quadratic optimization models, Working Paper, Universita degli Studi Roma Tre, Universita Telematica delle Scienze Umane and Universita di Roma, July 2010.
http://arxiv.org/ftp/arxiv/papers/1105/1105.3594.pdf

Examples

data(FTSE100)

INDTRACK1: Hang Seng Index and Constituents

Description

Weekly price data of the Hang Seng index and 31 constituents.

Usage

data(INDTRACK1)

Format

A data frame with 291 weekly observations of the index and 31 members of the Hang Seng index. The sample starts in March 1991 and ends in September 1997.

Details

The data set was used in the first two references below. Stocks with missing values during the sample period have been discarded. The data was downloaded from DATASTREAM and has been anonymized. The first columne refers to the index data itself. See the attached license file that is part of this package: ‘BeasleyLicence’.

Source

http://people.brunel.ac.uk/~mastjjb/jeb/info.html
http://people.brunel.ac.uk/~mastjjb/jeb/orlib/legal.html

References

Canakgoz, N.A. and J.E. Beasley (2008), Mixed-integer programming approaches for index tracking and enhanced indexation, European Journal of Operational Research, Vol. 196, 384–399.
Beasley, J.E. and N. Meade and T.-J. Chang (2003), An evolutionary heuristic for the index tracking problem, European Journal of Operational Research, Vol. 148, 621–643.
Beasley, J. E. (1990), OR-Library: Distributing Test Problems by Electronic Mail, Journal of the Operational Research Society, Vol. 41, No. 11, 1069–1072.

Examples

data(INDTRACK1)

INDTRACK2: DAX 100 Index and Constituents

Description

Weekly price data of the DAX 100 and 85 constituents.

Usage

data(INDTRACK2)

Format

A data frame with 291 weekly observations of the index and 85 members of the DAX 100 index. The sample starts in March 1991 and ends in September 1997.

Details

The data set was used in the first two references below. Stocks with missing values during the sample period have been discarded. The data was downloaded from DATASTREAM and has been anonymized. The first columne refers to the index data itself. See the attached license file that is part of this package: ‘BeasleyLicence’.

Source

http://people.brunel.ac.uk/~mastjjb/jeb/info.html
http://people.brunel.ac.uk/~mastjjb/jeb/orlib/legal.html

References

Canakgoz, N.A. and J.E. Beasley (2008), Mixed-integer programming approaches for index tracking and enhanced indexation, European Journal of Operational Research, Vol. 196, 384–399.
Beasley, J.E. and N. Meade and T.-J. Chang (2003), An evolutionary heuristic for the index tracking problem, European Journal of Operational Research, Vol. 148, 621–643.
Beasley, J. E. (1990), OR-Library: Distributing Test Problems by Electronic Mail, Journal of the Operational Research Society, Vol. 41, No. 11, 1069–1072.

Examples

data(INDTRACK2)

INDTRACK3: FTSE 100 Index and Constituents

Description

Weekly price data of of the FTSE 100 index and 89 constituents.

Usage

data(INDTRACK3)

Format

A data frame with 291 weekly observations of of the index and 89 members of the FTSE 100 index. The sample starts in March 1991 and ends in September 1997.

Details

The data set was used in the first two references below. Stocks with missing values during the sample period have been discarded. The data was downloaded from DATASTREAM and has been anonymized. The first columne refers to the index data itself. See the attached license file that is part of this package: ‘BeasleyLicence’.

Source

http://people.brunel.ac.uk/~mastjjb/jeb/info.html
http://people.brunel.ac.uk/~mastjjb/jeb/orlib/legal.html

References

Canakgoz, N.A. and J.E. Beasley (2008), Mixed-integer programming approaches for index tracking and enhanced indexation, European Journal of Operational Research, Vol. 196, 384–399.
Beasley, J.E. and N. Meade and T.-J. Chang (2003), An evolutionary heuristic for the index tracking problem, European Journal of Operational Research, Vol. 148, 621–643.
Beasley, J. E. (1990), OR-Library: Distributing Test Problems by Electronic Mail, Journal of the Operational Research Society, Vol. 41, No. 11, 1069–1072.

Examples

data(INDTRACK3)

INDTRACK4: S&P 100 Index and Constituents

Description

Weekly price data of S&P 100 index and 98 constituents.

Usage

data(INDTRACK4)

Format

A data frame with 291 weekly observations of the index 98 members of the S&P 100 index. The sample starts in March 1991 and ends in September 1997.

Details

The data set was used in the first two references below. Stocks with missing values during the sample period have been discarded. The data was downloaded from DATASTREAM and has been anonymized. The first columne refers to the index data itself. See the attached license file that is part of this package: ‘BeasleyLicence’.

Source

http://people.brunel.ac.uk/~mastjjb/jeb/info.html
http://people.brunel.ac.uk/~mastjjb/jeb/orlib/legal.html

References

Canakgoz, N.A. and J.E. Beasley (2008), Mixed-integer programming approaches for index tracking and enhanced indexation, European Journal of Operational Research, Vol. 196, 384–399.
Beasley, J.E. and N. Meade and T.-J. Chang (2003), An evolutionary heuristic for the index tracking problem, European Journal of Operational Research, Vol. 148, 621–643.
Beasley, J. E. (1990), OR-Library: Distributing Test Problems by Electronic Mail, Journal of the Operational Research Society, Vol. 41, No. 11, 1069–1072.

Examples

data(INDTRACK4)

INDTRACK5: Nikkei 225 Index and Constituents

Description

Weekly price data of Nikkei 225 index and 225 constituents.

