Specifies a portfolio from scratch.
portfolioSpec(
model = list(
type = "MV", optimize = "minRisk",
estimator = "covEstimator", tailRisk = list(),
params = list(alpha = 0.05)),
portfolio = list(
weights = NULL, targetReturn = NULL,
targetRisk = NULL, riskFreeRate = 0, nFrontierPoints = 50,
status = NA),
optim = list(
solver = "solveRquadprog",
objective = c("portfolioObjective", "portfolioReturn", "portfolioRisk"),
options = list(meq = 2), control = list(), trace = FALSE),
messages = list(
messages = FALSE, note = ""),
ampl = list(
ampl = FALSE, project = "ampl", solver = "ipopt",
protocol = FALSE, trace = FALSE)
)portfolioSpec
returns an S4 object of class "fPFOLIOSPEC".
a list, containing different arguments: type, estimator, params. See these arguments for further explanation.
a list, containing different arguments: weights, targetReturn, riskFreeRate, nFrontierPoints. See these arguments for further explanation.
a list with four entries, a character string solver denoting
the type of the solver to be used, a params list to pass further
arguments to the objective function to optimize, a control list
for all control settings of the solver, and a logical flag, trace
denoting if the optimization should be traced.
a list, for optional messages.
a list, controls settings for the R/AMPL interface.
To optimize a portfolio of assets we first have to specify it. All
settings which specify a portfolio of assets are respresented by a
S4 class named fPFOLIOSPEC.
setClass("fPFOLIOSPEC",
representation(
model = "list",
portfolio = "list",
optim = "list") )
An object of class fPFOLIOSPEC has three slots, named
@model, @portfolio, and @optim. The first
slot @model holds the model information, the second
slot @portfolio the portfolio information, and the last
slot @optim the information about the solver used for
optimization.
The default settings are as follows:
model = list(
type = "MV",
optimize = "minRisk",
estimator = "covEstimator",
tailRisk = list(),
params = list(alpha = 0.05, a = 2)),
portfolio = list(
weights = NULL,
targetReturn = NULL,
targetRisk = NULL,
riskFreeRate = 0,
nFrontierPoints = 50,
status = NA),
optim = list(
solver = "solveRquadprog",
objective = NULL,
parames = list(),
control = list(meq = 2),
trace = FALSE)
Model Slot:
Type of Model:
The list entry type from the @model slot describes
the type of the desired portfolio. The current implementation
supports three types of portfolios. This may be
a Markowitz mean -- variance portfolio named "MV",
a mean -- lower partial moment portfolio named "LPM", or
a mean -- CVaR condititional value-at-risk portfolio named "CVaR".
One can use the function getType to retrieve the current
setting and the function setType to modify this selection.
What to optimize?
The list entry optimize from the @model slot describes
what should be optimized. Two choices are psssible. Either
\code{"minRisk"}
which minimizes the risk if the target returns is given, or
\code{"maxReturn"}
which maximizes the return if the target risk is given.
One can use the function getOptimize to retrieve the current
setting and the function setOptimize to modify this selection.
How to estimate mean and covariance?
The list entry estimator from the @model slot requests
for a string that denotes the function name of the covariance
estimator which should be used for the estimation of risk.
In Markowitz' mean-variance portfolio model, type="MV", the
default function
\code{"covEstimator"}
is used which computes the standard column means of the multivariate assets data series and the standard covariance matrix. Alternative robust estimators include
\code{"covMcdEstimator"}
\code{"covOGKEstimator"}
\code{"mveEstimator"}
\code{"nnveEstimator"}
\code{"mcdEstimator"}
In addition a shrinkage covariance estimator named
\code{"shrinkEstimator"},
and a bagged covariance estimator named
\code{"baggedEstimator"}
are also available. Note, the experienced user can add his own function to estimate in any alternative way the mean and the covariance of the multivariate assets data series. In this case (s)he has to write a function, e.g. named
\code{myEstimator=function(x,spec=NULL,...)}
where x is a multivariate time series, spec optionally
the portfolio specification, if rquired, and ... additional
arguments passed to the users code. Note, myEstimator must
a return a named list, with at least the following two entries
\$mu and \$Sigma, which represent estimators for the
mean and covariance, respectively.
In the case of the Mean -- Lower-Partial-Moment portfolio,
type="LPM" we make use of the equivalence to Markowitz'
mean-variance portfolio with a modified covariance estimator, i.e.
\code{"lpmEstimator"},
Note, in this case the setting of type="LPM"
changes the covariance estimator function name
from any selection previously made to the function automatically
to "lpmEstimator" which returns the LPM mean and covariance
estimates.
One can use the function getEstimator to retrieve the current
setting and the function setEstimator to modify this selection.
