PortfolioCVaR class

Superclasses: AbstractPortfolio

PortfolioCVaR object for conditional value-at-risk portfolio optimization and analysis

Description

The PortfolioCVaR object implements conditional value-at-risk (CVaR) portfolio optimization and is derived from the abstract portfolio optimization class AbstractPortfolio. This object implements all methods in the AbstractPortfolio class along with methods that are specific to CVaR portfolio optimization.

The main workflow for CVaR portfolio optimization is to create an instance of a PortfolioCVaR object that completely specifies a portfolio optimization problem and to operate on the PortfolioCVaR object to obtain and analyze efficient portfolios. A CVaR optimization problem is completely specified with these four elements:

  • A universe of assets with scenarios of asset total returns for a period of interest, where scenarios comprise a collection of samples from the underlying probability distribution for asset total returns. This collection must be sufficiently large for asymptotic convergence of sample statistics. Note that asset return moments and related statistics are derived exclusively from the scenarios.

  • A portfolio set that specifies the set of portfolio choices in terms of a collection of constraints.

  • A model for portfolio return and risk proxies, which, for CVaR optimization, is either the gross or net mean of portfolio returns and the conditional value-at-risk of portfolio returns.

  • A probability level that specifies the probability that a loss is less than or equal to the value-at-risk. Typical values are 0.9 and 0.95, which indicate 10% and 5% loss probabilities.

After these four elements have been specified in an unambiguous way, it is possible to solve and analyze CVaR portfolio optimization problems.

The simplest CVaR portfolio optimization problem has:

  • Scenarios of asset total returns

  • A requirement that all portfolios have nonnegative weights that sum to 1 (the summation constraint is known as a budget constraint)

  • Built-in models for portfolio return and risk proxies that use scenarios of asset total returns

  • A probability level of 0.95

Given scenarios of asset returns in the variable AssetScenarios, this problem is completely specified by:

p = PortfolioCVaR('Scenarios', AssetScenarios, 'LowerBound', 0, 'Budget', 1, ...
'ProbabilityLevel', 0.95);

or equivalently by:

p = PortfolioCVaR;
p = setScenarios(p, AssetScenarios);
p = setDefaultConstraints(p);
p = setProbabilityLevel(p, 0.95);

To confirm that this is a valid portfolio optimization problem, the following method determines whether the set of PortfolioCVaR choices is bounded (a necessary condition for portfolio optimization).

[lb, ub, isbounded] = estimateBounds(p);

Given the problem specified in the PortfolioCVaR object p, the efficient frontier for this problem can be displayed with:

plotFrontier(p);

and efficient portfolios can be obtained with:

pwgt = estimateFrontier(p);

Construction

p = PortfolioCVaR constructs an empty PortfolioCVaR object for conditional value-at-risk portfolio optimization and analysis. You can then add elements to the PortfolioCVaR object using the supported add and set methods. For more information, see Constructing the PortfolioCVaR Object.

p = PortfolioCVaR(Name,Value) constructs a PortfolioCVaR object for conditional value-at-risk portfolio optimization and analysis with additional options specified by one or more Name,Value pair arguments. Name is a property name and Value is its corresponding value. Name must appear inside single quotes (''). You can specify several name-value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

p = PortfolioCVaR(p,Name,Value) constructs a PortfolioCVaR object for conditional value-at-risk portfolio optimization and analysis using a previously constructed PortfolioCVaR object p with additional options specified by one or more Name,Value pair arguments.

Input Arguments

p

(Optional) Previously constructed CVaR portfolio object (p).

Property Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'AInequality'

Linear inequality constraint matrix ([] or [matrix]).

Default: []

'AssetList'

Names or symbols of assets in the universe ([] or [vector cell of strings]).

Default: []

'bInequality'

Linear inequality constraint vector ([] or [vector]).

Default: []

'BuyCost'

Proportional purchase costs ([] or vector).

Default: []

'BuyTurnover'

Turnover constraint on purchases ([] or [scalar]).

Default: []

'GroupA'

Group A weights to be bounded by weights in group B ([] or [matrix]).

Default: []

'GroupB'

Group B weights ([] or [matrix]).

Default: []

'GroupMatrix'

Group membership matrix ([] or [matrix]).

Default: []

'InitPort'

Initial portfolio ([] or vector).

Default: []

'LowerBudget'

Lower-bound budget constraint ([] or [scalar]).

Default: []

'LowerGroup'

Lower-bound group constraint ([] or [vector]).

Default: []

'LowerRatio'

Minimum ratio of allocations between groups A and B ([] or [vector]).

Default: []

'Name'

Name for instance of the PortfolioCVaR object ([] or [string]).

Default: []

'NumAssets'

Number of assets in the universe ([] or [integer scalar]).

Default: []

'NumScenarios'

Number of scenarios ([] or [integer scalar]).

Default: []

'ProbabilityLevel'

Probability level which is 1 minus the probability of losses greater than the value-at-risk ([] or [scalar]).