Usage

data(INDTRACK5)

Format

A data frame with 291 weekly observations of the index and 225 members of the Nikkei 225 index. The sample starts in March 1991 and ends in September 1997.

Details

The data set was used in the first two references below. Stocks with missing values during the sample period have been discarded. The data was downloaded from DATASTREAM and has been anonymized. The first columne refers to the index data itself. See the attached license file that is part of this package: ‘BeasleyLicence’.

Source

http://people.brunel.ac.uk/~mastjjb/jeb/info.html
http://people.brunel.ac.uk/~mastjjb/jeb/orlib/legal.html

References

Canakgoz, N.A. and J.E. Beasley (2008), Mixed-integer programming approaches for index tracking and enhanced indexation, European Journal of Operational Research, Vol. 196, 384–399.
Beasley, J. E. (1990), OR-Library: Distributing Test Problems by Electronic Mail, Journal of the Operational Research Society, Vol. 41, No. 11, 1069–1072.

Examples

data(INDTRACK5)

INDTRACK6: S&P 500 Index and Constituents

Description

Weekly price data of S&P 500 index and 457 constituents.

Usage

data(INDTRACK6)

Format

A data frame with 291 weekly observations of the index and 457 members of the S&P 500 index. The sample starts in March 1991 and ends in September 1997.

Details

The data set was used in the first two references below. Stocks with missing values during the sample period have been discarded. The data was downloaded from DATASTREAM and has been anonymized. The first columne refers to the index data itself. See the attached license file that is part of this package: ‘BeasleyLicence’.

Source

http://people.brunel.ac.uk/~mastjjb/jeb/info.html
http://people.brunel.ac.uk/~mastjjb/jeb/orlib/legal.html

References

Canakgoz, N.A. and J.E. Beasley (2008), Mixed-integer programming approaches for index tracking and enhanced indexation, European Journal of Operational Research, Vol. 196, 384–399.
Beasley, J. E. (1990), OR-Library: Distributing Test Problems by Electronic Mail, Journal of the Operational Research Society, Vol. 41, No. 11, 1069–1072.

Examples

data(INDTRACK6)

Milano Indice Borsa Telematica

Description

Weekly price data of 226 MIBTEL constituents.

Usage

data(MIBTEL)

Format

A data frame with 265 weekly observations of 226 members of the Milano Indice Borsa Telematica index. The sample starts at 2003-03-03 and ends in 2008-03-24.

Details

The data set was used in the reference below. The authors adjusted the price data for dividends and have removed stocks if two or more consecutive missing values were found. In the remaining cases the NA entries have been replaced by interpolated values.

Source

http://host.uniroma3.it/docenti/cesarone/DataSets.htm
http://finance.yahoo.com/

References

Cesarone, F. and Scozzari, A. and Tardella, F.: Portfolio selection problems in practice: a comparison between linear and quadratic optimization models, Working Paper, Universita degli Studi Roma Tre, Universita Telematica delle Scienze Umane and Universita di Roma, July 2010.
http://arxiv.org/ftp/arxiv/papers/1105/1105.3594.pdf

Examples

data(MIBTEL)

Marginal Contribution to Risk

Description

This function returns the marginal contributions to portfolio risk, whereby the latter is defined in terms of the portfolio standard deviation.

Usage

mrc(weights, Sigma, percentage = TRUE)

Arguments

weights

Vector: portfolio weights.
Sigma

Matrix: Variance-covariance matrix of portfolio assets.
percentage

Logical, whether the marginal risk contributions shall be returned as percentages that sum to 100 (default) or as decimal numbers.

Details

The marginal contributions to risk are computed for a given dispersion matrix and weight vector.

Value

numeric, the marginal risk contributions of the portfolio's asset.

Author(s)

Bernhard Pfaff

Multi Asset Index Data

Description

Month-end price data of stock and bond indices and gold.

Usage

data(MultiAsset)

Format

A data frame with 85 month-end observations of stock and bond indices and gold, represented by the ETF SPDR Gold. The sample starts at 2004-11-30 and ends in 2011-11-30.

Details

The data set has been obtained from Yahoo Finance and hereby the unadjusted closing prices have been retrieved. If a month-end value was not reported, the value of the previous day has been used. The Yahoo mnemonics with the respective item description are listed below:

GSPC

United States: S \& P 500 Index (Equity)

RUA

United States: Russell 3000 Index (Equity)

GDAXI

Germany: DAX (XETRA) Index (Equity)

FTSE

United Kingdom: FTSE 100 Index (Equity)

N225

Japan: Nikkei 225 Index (Equity)

EEM

iShares: MSCI Emerging Markets Index (Equity)

DJCBTI

United States: Dow Jones CBOT Treasury Index (Bonds)

GREXP

Germany: REX-Performance Index (Bonds)

BG05.L

United Kingdom: Gilt All Index (Bonds)

GLD

United States: SPDR Gold Shares (Commodities)

Source

http://finance.yahoo.com/

Examples

data(MultiAsset)

NASDAQ

Description

Weekly price data of 2,196 NASDAQ constituents.

Usage

data(NASDAQ)

Format

A data frame with 265 weekly observations of 2196 members of the NASDAQ index. The sample starts at 2003-03-03 and ends in 2008-03-24.

Details

The data set was used in the reference below. The authors adjusted the price data for dividends and have removed stocks if two or more consecutive missing values were found. In the remaining cases the NA entries have been replaced by interpolated values.

