setBudget

Set up budget constraints

Syntax

obj = setBudget(obj,LowerBudget)

obj = setBudget(obj,LowerBudget,UpperBudget)

Description

obj = setBudget(obj,LowerBudget) sets up budget constraints for Portfolio, PortfolioCVaR, or PortfolioMAD objects. For details on the respective workflows when using these different objects, see Portfolio Object Workflow, PortfolioCVaR Object Workflow, and PortfolioMAD Object Workflow.

obj = setBudget(obj,LowerBudget,UpperBudget) sets up budget constraints for portfolio objects with an additional option for UpperBudget.

Examples

Set Budget Constraint for a Portfolio Object

Assume you have a fund that permits up to 10% leverage, which means that your portfolio can be from 100% to 110% invested in risky assets. Given a Portfolio object p, set the budget constraint.

p = Portfolio;
p = setBudget(p, 1, 1.1);
disp(p.LowerBudget);

     1

disp(p.UpperBudget);

    1.1000

Set Budget Constraint for a PortfolioCVaR Object

Assume you have a fund that permits up to 10% leverage, which means that your portfolio can be from 100% to 110% invested in risky assets. Given a CVaR portfolio object p, set the budget constraint.

p = PortfolioCVaR;
p = setBudget(p, 1, 1.1);
disp(p.LowerBudget);

     1

disp(p.UpperBudget);

    1.1000

Set Budget Constraint for a PortfolioMAD Object

Assume you have a fund that permits up to 10% leverage, which means that your portfolio can be from 100% to 110% invested in risky assets. Given PortfolioMAD object p, set the budget constraint.

p = PortfolioMAD;
p = setBudget(p, 1, 1.1);
disp(p.LowerBudget);

     1

disp(p.UpperBudget);

    1.1000

Control the Allocation of a Risk-Free Asset Using setBudget

Define mean and covariance of risk asset returns.

m = [ 0.05; 0.1; 0.12; 0.18; ];
C = [ 0.0064 0.00408 0.00192 0,; 
    0.00408 0.0289 0.0204 0.0119,;
    0.00192 0.0204 0.0576 0.0336,;
   0 0.0119 0.0336 0.1225];

Create a Portfolio object defining the risk-free rate.

p = Portfolio('RiskFreeRate',0.03, 'assetmean', m, 'assetcovar', C, ...
'lowerbudget', 1, 'upperbudget', 1, 'lowerbound', 0);

Create multiple Portfolio objects with different budgets on risky assets. By defining the risky assets, you can control how much is invested in a risk-free asset.

p = setBudget(p, 1, 1);    % allow 0% risk-free asset allocation, meaning fully invested in risky assets
p1 = setBudget(p, 0, 1);   % allow 0 to 100% risk-free asset allocation
p2 = setBudget(p, 0.7, 1);  % allow 0 to 30% risk-free asset allocation

plotFrontier(p); hold on; 
plotFrontier(p1);hold on;
plotFrontier(p2);
legend('Without risk-free asset', 'With risk-free asset in range [0,1]', 'With risk-free asset in range [0, 0.3]', 'location', 'best');

setBudget defines the bound for total weights for the allocated risky assets, and the remaining is automatically the bound for a risk-free asset. Use setBudget to control the level of allowed allocation to a risk-free asset. For additional information on using setBudget with a risk-free asset, see Leverage in Portfolio Optimization with a Risk-Free Asset.

Input Arguments

obj — Object for portfolio

object

Object for portfolio, specified using Portfolio, PortfolioCVaR, or PortfolioMAD object. For more information on creating a portfolio object, see

• Portfolio

• PortfolioCVaR

• PortfolioMAD

Data Types: object

LowerBudget — Lower-bound for budget constraint

scalar

Lower-bound for budget constraint, specified as a scalar for a Portfolio, PortfolioCVaR, or PortfolioMAD input object (obj).

Note

Given bounds for a budget constraint in either LowerBudget or UpperBudget, budget constraints require any portfolio in Port to satisfy:

LowerBudget <= sum(Port) <= UpperBudget

One or both constraints may be specified. The usual budget constraint for a fully invested portfolio is to have LowerBudget = UpperBudget = 1. However, if the portfolio has allocations in cash, the budget constraints can be used to specify the cash constraints. For example, if the portfolio can hold between 0% and 10% in cash, the budget constraint would be set up with

obj = setBudget(obj, 0.9, 1)

Data Types: double

UpperBudget — Upper-bound for budget constraint

scalar

Upper-bound for budget constraint, specified as a scalar for a Portfolio, PortfolioCVaR, or PortfolioMAD input object (obj).

Note

Given bounds for a budget constraint in either LowerBudget or UpperBudget, budget constraints require any portfolio in Port to satisfy:

LowerBudget <= sum(Port) <= UpperBudget

One or both constraints may be specified. The usual budget constraint for a fully invested portfolio is to have LowerBudget = UpperBudget = 1. However, if the portfolio has allocations in cash, the budget constraints can be used to specify the cash constraints. For example, if the portfolio can hold between 0% and 10% in cash, the budget constraint would be set up with

obj = setBudget(obj, 0.9, 1)

Data Types: double

Output Arguments

obj — Updated portfolio object

object for portfolio

Updated portfolio object, returned as a Portfolio, PortfolioCVaR, or PortfolioMAD object. For more information on creating a portfolio object, see

• Portfolio

• PortfolioCVaR

• PortfolioMAD

Tips

You can also use dot notation to set up the budget constraints.

obj = obj.setBudget(LowerBudget, UpperBudget);