portvrisk

Portfolio value at risk (VaR)

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.

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

Examples

Compute the Maximum Potential Loss in the Value of a Portfolio Over One Period of Time

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

Compute the Maximum Potential Loss in the Value of a Portfolio Over One Period of Time Using Actual Values

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

Input Arguments

PortReturn — Expected return of each portfolio over period

scalar numeric | vector

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

Data Types: double

PortRisk — Standard deviation of each portfolio over period

scalar numeric | vector

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

Data Types: double

RiskThreshold — Loss probability

0.05 (5%) (default) | scalar decimal | vector

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

Data Types: double

PortValue — Total value of asset portfolio

1 (default) | scalar numeric | vector

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

Note

If PortReturn and PortRisk are in dollar units, then PortValue should be 1. If PortReturn and PortRisk are on a percentage basis, then PortValue should be the total value of the portfolio.

Data Types: double

Output Arguments

ValueAtRisk — Estimated maximum loss in portfolio

vector

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

Note

If PortValue is not given, ValueAtRisk is presented on a per-unit basis. A value of 0 indicates no losses.