Source

http://host.uniroma3.it/docenti/cesarone/DataSets.htm
http://finance.yahoo.com/

References

Cesarone, F. and Scozzari, A. and Tardella, F.: Portfolio selection problems in practice: a comparison between linear and quadratic optimization models, Working Paper, Universita degli Studi Roma Tre, Universita Telematica delle Scienze Umane and Universita di Roma, July 2010.
http://arxiv.org/ftp/arxiv/papers/1105/1105.3594.pdf

Examples

data(NASDAQ)

Portfolio optimisation with average draw down constraint

Description

This function returns the result of a long-only portfolio optimization whereby the portfolio's (historic) average draw down is constrained to an upper limit.

Usage

PAveDD(PriceData, AveDD = 0.1, softBudget = FALSE, ...)

Arguments

PriceData

A rectangular array of price data.
AveDD

Numeric, the upper bound of the average portfolio draw down.
softBudget

Logical, whether the budget constraint shall be implemented as a soft constraint, i.e. the sum of the weights can be less than one. The default is to use an equality constraint.
...

Arguments are passed down to Rglpk_solve_LP

Details

This function implements a long-only portfolio optimisation with an average draw down constraint (see references below). The problem can be stated in the form of a linear program and GLPK is used as solver.

Value

An object of formal class "PortAdd".

Note

A warning is issued in case the solver had exit status not equal to zero.

Author(s)

Bernhard Pfaff

References

Chekhlov, A. and Uryasev, S. and Zabarankin, M., Portfolio Optimization with Drawdown Constraints, Department of Industrial and Systems Engineering, University of Florida, Research Report 2000-5, 2000, Gainesville, FL. Chekhlov, A. and Uryasev, S. and Zabarankin, M., Drawdown Measure in Portfolio Optimization, International Journal of Theoretical and Applied Finance, 2005, 8(1), 13–58.

See Also

"PortSol", "PortAdd", "PortDD", PMaxDD, PCDaR, PMinCDaR

Examples

## Not run: 
data(StockIndex)
popt <- PAveDD(PriceData = StockIndex, AveDD = 0.1, softBudget = TRUE)

## End(Not run)

Portfolio optimisation with conditional draw down at risk constraint

Description

This function returns the result of a long-only portfolio optimization whereby the portfolio's (historic) conditional draw down at risk is constrained to an upper limit.

Usage

PCDaR(PriceData, alpha = 0.95, bound = 0.05, softBudget = FALSE, ...)

Arguments

PriceData

A rectangular array of price data.
alpha

Numeric, the confidence level for which the conditional draw down shall be computed.
bound

Numeric, the upper bound of the conditional draw down.
softBudget

Logical, whether the budget constraint shall be implemented as a soft constraint, i.e. the sum of the weights can be less than one. The default is to use an equality constraint.
...

Arguments are passed down to Rglpk_solve_LP

Details

This function implements a long-only portfolio optimisation with a CDaR constraint (see references below). The problem can be stated in the form of a linear program and GLPK is used as solver.

Value

An object of formal class "PortAdd".

Note

A warning is issued in case the solver had exit status not equal to zero.

Author(s)

Bernhard Pfaff

References

Chekhlov, A. and Uryasev, S. and Zabarankin, M., Portfolio Optimization with Drawdown Constraints, Department of Industrial and Systems Engineering, University of Florida, Research Report 2000-5, 2000, Gainesville, FL. Chekhlov, A. and Uryasev, S. and Zabarankin, M., Drawdown Measure in Portfolio Optimization, International Journal of Theoretical and Applied Finance, 2005, 8(1), 13–58.

See Also

"PortSol", "PortCdd", "PortDD", PMaxDD, PAveDD, PMinCDaR

Examples

## Not run: 
data(StockIndex)
popt <- PCDaR(PriceData = StockIndex, alpha = 0.95,
              bound = 0.1, softBudget = TRUE)

## End(Not run)

Equal risk contributed portfolios

Description

This function solves for equal risk contributed portfolio weights.

Usage

PERC(Sigma, par = NULL, percentage = TRUE, optctrl = ctrl(), ...)

Arguments

Sigma

Matrix, the variance-covariance matrix of asset returns
par

Vector, the initial values of the weights.
percentage

Logical, whether the weights shall be returned as decimals or percentages (default).
optctrl

Object of class Rcpp_CTRL.
...

Ellipsis argument is passed down to nlminb().

Details

The objective function is the standard deviation of the marginal risk contributions, which is minimal, i.e. zero, if all contributions are equal. The weights are rescaled to sum to unity.

Value

An object of formal class "PortSol".

Note

The optimisation is conducted by calling nlminb(). Hereby, the arguments lower = 0 and upper = 1 have been specified.

Author(s)

Bernhard Pfaff

References

Maillard, S. and Roncalli, T. and Teiletche, J.: The Properties of Equally Weighted Risk Contribution Portfolios, Journal of Portfolio Management, Vol. 36, No. 4, Summer 2010, 60–70.

See Also

"PortSol"

Examples

data(MultiAsset)
Rets <- returnseries(MultiAsset, method = "discrete", trim = TRUE,
                     percentage = TRUE)
V <- cov(Rets)
ERC <- PERC(V)
ERC
w <- Weights(ERC)
w * V

Global Minimum Variance Portfolio

Description

This function returns the solution of the global minimum variance portfolio (long-only).

Usage

PGMV(Returns, percentage = TRUE, optctrl = ctrl(), ...)

Arguments

Returns

A rectangular array of return data.
percentage

Logical, whether the weights shall be returned as decimals or percentages (default).
optctrl

Object of class Rcpp_CTRL.
...

Arguments are passed down to cov.

Value

An object of formal class "PortSol".

Note

The optimisation is conducted by calling cccp().

