portopt

Portfolios on constrained efficient frontier

portopt has been partially removed and will no longer accept ConSet or varargin arguments. Use Portfolio instead to solve portfolio problems that are more than a long-only fully-invested portfolio. For information on the workflow when using Portfolio objects, see Portfolio Object Workflow. For more information on migrating portopt code to Portfolio, see portopt Migration to Portfolio Object.

Syntax

[PortRisk,PortReturn,PortWts] = portopt(ExpReturn,ExpCovariance)

[PortRisk,PortReturn,PortWts] = portopt(___,NumPorts,PortReturn)

portopt(___,NumPorts,PortReturn)

Description

[PortRisk,PortReturn,PortWts] = portopt(ExpReturn,ExpCovariance) sets up the most basic portfolio problem with weights greater than or equal to 0 that must sum to 1. All that is necessary to solve this problem is the mean and covariance of asset returns. By default, portopt returns 10 equally-spaced points on the efficient frontier.

portopt solves the "standard" mean-variance portfolio optimization problem for a long-only fully-invested investor with no additional constraints. Specifically, every portfolios on the efficient frontier has non-negative weights that sum to 1.

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.

[PortRisk,PortReturn,PortWts] = portopt(___,NumPorts,PortReturn) specifies options using one or more optional arguments in addition to the input arguments in the previous syntax.

portopt(___,NumPorts,PortReturn) returns a plot of the efficient frontier if portopt is invoked with no output arguments.

Examples

Plot the Risk-Return Efficient Frontier

Use portopt to connect 20 portfolios along the efficient frontier having evenly spaced returns. By default, choose among portfolios without short-selling and scale the value of the portfolio to 1.

ExpReturn = [0.1 0.2 0.15];

ExpCovariance = [0.005   -0.010    0.004
                -0.010    0.040   -0.002
                 0.004   -0.002    0.023];

NumPorts = 20;
portopt(ExpReturn, ExpCovariance, NumPorts)

Input Arguments

ExpReturn — Expected (mean) return of each asset

vector

Expected (mean) return of each asset, specified as a 1-by-number of assets (NASSETS) vector.

Data Types: double

ExpCovariance — Covariance of the asset returns

matrix

Covariance of the asset returns, specified as a NASSETS-by-NASSETS matrix.

Data Types: double

NumPorts — Number of portfolios generated along the efficient frontier

10 (default) | scalar numeric

(Optional) Number of portfolios generated along the efficient frontier, specified as a scalar numeric. Returns are equally spaced between the maximum possible return and the minimum risk point. If NumPorts is empty (entered as []), portopt computes 10 equally spaced points. If you specify 1, portopt returns the minimum-risk portfolio.

Note

If not over-ridden by PortReturn, these portfolios are spaced evenly from the minimum to the maximum return on the efficient frontier. If NumPorts = 1, then the minimum-risk portfolio is computed (positive integer).

Data Types: double

PortReturn — Target portfolio returns to be computed on the efficient frontier

[ ] (default) | vector

(Optional) Target portfolio returns to be computed on the efficient frontier, specified as a number of portfolios (NPORTS-by-1 vector). If not entered or empty, NumPorts equally spaced returns between the minimum and maximum possible values are used.

Note

portopt requires that if you set PortReturn, NumPorts should be empty. If you specify PortReturn with a nonempty vector, PortReturn overrides NumPorts. If any returns in PortReturn fall outside the range of returns on the efficient frontier, portopt generates a warning and the efficient portfolios closest to the endpoints of the efficient frontier are computed.

Data Types: double

Output Arguments

PortRisk — Standard deviation of each portfolio

vector

Standard deviation of each portfolio, returned as a NPORTS-by-1 vector.

PortWts is an NPORTS-by-NASSETS matrix of weights allocated to each asset. Each row represents a portfolio. The total of all weights in a portfolio is 1.

PortReturn — expected return of each portfolio

vector

Expected return of each portfolio, returned as a NPORTS-by-1 vector.

PortWts — Weights allocated to each asset

matrix

Weights allocated to each asset, returned as a NPORTS-by-NASSETS matrix. Each row represents a portfolio. The total of all weights in a portfolio is 1.

More About

Efficient Frontier

The efficient frontier is a key concept in modern portfolio theory (MPT) that represents a set of optimal portfolios offering the highest expected return for a given level of risk, or the lowest risk for a given level of expected return.

The efficient frontier illustrates the tradeoff between risk (often measured as the standard deviation of portfolio returns) and expected return. Investors aim to construct portfolios that lie on this frontier to maximize their returns for a given level of risk. Portfolios that lie on the efficient frontier are considered optimal because they provide the best possible expected return for their level of risk. Portfolios that lie below the frontier are suboptimal, as they do not provide sufficient return for the amount of risk taken. The efficient frontier emphasizes the importance of diversification. By combining different assets with varying returns and risks, investors can reduce the overall risk of the portfolio without sacrificing expected returns.

Version History

Introduced before R2006a