Description Usage Arguments Details Value Note Author(s) References See Also Examples
This function solves for equal risk contributed portfolio weights.
1 |
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 |
... |
Ellipsis argument is passed down to |
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.
An object of formal class "PortSol"
.
The optimisation is conducted by calling nlminb()
. Hereby, the
arguments lower = 0
and upper = 1
have been specified.
Bernhard Pfaff
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.
1 2 3 4 5 6 7 8 | data(MultiAsset)
Rets <- returnseries(MultiAsset, method = "discrete", trim = TRUE,
percentage = TRUE)
V <- cov(Rets)
ERC <- PERC(V)
ERC
w <- Weights(ERC)
w * V
|
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
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