Author(s)

Bernhard Pfaff

See Also

"PortSol"

Examples

data(MultiAsset)
Rets <- returnseries(MultiAsset, method = "discrete", trim = TRUE)
PGMV(Rets)

Methods for Function plot in Package graphics

Description

Additional arguments to the plot-method pertinent to the defined S4-classes in this package are detailed below.

Usage

## S4 method for signature 'PortDD'
plot(x, main = NULL, xlab = NULL, ylab = NULL,
col = c("black", "red"), grid = TRUE, invert = TRUE, ...)

Arguments

x

PortDD: an object that belongs to this virtual class.
main

character: The title of the plot.
xlab

character: The description of the x-axis.
ylab

character: The description of the y-axis.
col

character: Two-element vector of the names of the colors for the portfolio's draw downs and the optimal level.
grid

Logical: Whether to superimpose a grid on the plot.
invert

Logical: Whether the draw downs shall be plotted as negative numbers; the default is TRUE.
...

Ellipsis argument is passed to the generic plot function.

Author(s)

Bernhard Pfaff

Portfolio optimisation with maximum draw down constraint

Description

This function returns the result of a long-only portfolio optimization whereby the portfolio's (historic) draw down is constrained to an upper limit.

Usage

PMaxDD(PriceData, MaxDD = 0.1, softBudget = FALSE, ...)

Arguments

PriceData

A rectangular array of price data.
MaxDD

Numeric, the upper bound of the maximum draw down.
softBudget

Logical, whether the budget constraint shall be implemented as a soft constraint, i.e. the sum of the weights can be less than one. The default is to use an equality constraint.
...

Arguments are passed down to Rglpk_solve_LP

Details

This function implements a long-only portfolio optimisation with a maximum draw down constraint (see references below). The problem can be stated in the form of a linear program and GLPK is used as solver.

Value

An object of formal class "PortMdd".

Note

A warning is issued in case the solver had exit status not equal to zero.

Author(s)

Bernhard Pfaff

References

Chekhlov, A. and Uryasev, S. and Zabarankin, M., Portfolio Optimization with Drawdown Constraints, Department of Industrial and Systems Engineering, University of Florida, Research Report 2000-5, 2000, Gainesville, FL. Chekhlov, A. and Uryasev, S. and Zabarankin, M., Drawdown Measure in Portfolio Optimization, International Journal of Theoretical and Applied Finance, 2005, 8(1), 13–58.

See Also

"PortSol", "PortMdd", "PortDD", PCDaR, PAveDD, PMinCDaR

Examples

## Not run: 
data(StockIndex)
popt <- PMaxDD(PriceData = StockIndex, MaxDD = 0.1, softBudget = TRUE)

## End(Not run)

Most Diversified Portfolio

Description

This function returns the solution of the most diversified portfolio (long-only).

Usage

PMD(Returns, percentage = TRUE, optctrl = ctrl(),...)

Arguments

Returns

A rectangular array of return data.
percentage

Logical, whether the weights shall be returned as decimals or percentages (default).
optctrl

Object of class Rcpp_CTRL.
...

Arguments are passed down to cov().

Details

The optimisation problem is akin to that of a global minimum-variance portfolio, but instead of using the variance-covariance matrix of the asset returns, the correlation matrix is utilised as dispersion measure. The weights are then recovered by rescaling the optimal solution with the assets' standard deviations and normalizing, such that the weights sum to one.

Value

An object of formal class "PortSol".

Note

The optimisation is conducted by calling cccp().

Author(s)

Bernhard Pfaff

References

Choueifaty, Y. and Coignard, Y. (2008): Toward Maximum Diversification, Journal of Portfolio Management, Vol. 34, No. 4, 40–51.

Choueifaty, Y. and Coignard, Y. and Reynier, J. (2011): Properties of the Most Diversified Portfolio, Working Paper, http://papers.ssrn.com

See Also

"PortSol"

Examples

data(MultiAsset)
Rets <- returnseries(MultiAsset, method = "discrete", trim = TRUE)
PMD(Rets)

Portfolio optimisation for minimum conditional draw down at risk

Description

This function returns the result of a long-only portfolio optimization whereby the portfolio's (historic) conditional draw down at risk is minimized.

Usage

PMinCDaR(PriceData, alpha = 0.95, softBudget = FALSE, ...)

Arguments

PriceData

A rectangular array of price data.
alpha

Numeric, the confidence level for which the conditional draw down shall be computed.
softBudget

Logical, whether the budget constraint shall be implemented as a soft constraint, i.e. the sum of the weights can be less than one. The default is to use an equality constraint.
...

Arguments are passed down to Rglpk_solve_LP

Details

This function implements a long-only portfolio optimisation for a minimum conditional draw down at risk (see references below). The problem can be stated in the form of a linear program and GLPK is used as solver.

Value

An object of formal class "PortAdd".

Note

A warning is issued in case the solver had exit status not equal to zero.

Author(s)

Bernhard Pfaff

References

Chekhlov, A. and Uryasev, S. and Zabarankin, M., Portfolio Optimization with Drawdown Constraints, Department of Industrial and Systems Engineering, University of Florida, Research Report 2000-5, 2000, Gainesville, FL. Chekhlov, A. and Uryasev, S. and Zabarankin, M., Drawdown Measure in Portfolio Optimization, International Journal of Theoretical and Applied Finance, 2005, 8(1), 13–58.

See Also

"PortSol", "PortCdd", "PortDD", PMaxDD, PAveDD, PCDaR

Examples

## Not run: 
data(StockIndex)
popt <- PMinCDaR(PriceData = StockIndex, alpha = 0.95, softBudget = FALSE)

## End(Not run)

Minimum Tail Dependent Portfolio

Description

This function computes the solution of a minimum tail dependent portfolio (long-only).