Tail Risk List:
The list entry tailRisk from the @model slot is an empty
list. It can be used to add tail risk budget constrains to the
optimization. In this case a square matrix of the size of the
number of assets is expected as list entry, which contains bivariate
tail risk measures, i.e. the tail dependence coefficients estaimated
via a copulae approach.
Use the function setType to modify this selection.
The list entry parameters from the @model slot is a
list with additional parameters used in different situations. It can
be ebhanced by the user if needed.
By default it contains the exponent a=2, the parameter needed
for "LPM" portfolio optimization,
and it contains the targetAlpha=0.05, the confidence level
for "CVaR" portfolio optimization.
Use the function setParams to modify this selection.
Portfolio Slot:
The values weights, targetReturn, and targetRisk
from the portfolio slot have to be considered in common. By
default all three are set to NULL. If this is the case, then
it is assumed that an equal weight portfolio should be calculated.
If only one of the three values is different from NULL then
the following procedure will be startet.
If the weights are specified then it is assumed that a feasible
portfolio should be considered.
If the target return is fixed then it is assumed that the efficient
portfolio with the minimal risk will be considered.
And finally if the risk is fixed, then the return should be maximized.
Use the functions setWeights, setTargetReturn, and
setTargetRisk to modify this selection.Note, the change in of
the three functions will influence the settings of the other two.
The riskFreeRate=0 is also stored in the portfolio slot.
Its value defaults to zero. It can be changed by the user.
Use the function setRiskFreeRate to modify this selection.
The number of frontier points reqauired by the calculation of
the portfolioFrontier is obtained from the value of
nFrontierPoints=50 hold in the portfolio slot.
Its value defaults to 50. It can be changed by the user.
Use the function setNFrontierPoints to modify this selection.
The final status of portfolio optimization is returned
and stored in the portfolio slot. Before optimization the
value is unset to NA, after optimization a value of
status=0 means a successful termination. For other
values we recommend to inspect the help page of the selected
solver, the name of the solver can be returned by the function
getSolver.
Use the function setSolver to reset the value to NA
if it should be required.
Optim Slot:
The name of the default solver used for optimization can be retrieved
calling the function getSolver. The default value for the
value solver in the specification is set to NULL
which means that the best solver availalbe will be autoselected
and used. Before optimization the user can change the setting
to another solver. Be aware, that a possible personal change will
be overwritten by the function setType, so call
setSolver after setting the type of the portfolio.
The logical flag trace in the slot optim allows
to trace optionally the portfolio optimization process. By
default this will not be the case since the default value is
trace=FALSE. Use the fanction setTrace to modify
the selection.
Retrieving and Modifying Specification Settings:
Information about the current portfolio specification can be retrieved
by "get" functions. These include:
getType | Extracts portfolio type from specification, |
getOptimize | Extracts what to optimize from specification, |
getEstimator | Extracts type of covariance estimator, |
getTailRisk | Extracts list of tail dependency risk matrixes, |
getParams | Extracts parameters from specification, |
getWeights | Extracts weights from a portfolio object, |
getTargetReturn | Extracts target return from specification, |
getTargetRisk | Extracts target riks from specification, |
getAlpha | Extracts target VaR-alpha specification, |
getRiskFreeRate | Extracts risk free rate from specification, |
getNFrontierPoints | Extracts number of frontier points, |
getStatus | Extracts the status of optimization, |
getSolver | Extracts solver from specification, |
getTrace | Extracts solver's trace flag. |
For details we refer to link{getSpec}.
To modify the setting from a portfolio specification use the
"set" functions:
setType | Sets type of portfolio optimization, |
setOptimize | Sets what to optimize, min risk or max return, |
setEstimator | Sets names of mean and covariance estimators, |
setParams | Sets optional model parameters, |
setWeights | Sets weights vector, |
setTargetReturn | Sets target return value, |
setTargetRisk | Sets target risk value, |
setTargetAlpha | Sets CVaR target alpha value, |
setRiskFreeRate | Sets risk-free rate value, |
setNFrontierPoints | Sets number of frontier points, |
setStatus | Sets status value, |
setSolver | Sets the type of solver to be used, |
setTrace | Sets the logical trace flag. |
For details we refer to link{setSpec}.
Printing Specification Settings:
There is a generic print function to print information from
specification. What is printed depends on the values of the
settings. For example print(portfolioSpec()) returns
the type of portfolio, the name of the covariance estimator,
the portfolios risk free rate, and the desired solver.
Wuertz, D., Chalabi, Y., Chen W., Ellis A. (2009); Portfolio Optimization with R/Rmetrics, Rmetrics eBook, Rmetrics Association and Finance Online, Zurich.