Portfolio Optimization Functions

The portfolio optimization functions assist portfolio managers in constructing portfolios that optimize risk and return.

Capital Allocation	Description
portalloc	Computes the optimal risky portfolio on the efficient frontier, based on the risk-free rate, the borrowing rate, and the investor's degree of risk aversion. Also generates the capital allocation line, which provides the optimal allocation of funds between the risky portfolio and the risk-free asset.

Efficient Frontier Computation	Description
frontier	Computes portfolios along the efficient frontier for a given group of assets. Generates a surface of efficient frontiers showing how asset allocation influences risk and return over time.
portopt	Computes portfolios along the efficient frontier for a given group of assets. The computation is based on a set of user-specified linear constraints. Typically, these constraints are generated using the constraint specification functions described below. Warning portopt has been partially removed and will no longer accept ConSet or varargin arguments. portopt will only solve the portfolio problem for long-only fully invested portfolios. Use Portfolio instead. For more information on migrating portopt code to Portfolio, see portopt Migration to Portfolio Object.

Constraint Specification	Description
portcons	Generates the portfolio constraints matrix for a portfolio of asset investments using linear inequalities. The inequalities are of the type A*Wts' <= b, where Wts is a row vector of weights.
portvrisk	Portfolio value at risk (VaR) returns the maximum potential loss in the value of a portfolio over one period of time, given the loss probability level RiskThreshold.
pcalims	Asset minimum and maximum allocation. Generates a constraint set to fix the minimum and maximum weight for each individual asset.
pcgcomp	Group-to-group ratio constraint. Generates a constraint set specifying the maximum and minimum ratios between pairs of groups.
pcglims	Asset group minimum and maximum allocation. Generates a constraint set to fix the minimum and maximum total weight for each defined group of assets.
pcpval	Total portfolio value. Generates a constraint set to fix the total value of the portfolio.

Constraint Conversion	Description
abs2active	Transforms a constraint matrix expressed in absolute weight format to an equivalent matrix expressed in active weight format.
active2abs	Transforms a constraint matrix expressed in active weight format to an equivalent matrix expressed in absolute weight format.

Note

An alternative to using these portfolio optimization functions is to use the Portfolio object (Portfolio) 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.