Usage

PMTD(Returns, method = c("EmpTC", "EVT"), k = NULL, percentage = TRUE,
     optctrl = ctrl(),...)

Arguments

Returns

A rectangular array of return data.
method

Character, the type of non-parametric estimation.
k

Integer, the threshold value for the order statistic. If left NULL, then k = sqrt(nrow(x)) is used.
percentage

Logical, whether the weights shall be returned as decimals or percentages (default).
optctrl

Object of class Rcpp_CTRL.
...

Arguments are passed down to rank.

Details

Akin to the optimisation of a global minimum-variance portfolio, the minimum tail dependennt portfolio is determined by replacing the variance-covariance matrix with the matrix of the lower tail dependence coefficients as returned by tdc.

Value

An object of formal class "PortSol".

Note

The optimisation is conducted by calling cccp().

Author(s)

Bernhard Pfaff

See Also

tdc, "PortSol"

Examples

data(StockIndex)
Rets <- returnseries(StockIndex, method = "discrete", trim = TRUE,
                     percentage = TRUE)
PMTD(Rets)

Class "PortAdd"

Description

This class is intended to hold the results from a portfolio optimisation with a constraint on its average draw down.

Objects from the Class

Objects can be created by calls of the form new("PortAdd", ...). This class extends the "PortSol" class.

Slots

AveDD:

Numeric, the average draw down.

DrawDown:

timeSeries, the hsitoric portfolio's draw downs.

weights:

Numeric, vector of optimal weights.

opt:

List, the result of the call to GLPK.

type:

Character, the type of the optimized portfolio.

call:

The call to the function that created the object.

Extends

Class "PortSol", directly.

Methods

No methods defined with class "PortAdd" in the signature.

Author(s)

Bernhard Pfaff

See Also

"PortSol", "PortMdd", "PortCdd"

Examples

showClass("PortAdd")

Class "PortCdd"

Description

This class is intended to hold the results from a portfolio optimisation with a constraint on its average draw down.

Objects from the Class

Objects can be created by calls of the form new("PortCdd", ...). This class extends the "PortSol" class.

Slots

CDaR:

Numeric, the conditional draw down at risk.

thresh:

Numeric, threshold value for draw downs at the α\alpha level.

DrawDown:

timeSeries, the hsitoric portfolios draw downs.

weights:

Numeric, vector of optimal weights.

opt:

List, the result of the call to GLPK.

type:

Character, the type of the optimized portfolio.

call:

The call to the function that created the object.

Extends

Class "PortSol", directly.

Methods

No methods defined with class "PortCdd" in the signature.

Author(s)

Bernhard Pfaff

See Also

"PortSol", "PortMdd", "PortAdd"

Examples

showClass("PortCdd")

Class "PortDD"

Description

Class union of "PortAdd", "PortCdd" and "PortMdd"

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

DrawDowns

signature(object = "PortDD"): Returns the portfolio draw downs.

plot

signature(object = "PortDD"): Time series plot of draw downs.

Note

This virtual class is intended for specifying methods that are common to all type of draw down portfolios.

Author(s)

Bernhard Pfaff

See Also

"PortAdd", "PortMdd", "PortCdd", PMinCDaR, PCDaR, PAveDD, PMaxDD

Examples

showClass("PortDD")

Class "PortMdd"

Description

This class is intended to hold the results from a portfolio optimisation with a constraint on its maximum draw down.

Objects from the Class

Objects can be created by calls of the form new("PortMdd", ...). This class extends the "PortSol" class.

Slots

MaxDD:

Numeric, the maximum draw down.

DrawDown:

timeSeries, the hsitoric portfolio's draw downs.

weights:

Numeric, vector of optimal weights.

opt:

List, the result of the call to GLPK.

type:

Character, the type of the optimized portfolio.

call:

The call to the function that created the object.

Extends

Class "PortSol", directly.

Methods

No methods defined with class "PortMdd" in the signature.

Author(s)

Bernhard Pfaff

See Also

"PortSol", "PortAdd", "PortCdd"

Examples

showClass("PortMdd")

Class "PortSol"

Description

This class is intended to hold the results for the weights of an optimal portfolio. Currently, this class is used for minimum-variance and equal-risk-contributed portfolios. It can further be used to store the results of optimal factor weights according to one of the aforementioned portfolio types.

Objects from the Class

Objects can be created by calls of the form new("PortSol", ...).

Slots

weights:

Numeric, vector of optimal weights.

opt:

List, the result of the call to the optimizing function.

type:

Character, the type of the optimized portfolio.

call:

The call to the function that created the object.

Methods

show

signature(object = "PortSol"): Returns the portfolio type as text with the optimal weights from the object.

Solution

signature(object = "PortSol"): Returns the list object of the optimizer, i.e. the slot opt from the object.

Weights

signature(object = "PortSol"): Returns the list object of the optimizer, i.e. the slot weights from the object.

update

signature(object = "PortSol"): updates object by calling the issuing function with altered arguments.

Author(s)

Bernhard Pfaff

Examples

showClass("PortSol")

Convert Returns from continuous to discrete and vice versa

Description

Either continuous returns or discrete returns can be converted into the other type.

Usage

returnconvert(y, convdir = c("cont2disc", "disc2cont"), percentage = TRUE)

Arguments

y

Objects of classes: numeric, matrix, data.frame, ts, mts, and timeSeries are supported.
convdir

Character, the type of return conversion.
percentage

Logical, if TRUE (the default) the returns, y, are expressed as percentages.

Value

An object of the same class as y, containing the converted returns.