Default: []

'RiskFreeRate'

Risk-free rate ([] or scalar).

Default: []

'SellCost'

Proportional sales costs ([] or vector).

Default: []

'SellTurnover'

Turnover constraint on sales ([] or [scalar]).

Default: []

'Turnover'

Turnover constraint ([] or [scalar]).

Default: []

'UpperBound'

Upper-bound constraint ([] or [vector]).

Default: []

'UpperBudget'

Upper-bound budget constraint ([] or [scalar]).

Default: []

'UpperGroup'

Upper-bound group constraint ([] or [vector]).

Default: []

'UpperRatio'

Maximum ratio of allocations between groups A and B ([] or [vector]).

Default: []

Properties

The following properties are from the PortfolioCVaR class.

BuyCost

Proportional purchase costs ([] or vector).

Attributes:

SetAccesspublic
GetAccesspublic

BuyTurnover

Turnover constraint on purchases ([] or [scalar]).

Attributes:

SetAccesspublic
GetAccesspublic

NumScenarios

Number of scenarios ([] or [integer scalar]).

Attributes:

SetAccessprivate
GetAccesspublic

ProbabilityLevel

Value-at-risk probability level which is 1 − (loss probability) ([] or [scalar]).

Attributes:

SetAccesspublic
GetAccesspublic

RiskFreeRate

Risk-free rate ([] or scalar).

Attributes:

SetAccesspublic
GetAccesspublic

SellCost

Proportional sales costs ([] or vector).

Attributes:

SetAccesspublic
GetAccesspublic

SellTurnover

Turnover constraint on sales ([] or [scalar]).

Attributes:

SetAccesspublic
GetAccesspublic

Turnover

Turnover constraint ([] or [scalar]).

Attributes:

SetAccesspublic
GetAccesspublic

Properties

The following properties are inherited from the AbstractPortfolio class.

AEquality

Linear equality constraint matrix ([] or [matrix]).

Attributes:

SetAccesspublic
GetAccesspublic

AInequality

Linear inequality constraint matrix ([] or [matrix]).

Attributes:

SetAccesspublic
GetAccesspublic

AssetList

Names or symbols of assets in the universe ([] or [vector cell of strings]).

Attributes:

SetAccesspublic
GetAccesspublic

bEquality

Linear equality constraint vector ([] or [vector]).

Attributes:

SetAccesspublic
GetAccesspublic

bInequality

Linear inequality constraint vector ([] or [vector]).

Attributes:

SetAccesspublic
GetAccesspublic

GroupA

Group A weights to be bounded by group B ([] or [matrix]).

Attributes:

SetAccesspublic
GetAccesspublic

GroupB

Group B weights ([] or [matrix]).

Attributes:

SetAccesspublic
GetAccesspublic

GroupMatrix

Group membership matrix ([] or [matrix]).

Attributes:

SetAccesspublic
GetAccesspublic

InitPort

Initial portfolio ([] or vector).

Attributes:

SetAccesspublic
GetAccesspublic

LowerBound

Lower-bound constraint ([] or [vector]).

Attributes:

SetAccesspublic
GetAccesspublic

LowerBudget

Lower-bound budget constraint ([] or [scalar]).

Attributes:

SetAccesspublic
GetAccesspublic

LowerGroup

Lower-bound group constraint ([] or [vector]).

Attributes:

SetAccesspublic
GetAccesspublic

LowerRatio

Minimum ratio of allocations between groups A and B ([] or [vector]).

Attributes:

SetAccesspublic
GetAccesspublic

Name

Name for instance of the PortfolioCVaR object ([] or [string]).

Attributes:

SetAccesspublic
GetAccesspublic

NumAssets

Number of assets in the universe ([] or [integer scalar]).

Attributes:

SetAccesspublic
GetAccesspublic

UpperBound

Upper-bound constraint ([] or [vector]).

Attributes:

SetAccesspublic
GetAccesspublic

UpperBudget

Upper-bound budget constraint ([] or [scalar]).

Attributes:

SetAccesspublic
GetAccesspublic

UpperGroup

Upper-bound group constraint ([] or [vector]).

Attributes:

SetAccesspublic
GetAccesspublic

UpperRatio

Maximum ratio of allocations between groups A and B ([] or [vector]).

