Description Usage Arguments Details Value References

Specifies a portfolio from scratch.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
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)
)
``` |

`model` |
a list, containing different arguments: type, estimator, params. See these arguments for further explanation. |

`portfolio` |
a list, containing different arguments: weights, targetReturn, riskFreeRate, nFrontierPoints. See these arguments for further explanation. |

`optim` |
a list with four entries, a character string |

`messages` |
a list, for optional messages. |

`ampl` |
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`

.

1 2 3 4 5 6 | ```
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:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
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

1 2 | ```
\code{"minRisk"}
``` |

which minimizes the risk if the target returns is given, or

1 2 | ```
\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

1 2 | ```
\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

1 2 3 4 5 6 | ```
\code{"covMcdEstimator"}
\code{"covOGKEstimator"}
\code{"mveEstimator"}
\code{"nnveEstimator"}
\code{"mcdEstimator"}
``` |

In addition a shrinkage covariance estimator named

1 2 | ```
\code{"shrinkEstimator"},
``` |

and a bagged covariance estimator named

1 2 3 | ```
\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

1 2 3 |

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.

1 2 | ```
\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.

`portfolioSpec`

returns an S4 object of class `"fPFOLIOSPEC"`

.

Wuertz, D., Chalabi, Y., Chen W., Ellis A. (2009);
*Portfolio Optimization with R/Rmetrics*,
Rmetrics eBook, Rmetrics Association and Finance Online, Zurich.

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