Methods

y = "data.frame"

The calculation is applied per column of the data.frame and only if all columns are numeric.

y = "matrix"

The calculation is applied per column of the matrix.

y = "mts"

The calculation is applied per column of the mts object. The attributes are preserved and an object of the same class is returned.

y = "numeric"

Calculation of the returns.

y = "timeSeries"

The calculation is applied per column of the timeSeries object and an object of the same class is returned.

y = "ts"

Calculation of the returns. The attributes are preserved and an object of the same class is returned.

y = "xts"

Calculation of the returns. The attributes are preserved and an object of the same class is returned.

y = "zoo"

Calculation of the returns. The attributes are preserved and an object of the same class is returned.

Author(s)

Bernhard Pfaff

Examples

data(StockIndex)
yc <- diff(log(StockIndex[, "SP500"])) * 100
yd <- returnseries(StockIndex[, "SP500"], method = "discrete",
                   percentage = TRUE, trim = TRUE)
yconv <- returnconvert(yd, convdir = "disc2cont",
                       percentage = TRUE)
all.equal(yc, yconv)

Continuous and discrete returns

Description

Either continuous returns or discrete returns are computed for an object. The returns can be expressed as percenatges and the first NA value can be trimmed.

Usage

returnseries(y, method = c("continuous", "discrete"), percentage = TRUE,
             trim = FALSE, compound = FALSE)

Arguments

y

Objects of classes: numeric, matrix, data.frame, ts, mts, and timeSeries are supported.
method

Character, the type of return to be computed.
percentage

Logical, if TRUE (the default) the returns are expressed as percenatges.
trim

Logical, if FALSE (the default) the first value is set to NA such that the length of the return series coincides with the length of the series in levels.
compound

Logical, if FALSE (the default), then simple returns are computed and otherwise compounded returns.

Value

An object of the same class as y, containing the truncated series.

Methods

y = "data.frame"

The calculation is applied per column of the data.frame and only if all columns are numeric.

y = "matrix"

The calculation is applied per column of the matrix.

y = "mts"

The calculation is applied per column of the mts object. The attributes are preserved and an object of the same class is returned.

y = "numeric"

Calculation of the es trend.

y = "timeSeries"

The calculation is applied per column of the timeSeries object and an object of the same class is returned.

y = "ts"

Calculation of the returns. The attributes are preserved and an object of the same class is returned.

y = "xts"

Calculation of the returns. The attributes are preserved and an object of the same class is returned.

y = "zoo"

Calculation of the returns. The attributes are preserved and an object of the same class is returned.

Author(s)

Bernhard Pfaff

Examples

data(StockIndex)
y <- StockIndex[, "SP500"]
ret <- returnseries(y)
head(ret)

Standard & Poor's 500

Description

Weekly price data of 476 S&P 500 constituents.

Usage

data(SP500)

Format

A data frame with 265 weekly observations of 476 members of the S&P 500 index. The sample starts at 2003-03-03 and ends in 2008-03-24.

Details

The data set was used in the reference below. The authors adjusted the price data for dividends and have removed stocks if two or more consecutive missing values were found. In the remaining cases the NA entries have been replaced by interpolated values.

Source

http://host.uniroma3.it/docenti/cesarone/DataSets.htm
http://finance.yahoo.com/

References

Cesarone, F. and Scozzari, A. and Tardella, F.: Portfolio selection problems in practice: a comparison between linear and quadratic optimization models, Working Paper, Universita degli Studi Roma Tre, Universita Telematica delle Scienze Umane and Universita di Roma, July 2010.
http://arxiv.org/ftp/arxiv/papers/1105/1105.3594.pdf

Examples

data(SP500)

Square root of a quadratic matrix

Description

This function returns the square root of a quadratic and diagonalisable matrix.

Usage

sqrm(x, ...)

Arguments

x

matrix, must be quadratic.
...

The ellipsis argument is passed down to eigen().

Details

The computation of the square root of a matrix is based upon its eigen values and corresponding eigen vectors. The square matrix AA is diagonisable if there is a matrix VV such that D=V−1AVD = V^{-1}AV, whereby DD is a diagonal matrix. This is only achieved if the eigen vectors of the (n×n)(n \times n) matrix AA constitute a basis of dimension nn. The square root of AA is then A1/2=VD1/2V′A^{1/2} = V D^{1/2} V'.

Value

A matrix object and a scalar in case a (1×1)(1 \times 1) matrix has been provided.

Author(s)

Bernhard Pfaff

See Also

eigen

Examples

data(StockIndex)
S <- cov(StockIndex)
SR <- sqrm(S)
all.equal(crossprod(SR), S)

Stock Index Data

Description

Month-end price data of six stock indices.

Usage

data(StockIndex)

Format

A data frame with 240 month-end observations of six stock indices: SP 500, Nikkei 225, FTSE 100, CAC40, GDAX and Hang Seng index. The sample starts at 1991-07-31 and ends in 2011-06-30.

Details

The data set has been obtained from Yahoo Finance and hereby the unadjusted closing prices have been retrieved.

Source

http://finance.yahoo.com/

Examples

data(StockIndex)

Stock Index Data

Description

Adjusted month-end price data of six stock indices.

Usage

data(StockIndexAdj)

Format

A data frame with 240 month-end observations of six stock indices: SP 500, Nikkei 225, FTSE 100, CAC40, GDAX and Hang Seng index. The sample starts at 1991-07-31 and ends in 2011-06-30.

Details

The data set has been obtained from Yahoo Finance and hereby the adjusted closing prices have been retrieved.

Source

http://finance.yahoo.com/

Examples

data(StockIndexAdj)

Stock Index Data

Description

Adjusted daily price data of six stock indices.

