Portfolios on constrained efficient frontier
portopt has been partially removed and will no longer accept
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.
sets up the most basic portfolio problem with weights greater than or equal to
PortWts] = portopt(
0 that must sum to
1. All that is
necessary to solve this problem is the mean and covariance of asset returns. By
portopt returns 10 equally-spaced points on the
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.
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
Portfolio objects, see Portfolio Object Workflow.
specifies options using one or more optional arguments in addition to the input
arguments in the previous syntax.
PortWts] = portopt(___,
returns a plot of the efficient frontier if
portopt is invoked
with no output arguments.
Plot the Risk-Return Efficient Frontier
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)
ExpReturn — Expected (mean) return of each asset
Expected (mean) return of each asset, specified as a
1-by-number of assets (
ExpCovariance — Covariance of the asset returns
Covariance of the asset returns, specified as a
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
portopt returns the
If not over-ridden by
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).
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
1 vector). If not
entered or empty,
NumPorts equally spaced returns
between the minimum and maximum possible values are used.
portopt requires that if you set
should be empty. If you specify
PortReturn with a
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.
PortRisk — Standard deviation of each portfolio
Standard deviation of each portfolio, returned as a
PortWts is an
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
Expected return of each portfolio, returned as a
PortWts — Weights allocated to each asset
Weights allocated to each asset, returned as a
NASSETS matrix. Each row
represents a portfolio. The total of all weights in a portfolio is 1.
Introduced before R2006a
- Portfolio Construction Examples
- Plotting an Efficient Frontier Using portopt
- Portfolio Selection and Risk Aversion
- Bond Portfolio Optimization Using Portfolio Object
- Active Returns and Tracking Error Efficient Frontier
- portopt Migration to Portfolio Object
- Analyzing Portfolios
- Portfolio Optimization Functions