frontcon (Financial Toolbox)

Mean-variance efficient frontier.

Syntax

[PortRisk, PortReturn, PortWts] = frontcon(ExpReturn, 
ExpCovariance, NumPorts, PortReturn, AssetBounds, Groups, 
GroupBounds)

Arguments


`ExpReturn`	`1`-by-number of assets (`NASSETS`) vector specifying the expected (mean) return of each asset.
`ExpCovariance`	`NASSETS`-by-`NASSETS` matrix specifying the covariance of asset returns.
`NumPorts`	Number of portfolios generated along the efficient frontier. Returns are equally spaced between the maximum possible return and the minimum risk point. If `NumPorts` is empty (entered as `[]),` computes `10` equally spaced points. When entering a target rate of return (`PortReturn`), enter `NumPorts` as an empty matrix `[]`.
`PortReturn`	Vector of length equal to the number of portfolios (`NPORTS`) containing the target return values on the frontier. If `PortReturn` is not entered or `[],` `NumPorts` equally spaced returns between the minimum and maximum possible values are used.
`PortReturn`
`AssetBounds`	`2`-by-`NASSETS` matrix containing the lower and upper bounds on the weight allocated to each asset in the portfolio. Default lower bound = all `0`s (no short-selling). Default upper bound = all `1`s (any asset may constitute the entire portfolio).
`Groups`	Number of groups (`NGROUPS)`-by-`NASSETS` matrix specifying `NGROUPS` asset groups or classes. Each row specifies a group. `Groups(i,j) = 1` (`j`'th asset belongs in the `i`'th group). `Groups(i,j) = 0` (`j`'th asset not a member of the `i`'th group).
`GroupBounds`	`NGROUPS`-by-`2` matrix specifying, for each group, the lower and upper bounds of the total weights of all assets in that group. Default lower bound = all `0`s. Default upper bound = all `1`s.

Description

[PortRisk, PortReturn, PortWts] = frontcon(ExpReturn, 
ExpCovariance, NumPorts, PortReturn, AssetBounds, Groups, 
GroupBounds)

returns the mean-variance efficient frontier with user-specified 
asset constraints, covariance, and returns. For a collection of NASSETS risky 
assets, computes a portfolio of asset investment weights that minimize the risk 
for given values of the expected return. The portfolio risk is minimized subject 
to constraints on the asset weights or on groups of asset weights.

PortRisk is an NPORTS-by-1 vector of the standard deviation of each portfolio.

PortReturn is a NPORTS-by-1 vector of the expected return of each portfolio.

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.

frontcon generates a plot of the efficient frontier if you invoke it without output arguments.

The asset returns are assumed to be jointly normal, with expected mean returns of ExpReturn and return covariance ExpCovariance. The variance of a portfolio with 1-by-NASSET weights PortWts is given by
PortVar = PortWts*ExpCovariance*PortWts'. The portfolio expected return is PortReturn = dot(ExpReturn, PortWts).

Examples

Given three assets with expected returns of

ExpReturn = [0.1 0.2 0.15]

and expected covariance of

 ExpCovariance = [
    0.0100   -0.0061    0.0042 
   -0.0061    0.0400   -0.0252 
    0.0042   -0.0252    0.0225 ]

compute the mean-variance efficient frontier for four points (NumPorts = 4):

[PortRisk,PortReturn,PortWts] = frontcon... 
(ExpReturn,ExpCovariance,NumPorts)
PortRisk =

    0.0426
    0.0483
    0.1089
    0.2000
PortReturn =

    0.1569
    0.1713
    0.1856
    0.2000
PortWts =

    0.2134    0.3518    0.4348
    0.0096    0.4352    0.5552
         0    0.7128    0.2872
         0    1.0000    0.0000