Usage

data(StockIndexAdj)

Format

A data frame with 5,202 daily observations of six stock indices: SP 500, Nikkei 225, FTSE 100, CAC40, GDAX and Hang Seng index. The sample starts at 1991-07-01 and ends in 2011-06-30.

Details

The data set has been obtained from Yahoo Finance and hereby the adjusted closing prices have been retrieved.

Source

http://finance.yahoo.com/

Examples

data(StockIndexAdjD)

Tail Dependence Coefficient

Description

This function returns the pairwise tail dependence coefficients between NN series. The TDCs are estimated non-parametrically by either the empirical tail copula or based on the stable tail-dependence function.

Usage

tdc(x, method = c("EmpTC", "EVT"), lower = TRUE, k = NULL, ...)

Arguments

x

Matrix, or an object that can be coerced to it.
method

Character, the type of non-parametric estimation.
lower

Logical, if TRUE (default), lower TDC are computed and upper TDC, else.
k

Integer, the threshold value for the order statistic. If left NULL, then k = sqrt(nrow(x)) is used.
...

Ellipsis, arguments are passed down to rank.

Details

For a matrix or an object that can be coerced to it with ncol(x) >= 2, the pair wise tail dependencies are estimated non-parametrically and returned as a symmetric matrix. The threshold value k is the upper/lower bound for the order statistics to be considered. The diagonal elements are always equal to one, because a series has a dependence of one with itself, of course.

Value

A matrix with the tail dependent coefficients.

Author(s)

Bernhard Pfaff

References

Schmidt, R. and Stadtm\"uller, U., Nonparametric estimation of tail dependence, The Scandinavian Journal of Statistics, 33, 307–335.

See Also

PMTD

Examples

data(StockIndex)
Rets <- returnseries(StockIndex, method = "discrete", trim = TRUE,
                     percentage = TRUE)
tdc(Rets, method = "EmpTC")
tdc(Rets, method = "EVT")

Bilson Trend

Description

Calculation of the Bilson Trend as a technical trading indicator.

Usage

trdbilson(y, exponent)

Arguments

y

Objects of classes: numeric, matrix, data.frame, ts, mts, and timeSeries are supported.
exponent

Numeric, the value for α\alpha in the equation below.

Details

The Bilson trend is calculated according to the formula:

z=sign(y)×∣y∣(1−∣y∣α)z = sign(y) \times |y|^{(1 - |y|^\alpha)}

Value

An object of the same class as y, containing the computed Bilson trend values.

Methods

y = "data.frame"

The calculation is applied per column of the data.frame and only if all columns are numeric.

y = "matrix"

The calculation is applied per column of the matrix.

y = "mts"

The calculation is applied per column of the mts object. The attributes are preserved and an object of the same class is returned.

y = "numeric"

Calculation of the bilson trend.

y = "timeSeries"

The calculation is applied per column of the timeSeries object and an object of the same class is returned.

y = "ts"

Calculation of the bilson trend. The attributes are preserved and an object of the same class is returned.

y = "xts"

Calculation of the bilson trend. The attributes are preserved and an object of the same class is returned.

y = "zoo"

Calculation of the bilson trend. The attributes are preserved and an object of the same class is returned.

Author(s)

Bernhard Pfaff

See Also

trdbinary, trdes, trdhp, trdsma, trdwma, capser

Examples

data(StockIndex)
y <- StockIndex[, "SP500"]
yret <- diff(log(y))
bilson <- trdbilson(yret, exponent = 2)
head(bilson)

Binary Trend

Description

Calculation of the Binary Trend as a technical trading indicator.

Usage

trdbinary(y)

Arguments

y

Objects of classes: numeric, matrix, data.frame, ts, mts, and timeSeries are supported.

Details

The Binary trend is calculated according to the formula:

z=sign(y)×min⁡(∣4/πarctan⁡(y)∣,1)z = sign(y) \times \min(|4 / \pi \arctan(y)|, 1)

Value

An object of the same class as y, containing the computed Binary trend values.

Methods

y = "data.frame"

The calculation is applied per column of the data.frame and only if all columns are numeric.

y = "matrix"

The calculation is applied per column of the matrix.

y = "mts"

The calculation is applied per column of the mts object. The attributes are preserved and an object of the same class is returned.

y = "numeric"

Calculation of the binary trend.

y = "timeSeries"

The calculation is applied per column of the timeSeries object and an object of the same class is returned.

y = "ts"

Calculation of the binary trend. The attributes are preserved and an object of the same class is returned.

y = "xts"

Calculation of the binary trend. The attributes are preserved and an object of the same class is returned.

y = "zoo"

Calculation of the binary trend. The attributes are preserved and an object of the same class is returned.

Author(s)

Bernhard Pfaff

See Also

trdbilson, trdes, trdhp, trdsma, trdwma, capser

Examples

data(StockIndex)
y <- StockIndex[, "SP500"]
yret <- diff(log(y))
binary <- trdbinary(yret)
head(binary)

Exponentially Smoothed Trend

Description

Calculation of the exponentially smoothed trend as a technical trading indicator.

Usage

trdes(y, lambda, init = NULL)

Arguments

y

Objects of classes: numeric, matrix, data.frame, ts, mts, and timeSeries are supported.
lambda

Numeric, the smoothing parameter for λ\lambda in the equation below. The value for the parameter must be in the interval 0<λ<10 < \lambda < 1.
init

The initial value in the recursive calculation of the filter. Specifies the initial values of the time series just prior to the start value, in reverse time order. The default, i.e. NULL, is a set of zeros.

