# PGMV: Global Minimum Variance Portfolio In FRAPO: Financial Risk Modelling and Portfolio Optimisation with R

## Description

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

## Usage

 `1` ```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

`"PortSol"`

## Examples

 ```1 2 3``` ```data(MultiAsset) Rets <- returnseries(MultiAsset, method = "discrete", trim = TRUE) PGMV(Rets) ```

### Example output

```Loading required package: cccp
Using the GLPK callable library version 4.52
Financial Risk Modelling and Portfolio Optimisation with R (version 0.4-1)

Iteration: 0
pobj: 0.396694
dobj: -0.797435
pinf: 3.31531
dinf: 4.86496
dgap: 16.2746

Iteration: 1
pobj: 0.429327
dobj: -0.591061
pinf: 0.316147
dinf: 0.463922
dgap: 2.37423

Iteration: 2
pobj: 0.430326
dobj: -0.102681
pinf: 0.0657035
dinf: 0.0964149
dgap: 0.761109

Iteration: 3
pobj: 0.393718
dobj: 0.179723
pinf: 0.0131117
dinf: 0.0192405
dgap: 0.243563

Iteration: 4
pobj: 0.355241
dobj: 0.2805
pinf: 0.00187089
dinf: 0.00274539
dgap: 0.0767899

Iteration: 5
pobj: 0.340985
dobj: 0.320463
pinf: 0.000260152
dinf: 0.000381753
dgap: 0.0206442

Iteration: 6
pobj: 0.335827
dobj: 0.329761
pinf: 3.0625e-05
dinf: 4.49398e-05
dgap: 0.00607401

Iteration: 7
pobj: 0.334207
dobj: 0.332124
pinf: 6.53239e-06
dinf: 9.58579e-06
dgap: 0.00208414

Iteration: 8
pobj: 0.333389
dobj: 0.332899
pinf: 2.53131e-14
dinf: 1.15378e-15
dgap: 0.000490514

Iteration: 9
pobj: 0.333219
dobj: 0.333109
pinf: 4.77396e-14
dinf: 1.5263e-15
dgap: 0.000110014

Iteration: 10
pobj: 0.333181
dobj: 0.333165
pinf: 9.32587e-14
dinf: 1.03555e-15
dgap: 1.65065e-05

Iteration: 11
pobj: 0.333176
dobj: 0.333173
pinf: 1.82299e-13
dinf: 1.20601e-15
dgap: 2.15942e-06

Iteration: 12
pobj: 0.333174
dobj: 0.333174
pinf: 3.55715e-13
dinf: 1.49365e-15
dgap: 2.62284e-07

Optimal solution found.

Optimal weights for porfolio of type:
Global Minimum Variance

GSPC     RUA   GDAXI    FTSE    N225     EEM  DJCBTI   GREXP  BG05.L     GLD
4.8891  0.0000  4.3411  0.0045  1.7276  0.0000  0.0000 87.8716  0.9589  0.2071
```

FRAPO documentation built on May 2, 2019, 6:33 a.m.