Portfolio Optimization Functions

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

Capital AllocationDescription

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 ComputationDescription

frontcon

Computes portfolios along the efficient frontier for a given group of assets. The computation is based on sets of constraints representing the maximum and minimum weights for each asset, and the maximum and minimum total weight for specified groups of assets.

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.

Constraint SpecificationDescription

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 ConversionDescription

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.

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