Details

The exponetially smoothed trend is calculated according to the formula:

zt=λyt+(1−λ)∗zt−1z_t = \lambda y_t + (1 - \lambda) * z_{t-1}

Value

An object of the same class as y, containing the computed exponetially smoothed values.

Methods

y = "data.frame"

The calculation is applied per column of the data.frame and only if all columns are numeric.

y = "matrix"

The calculation is applied per column of the matrix.

y = "mts"

The calculation is applied per column of the mts object. The attributes are preserved and an object of the same class is returned.

y = "numeric"

Calculation of the es trend.

y = "timeSeries"

The calculation is applied per column of the timeSeries object and an object of the same class is returned.

y = "ts"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

y = "xts"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

y = "zoo"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

Author(s)

Bernhard Pfaff

See Also

filter, trdbilson, trdbinary, trdhp, trdsma, trdwma, capser

Examples

data(StockIndex)
y <- StockIndex[, "SP500"]
yret <- diff(log(y))
es <- trdes(yret, lambda = 0.95)
head(es)

Hodrick-Prescott Filter

Description

Calculation of the Hodrick-Prescott filter as a technical trading indicator.

Usage

trdhp(y, lambda)

Arguments

y

Objects of classes: numeric, matrix, data.frame, ts, mts, and timeSeries are supported.
lambda

Numeric, the value for λ\lambda in the equation below.

Details

The Hodrick-Prescott filter is calculated according to the formula:

min⁡(τt)=∑t=1T(yt−τt)2+λ∑t=2T−1(Δ2τt+1)2\min (\tau_t) = \sum_{t = 1}^T (y_t - \tau_t)^2 + \lambda \sum_{t = 2}^{T-1} (\Delta^2 \tau_{t+1})^2

Value

An object of the same class as y, containing the computed Hodrick-Prescott values.

Methods

y = "data.frame"

The calculation is applied per column of the data.frame and only if all columns are numeric.

y = "matrix"

The calculation is applied per column of the matrix.

y = "mts"

The calculation is applied per column of the mts object. The attributes are preserved and an object of the same class is returned.

y = "numeric"

Calculation of the bilson trend.

y = "timeSeries"

The calculation is applied per column of the timeSeries object and an object of the same class is returned.

y = "ts"

Calculation of the bilson trend. The attributes are preserved and an object of the same class is returned.

y = "xts"

Calculation of the bilson trend. The attributes are preserved and an object of the same class is returned.

y = "zoo"

Calculation of the bilson trend. The attributes are preserved and an object of the same class is returned.

Author(s)

Bernhard Pfaff

References

Hodrick, R. and E.C. Prescott (1997), Postwar U.S. Business Cycles: An Empirical Investigation, Journal of Money, Credit and Banking 29(1).

See Also

trdbinary, trdes, trdbilson, trdsma, trdwma, capser

Examples

data(StockIndex)
y <- StockIndex[, "SP500"]
hp <- trdhp(y, lambda = 1600)
head(hp)

Simple Moving Average

Description

Calculation of a right ended simple moving average with equal weights determined by n.periods.

Usage

trdsma(y, n.periods, trim = FALSE)

Arguments

y

Objects of classes: numeric, matrix, data.frame, ts, mts, and timeSeries are supported.
n.periods

Integer, the number of periods to be included in the calculation of the simple moving average.
trim

Logical, if FALSE (the default) the first value is set to NA, otherwise the object is trimmed by the first obeservation.

Value

An object of the same class as y, containing the computed simple moving averages.

Methods

y = "data.frame"

The calculation is applied per column of the data.frame and only if all columns are numeric.

y = "matrix"

The calculation is applied per column of the matrix.

y = "mts"

The calculation is applied per column of the mts object. The attributes are preserved and an object of the same class is returned.

y = "numeric"

Calculation of the es trend.

y = "timeSeries"

The calculation is applied per column of the timeSeries object and an object of the same class is returned.

y = "ts"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

y = "xts"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

y = "zoo"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

Author(s)

Bernhard Pfaff

See Also

filter, trdbilson, trdbinary, trdhp, trdwma, capser, trdes

Examples

data(StockIndex)
y <- StockIndex[, "SP500"]
sma <- trdsma(y, n.periods = 24)
head(sma, 30)

Weighted Moving Average

Description

Calculation of a right ended weighted moving average with weights according to weights.

Usage

trdwma(y, weights, trim = FALSE)

Arguments

y

Objects of classes: numeric, matrix, data.frame, ts, mts, and timeSeries are supported.
weights

Numeric, a vector containing the weights.
trim

Logical, if FALSE (the default) the first value is set to NA, otherwise the object is trimmed by the first obeservation.

Details

If the sum of the weights is greater than unity, a warning is issued.

Value

An object of the same class as y, containing the computed weighted moving averages.

Methods

y = "data.frame"

The calculation is applied per column of the data.frame and only if all columns are numeric.

y = "matrix"

The calculation is applied per column of the matrix.

y = "mts"

The calculation is applied per column of the mts object. The attributes are preserved and an object of the same class is returned.

y = "numeric"

Calculation of the es trend.

y = "timeSeries"

The calculation is applied per column of the timeSeries object and an object of the same class is returned.

y = "ts"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

y = "xts"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

y = "zoo"

Calculation of the es trend. The attributes are preserved and an object of the same class is returned.

Author(s)

Bernhard Pfaff

See Also

filter, trdbilson, trdbinary, trdhp, trdes, trdsma, capser

Examples

data(StockIndex)
y <- StockIndex[, "SP500"]
wma <- trdwma(y, weights = c(0.4, 0.3, 0.2, 0.1))
head(wma, 30)