frontier

Rolling efficient frontier

Syntax

[PortWts,AllMean,AllCovariance] = frontier(Universe,Window,Offset,NumPorts)

[PortWts,AllMean,AllCovariance] = frontier(___,ActiveMap,Conset,NumNonNan)

Description

[PortWts,AllMean,AllCovariance] = frontier(Universe,Window,Offset,NumPorts) generates a surface of efficient frontiers showing how asset allocation influences risk and return over time.

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.

[PortWts,AllMean,AllCovariance] = frontier(___,ActiveMap,Conset,NumNonNan) specifies options using one or more optional arguments in addition to the input arguments in the previous syntax.

Input Arguments

Universe — Total return data for a group of securities

array

Total return data for a group of securities, specified as a number of observations (NUMOBS) by number of assets plus one (NASSETS + 1) time series array. Each row represents an observation. Column 1 contains MATLAB^® serial date numbers. The remaining columns contain the total return data for each security.

Data Types: double

Window — Number of data periods used to calculate each frontier

positive integer

Number of data periods used to calculate each frontier, specified as a positive integer value.

Data Types: double

Offset — Increment in number of periods between each frontier

numeric

Increment in number of periods between each frontier, specified as a numeric value.

Data Types: double

NumPorts — Number of portfolios to calculate on each frontier

positive integer

Number of portfolios to calculate on each frontier, specified as a positive integer.

Data Types: double

ActiveMap — Indicates if an asset is part of the Universe on the corresponding date

NUMOBS-by-NASSETS matrix of 1's (all assets active on all dates) (default) | matrix

(Optional) Indicates if an asset is part of the Universe on the corresponding date, specified as a number of observations (NUMOBS) by number of assets (NASSETS) matrix with Boolean elements corresponding to the Universe.

Data Types: double

Conset — Constraint matrix for a portfolio of asset investments

matrix

Constraint matrix for a portfolio of asset investments, specified using portcons with the 'Default' constraint type. This single constraint matrix is applied to each frontier..

Data Types: double

NumNonNan — Minimum number of non-NaN points for each active asset in each window of data

Window - NASSETS (default) | numeric value

Minimum number of non-NaN points for each active asset in each window of data needed to perform the optimization, specified as a numeric value.

Data Types: double

Output Arguments

PortWts — Weights allocated to each asset

matrix

Weights allocated to each asset., returned as a number of curves (NCURVES)-by-1 cell array, where each element is a NPORTS-by-NASSETS matrix of weights.

AllMean — Expected asset returns used to generate each curve on the surface

vector

Expected asset returns used to generate each curve on the surface, returned as an NCURVES-by-1 cell array, where each element is a 1-by-NASSETS vector of the expected asset returns.

AllCovariance — Covariance matrix used to generate each curve on the surface

vector

Covariance matrix used to generate each curve on the surface, returned as an NCURVES-by-1 cell array, where each element is a NASSETS-by-NASSETS vector.

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