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portvrisk

Portfolio value at risk (VaR)

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Syntax

ValueAtRisk = portvrisk(PortReturn,PortRisk)
ValueAtRisk = portvrisk(___,RiskThreshold,PortValue)

Description

ValueAtRisk = portvrisk(PortReturn,PortRisk) returns the maximum potential loss in the value of a portfolio over one period of time (that is, monthly, quarterly, yearly, and so on) given the loss probability level. portvrisk calculates ValueAtRisk using a normal distribution.

Note

An alternative for portfolio optimization is to use the Portfolio object for mean-variance portfolio optimization. This object supports gross or net portfolio returns as the return proxy, the variance of portfolio returns as the risk proxy, and a portfolio set that is any combination of the specified constraints to form a portfolio set. For information on the workflow when using Portfolio objects, see Portfolio Object Workflow.

example

ValueAtRisk = portvrisk(___,RiskThreshold,PortValue) adds optional arguments for RiskThreshold and PortValue.

example

Examples

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Open Live Script

This example shows how to return the maximum potential loss in the value of a portfolio over one period of time, where ValueAtRisk is computed on a per-unit basis.

PortReturn = 0.29/100;
PortRisk = 3.08/100;
RiskThreshold = [0.01;0.05;0.10];
PortValue = 1;
ValueAtRisk = portvrisk(PortReturn,PortRisk,... 
RiskThreshold,PortValue)
ValueAtRisk = 3×1

    0.0688
    0.0478
    0.0366
Open Live Script

This example shows how to return the maximum potential loss in the value of a portfolio over one period of time, where ValueAtRisk is computed with actual values.

PortReturn = [0.29/100;0.30/100];
PortRisk = [3.08/100;3.15/100];
RiskThreshold = 0.10;
PortValue = [1000000000;500000000];
ValueAtRisk = portvrisk(PortReturn,PortRisk,...
RiskThreshold,PortValue)
ValueAtRisk = 2×1
107 ×

    3.6572
    1.8684
Open Live Script

This example shows how to return the maximum potential loss in the value of a portfolio over one period of time, where the portfolio return (PortReturn) and risk (PortRisk) are specified in dollar units. The returned ValueAtRisk is also in dollar units. Note that the PortValue input for portvrisk is not used in this example. PortValue is only used as a scaling factor to convert from percent to dollars when PortReturn and PortRisk are specified on a percentage basis.

PortReturn = [2900000;1500000];
PortRisk = [30800000;15750000];
RiskThreshold = 0.10;
ValueAtRisk = portvrisk(PortReturn,PortRisk,RiskThreshold)
ValueAtRisk = 2×1
107 ×

    3.6572
    1.8684

Input Arguments

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Expected return of each portfolio over the period, specified as a scalar numeric or an NPORTS-by-1 vector.

Data Types: double

Standard deviation of each portfolio over period, specified as a scalar numeric or NPORTS-by-1 vector.

Data Types: double

(Optional) Loss probability, specified as a scalar decimal or an NPORTS-by-1 vector.

Data Types: double

(Optional) Total value of asset portfolio, specified as a scalar numeric or an NPORTS-by-1 vector.

Note

The PortValue input is used as a scaling factor for ValueAtRisk. The ValueAtRisk output is computed using the PortReturn and PortRisk inputs first, and then scaled by PortValue. Therefore, if you specify PortValue in dollar units, then PortReturn and PortRisk must be given on a percentage basis. Conversely, when PortReturn and PortRisk are specified in dollar units, PortValue must be 1 (default value).

Data Types: double

Output Arguments

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Estimated maximum loss in the portfolio, returned as an NPORTS-by-1 vector. ValueAtRisk is predicted with a confidence probability of 1 − RiskThreshold.

Note

When PortValue is the default value of 1, ValueAtRisk is presented as a percent. A value of 0 for ValueAtRisk indicates no losses.

Version History

Introduced before R2006a

See Also

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