portfolioRiskContribution
Compute individual asset risk contribution to overall portfolio volatility
Since R2022a
Syntax
Description
computes individual asset risk contribution to overall portfolio volatility and
returns riskCont
= portfolioRiskContribution(portWeights
,Sigma
)riskCont
as a matrix of risk contributions.
specifies an option using a name-value argument in addition to the input
arguments in the previous syntax.riskCont
= portfolioRiskContribution(___,Name=Value
)
Examples
Compute Individual Asset Risk Contribution
Use portfolioRiskContribution
to compute the risk contribution per asset with respect to the portfolio total risk.
Assume the returns covariance matrix is given by the following values.
Sigma = [0.0100 0.0075 0.0100 0.0150 0.0075 0.0225 0.0150 0.0225 0.0100 0.0150 0.0400 0.0450 0.0150 0.0225 0.0450 0.0900];
The portWeights
are the following values:
portWeights = [0.4101; 0.2734; 0.1899; 0.1266];
Use portfolioRiskContribution
to compute the percent of risk contribution per asset.
riskCont = portfolioRiskContribution(portWeights,Sigma)
riskCont = 4×1
0.2500
0.2500
0.2500
0.2500
The default is to compute the relative risk contribution. However, you can compute the absolute risk contribution by using the name-value argument RiskContributionType="absolute"
. Use portfolioRiskContribution
to compute each asset's relative risk contribution.
riskCont = portfolioRiskContribution(portWeights,Sigma,RiskContributionType="relative")
riskCont = 4×1
0.2500
0.2500
0.2500
0.2500
Compute Individual Asset Risk Contribution When Returns Contain NaN
Values
Use portfolioRiskContribution
to compute the risk contribution of each asset with respect to the portfolio total risk when the assets returns used to compute the variance have NaN
values.
Assume the returns covariance matrix is given by the following values.
load('CAPMuniverse.mat','AssetsTimeTable') Sigma = cov(AssetsTimeTable{:,1:12},'partialrows')
Sigma = 12×12
0.0012 0.0005 0.0005 0.0005 0.0005 0.0001 0.0004 0.0003 0.0006 0.0003 0.0005 0.0006
0.0005 0.0023 0.0007 0.0005 0.0009 0.0001 0.0005 0.0003 0.0006 0.0004 0.0006 0.0011
0.0005 0.0007 0.0012 0.0006 0.0007 0.0000 0.0006 0.0004 0.0007 0.0005 0.0008 0.0008
0.0005 0.0005 0.0006 0.0009 0.0006 0.0000 0.0005 0.0003 0.0006 0.0004 0.0005 0.0006
0.0005 0.0009 0.0007 0.0006 0.0017 0.0002 0.0005 0.0003 0.0005 0.0004 0.0007 0.0010
0.0001 0.0001 0.0000 0.0000 0.0002 0.0006 -0.0000 0.0000 0.0000 0.0000 0.0000 0.0002
0.0004 0.0005 0.0006 0.0005 0.0005 -0.0000 0.0009 0.0003 0.0005 0.0003 0.0005 0.0005
0.0003 0.0003 0.0004 0.0003 0.0003 0.0000 0.0003 0.0004 0.0003 0.0002 0.0004 0.0004
0.0006 0.0006 0.0007 0.0006 0.0005 0.0000 0.0005 0.0003 0.0010 0.0005 0.0006 0.0006
0.0003 0.0004 0.0005 0.0004 0.0004 0.0000 0.0003 0.0002 0.0005 0.0006 0.0004 0.0005
⋮
The risk parity portfolio is subject to the following weights for all the assets.
portWeights = [0.1; 0.1; 0.1; 0.03; 0.1; 0.1; 0.1; 0.05; 0.1; 0.1; 0.1; 0.1];
Use portfolioRiskContribution
to compute the percentage risk contribution per asset.
riskCont = portfolioRiskContribution(portWeights,Sigma)
riskCont = 12×1
0.0911
0.1261
0.1103
0.0251
0.1197
0.0203
0.0805
0.0258
0.0978
0.0660
⋮
The default values returned by portfolioRiskContribution
are the relative risk contribution of the individual assets to the overall portfolio risk. Also, you can compute the absolute risk contribution by using the name-value argument RiskContributionType="absolute"
. Use portfolioRiskContribution
to compute each asset's absolute risk contribution.
riskCont = portfolioRiskContribution(portWeights,Sigma,RiskContributionType="absolute")
riskCont = 12×1
0.0023
0.0031
0.0027
0.0006
0.0030
0.0005
0.0020
0.0006
0.0024
0.0016
⋮
Compute Individual Asset Risk Contribution When portWeights
Is Matrix
Use portfolioRiskContribution
to compute the risk contribution per asset with respect to the portfolio total risk when portWeights
is a matrix.
Assume the returns covariance matrix is given by the following values.
Sigma = [0.0100 0.0075 0.0100 0.0150 0.0075 0.0225 0.0150 0.0225 0.0100 0.0150 0.0400 0.0450 0.0150 0.0225 0.0450 0.0900];
The matrix of portWeights
is the values:
portWeights = [0.25 0.10 0.10828; 0.25 0.20 0.17197; 0.25 0.30 0.28026; 0.25 0.40 0.43949];
Use portfolioRiskContribution
to compute the percent of risk contribution per asset.
riskCont = portfolioRiskContribution(portWeights,Sigma)
riskCont = 4×3
0.1083 0.0308 0.0322
0.1720 0.1005 0.0816
0.2803 0.2735 0.2455
0.4395 0.5952 0.6407
The default is to compute the relative risk contribution. However, you can compute the absolute risk contribution by using the name-value argument RiskContributionType="absolute"
. Use portfolioRiskContribution
to compute each asset's absolute risk contribution.
riskCont = portfolioRiskContribution(portWeights,Sigma,RiskContributionType="absolute")
riskCont = 4×3
0.0170 0.0060 0.0064
0.0269 0.0194 0.0162
0.0439 0.0528 0.0488
0.0688 0.1149 0.1274
Input Arguments
portWeights
— Portfolio weights
matrix
Portfolio weights, specified using an
NumAssets
-by-NumPortfolios
matrix.
portWeights
must be nonempty, numeric, finite, and
real. portWeights
can be negative and does not need to
sum to 1
. portWeights
and
Sigma
must have the same number of
NumAssets
.
Data Types: double
Sigma
— Covariance matrix of returns
positive semidefinite covariance matrix
Covariance matrix of returns, specified using an
NumAssets
-by-NumAssets
positive
semidefinite covariance matrix. Sigma
and
portWeights
must have the same number of
NumAssets
.
Note
If Sigma
is not a positive symmetric positive
semidefinite matrix, use nearcorr
to create a positive semidefinite
matrix.
Data Types: double
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Example: riskCont =
portfolioRiskContribution(portWeights,Sigma,RiskContributionType="relative")
RiskContributionType
— Type of risk contribution to compute
"relative"
(relative risk
contribution) (default) | character vector with value of 'relative'
or
'absolute'
| string with value of "relative"
or
"absolute"
Type of risk contribution to compute, specified as
RiskContributionType
and a scalar character
vector or string:
"relative"
— Computes the relative contribution."absolute"
— Computes the absolute risk contribution.
Data Types: char
| string
Output Arguments
riskCont
— Risk contributions
matrix
Risk contributions, returned as a matrix. The default values returned by
portfolioRiskContribution
are the relative
contribution of the assets to the portfolio. However,
portfolioRiskContribution
can also return the
absolute risk contribution by passing the name-value argument
RiskContributionType
with a value of
"absolute"
.
Version History
Introduced in R2022a
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