Attributes:

SetAccesspublic
GetAccesspublic

Inherited Methods

The following methods are inherited from the AbstractPortfolio class.

addEquality

Add equality constraints for portfolio weights to existing constraints.

addGroupRatio

Add group ratio constraints for portfolio weights to existing constraints.

addGroups

Add group constraints for portfolio weights to existing constraints.

addInequality

Add inequality constraints for portfolio weights to existing constraints.

checkFeasibility

Determine if portfolios are members of the set of feasible portfolios.

estimateBounds

Determine if set of feasible portfolios is nonempty and bounded.

estimateFrontier

Estimate portfolios on the entire efficient frontier.

estimateFrontierByReturn

Estimate portfolios on the efficient frontier with targeted returns or return proxies.

estimateFrontierByRisk

Estimate portfolios on the efficient frontier with targeted risks or risk proxies.

estimateFrontierLimits

Estimate portfolios at the extreme ends of the efficient frontier (minimum risk and maximum return).

estimatePortReturn

Estimate return or return proxy for specified portfolios.

estimatePortRisk

Estimate risk or risk proxy for specified portfolios.

getBounds

Get lower and upper bounds from the object.

getBudget

Get lower and upper budget constraints from the object.

getEquality

Get equality constraint matrix and vector from the object.

getGroupRatio

Get base matrix, comparison matrix, and lower and upper bounds for group ratio constraints from the object.

getGroups

Get group matrix and lower and upper bounds for group constraints from the object.

getInequality

Get inequality constraint matrix and vector from the object.

plotFrontier

Plot efficient frontier and optionally obtain risks and returns for portfolios on the efficient frontier.

setAssetList

Set up a list of asset names and symbols to be associated with assets in the universe.

setBounds

Set up lower and upper bounds for portfolio weights.

setBudget

Set up lower and upper budget constraints for portfolio weights.

setDefaultConstraints

Set up default constraints for portfolio weights (nonnegative weights that must sum to 1).

setEquality

Set up equality constraints for portfolio weights.

setGroupRatio

Set up group ratio constraints for portfolio weights.

setGroups

Set up group constraints for portfolio weights.

setInequality

Set up inequality constraints for portfolio weights.

setInitPort

Set up initial portfolio weights.

setOptions

Set up hidden control properties in object (not implemented).

setSolver

Set up solver to estimate efficient portfolios.

Methods

estimatePortStd

Estimate standard deviation of portfolio returns.

estimatePortVaR

Estimate value-at-risk for portfolio.

estimateScenarioMoments

Estimate mean and covariance of scenarios.

simulateNormalScenariosByData

Simulate multivariate normal asset return scenarios from data.

simulateNormalScenariosByMoments

Simulate multivariate normal asset return scenarios from a mean and covariance of asset returns.

getCosts

Get purchase and sales proportional transaction costs from the object.

getOneWayTurnover

Get one-way portfolio turnover constraints.

getScenarios

Obtain scenarios from PortfolioCVaR object.

setCosts

Set up purchase and sale proportional transaction costs for assets in the universe.

setOneWayTurnover

Set up one-way portfolio turnover constraints.

setProbabilityLevel

Set probability level for VaR and CVaR calculations.

setScenarios

Set asset returns scenarios by direct matrix.

setTurnover

Set up average turnover constraints for portfolio weights.

Definitions

Conditional Value-at-Risk Portfolio Optimization

For more information on the theory and definition of conditional value-at-risk optimization supported by portfolio optimization tools in Financial Toolbox™, see Portfolio Optimization Theory.

Copy Semantics

Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB® documentation.

Examples

expand all

Construct a PortfolioCVaR Object and Determine Efficient Portfolios

Create efficient portfolios:

load CAPMuniverse

p = PortfolioCVaR('AssetList',Assets(1:12));
p = simulateNormalScenariosByData(p, Data(:,1:12), 20000 ,'missingdata',true);
p = setDefaultConstraints(p);
p = setProbabilityLevel(p, 0.95);

plotFrontier(p);

pwgt = estimateFrontier(p, 5);

pnames = cell(1,5);
for i = 1:5
	pnames{i} = sprintf('Port%d',i);
end

Blotter = dataset([{pwgt},pnames],'obsnames',p.AssetList);

disp(Blotter);
            Port1         Port2         Port3         Port4          Port5     
    AAPL      0.010984      0.073246       0.11933        0.13068    1.5092e-14
    AMZN             0             0    1.4267e-32     1.7466e-17    2.8997e-14
    CSCO    5.8775e-39    3.6417e-33    6.9925e-34     8.3654e-17    4.1869e-14
    DELL      0.022454             0    1.2932e-32      -9.49e-35    3.9048e-14
    EBAY             0    1.5317e-33    8.1605e-34     1.5485e-17    1.3394e-15
    GOOG       0.20335       0.38055       0.56242        0.75932             1
    HPQ       0.041724     0.0099223    4.1255e-33    -2.3367e-33    3.8894e-14
    IBM        0.44482       0.36453       0.26282           0.11    3.7902e-14
    INTC    5.8775e-39    1.6033e-32    1.3337e-33     7.7037e-34    3.8264e-14
    MSFT       0.27667       0.17175      0.055435     1.0123e-33    4.0873e-14
    ORCL    8.8162e-39             0    1.0637e-32     6.9656e-18    3.7811e-14
    YHOO             0             0    3.5171e-33     8.8891e-19     3.535e-14

References

For a complete list of references for the PortfolioCVaR object and portfolio optimization tools, see Portfolio Optimization.

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