PERC: Equal risk contributed portfolios

In FRAPO: Financial Risk Modelling and Portfolio Optimisation with R

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 

Example output

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

Iteration: 0
pobj: 0
dobj: 11.101
pinf: 1
dinf: 1
dgap: 11

Iteration: 1
pobj: -2.10712
dobj: 5.25833
pinf: 0.653234
dinf: 0.531986
dgap: 6.608

Iteration: 2
pobj: 1.22151
dobj: 3.25587
pinf: 0.168427
dinf: 0.050526
dgap: 0.801752

Iteration: 3
pobj: 3.6259
dobj: 3.59516
pinf: 0.00939849
dinf: 0.00506335
dgap: 0.182164

Iteration: 4
pobj: 3.75322
dobj: 3.74139
pinf: 0.000730021
dinf: 0.000588514
dgap: 0.023322

Iteration: 5
pobj: 3.76389
dobj: 3.76315
pinf: 3.94956e-05
dinf: 3.62131e-05
dgap: 0.00135514

Iteration: 6
pobj: 3.76447
dobj: 3.76444
pinf: 1.98401e-06
dinf: 1.83156e-06
dgap: 6.85151e-05

Iteration: 7
pobj: 3.7645
dobj: 3.7645
pinf: 9.90419e-08
dinf: 9.14628e-08
dgap: 3.42912e-06

Optimal solution found.


Optimal weights for porfolio of type:
Equal Risk Contribution

   GSPC     RUA   GDAXI    FTSE    N225     EEM  DJCBTI   GREXP  BG05.L     GLD 
 3.8054  3.6747  3.5213  4.1548  3.5842  2.1787 16.4074 41.9811 15.8761  4.8162 

            GSPC       RUA       GDAXI       FTSE        N225        EEM
GSPC    85.75262  88.98534   90.733479  68.797280   77.330799  122.75303
RUA     85.93015  89.58203   91.842308  69.278559   79.024474  124.25395
GDAXI   83.96010  88.00777  120.665749  76.726567   93.055543  128.28857
FTSE    75.11465  78.32945   90.530261  77.720521   79.560874  118.47711
N225    72.83627  77.07787   94.717910  68.634330  130.777647  119.27735
EEM     70.27835  73.66691   79.372848  62.125579   72.502355  137.98852
DJCBTI -34.16716 -37.75774  -55.013153 -31.511405  -51.615579  -54.09979
GREXP  -86.77186 -91.71794 -116.187997 -71.028970 -100.172341 -131.38567
BG05.L -17.91623 -19.58586  -15.758015  -9.141586  -18.543923  -23.84658
GLD     10.99006  11.72112   -6.982726   5.305884    5.438255   62.65278
           DJCBTI     GREXP    BG05.L        GLD
GSPC    -7.924426 -7.865479 -4.294412   8.683427
RUA     -8.456528 -8.028375 -4.533429   8.943084
GDAXI  -11.806762 -9.745697 -3.495135  -5.105303
FTSE    -7.979581 -7.029674 -2.392390   4.577225
N225   -11.275478 -8.552426 -4.186527   4.047119
EEM     -7.183629 -6.818418 -3.272446  28.341373
DJCBTI  47.098080 18.837485 28.405602  41.200315
GREXP   48.198726 43.919812 36.359998  25.246859
BG05.L  27.485644 13.750330 36.830877  11.583105
GLD     12.093953  2.896426  3.513912 145.868560

FRAPO documentation built on May 2, 2019, 5:24 p.m.