If a PortfolioCVaR object is destroyed when modifying, remember to pass an
existing object into the `PortfolioCVaR`

object if you want to
modify it, otherwise it creates a new object. See Creating the PortfolioCVaR Object for details.

If you get matrix incompatibility or "non-conformable" errors, the representation of data in the tools follows a specific set of basic rules described in Conventions for Representation of Data.

If the `'cuttingplane'`

solver displays the following
warning:

Warning: Max iterations reached. Consider modifying the solver options, or using fmincon. > In @PortfolioCVaR\private\cvar_cuttingplane_solver at 255 In @PortfolioCVaR\private\cvar_optim_min_risk at 85 In PortfolioCVaR.estimateFrontier at 69

This warning is usually related to portfolios in the lower-left end of the efficient frontier. The cutting plane solver may have gotten very close to the solution, but there may be too many portfolios with very similar risks and returns in that neighborhood, and the solver runs out of iterations before reaching the desired accuracy.

To correct this problem, you can use `setSolver`

to make any of these changes:

Increase the maximum number of iterations (

`'MaxIter'`

).Relax the stopping tolerances (

`'AbsTol'`

and/or`'RelTol'`

).Use a different master solver algorithm (

`'MasterSolverOptions'`

).Alternatively, you can try the

`'fmincon'`

solver.

When the default maximum number of iterations of the
`'cuttingplane'`

solver is reached, the solver usually needs
many more iterations to reach the accuracy required by the default stopping
tolerances. You may want to combine increasing the number of iterations (e.g.,
multiply by 5) with relaxing the stopping tolerances (e.g., multiply by 10 or 100).
Since the CVaR is a stochastic optimization problem, the accuracy of the solution is
relative to the scenario sample, so a looser stopping tolerance may be acceptable.
Keep in mind that the solution time may increase significantly when you increase the
number of iterations. For example, doubling the number of iterations more than
doubles the solution time. Sometimes using a different master solver (e.g.,
switching to `'interior-point'`

if you are using the default
`'simplex'`

) can get the `'cuttingplane'`

solver to converge without changing the maximum number of iterations.

Alternatively, the `'fmincon'`

solver may be faster than the
`'cuttingplane'`

solver for problems where cutting plane
reaches the maximum number of iterations.

If the `'cuttingplane'`

solver generates the following
error:

Error using cvar_cuttingplane_solver (line 251) Could not solve the problem. Consider modifying the solver options, or using fmincon. Error in cvar_optim_by_return (line 100) [x,~,~,exitflag] = cvar_cuttingplane_solver(... Error in PortfolioCVaR/estimateFrontier (line 80) pwgt = cvar_optim_by_return(obj, r(2:end-1), obj.NumAssets, ...

To correct this problem, you can use `setSolver`

to make any of these changes:

Modify the master solver options (

`'MasterSolverOptions'`

), for example, change the algorithm (`'Algorithm'`

) or the termination tolerance (`'TolFun'`

).Alternatively, you can try the

`'fmincon'`

solver.

If asset return data has missing or `NaN`

values, the `simulateNormalScenariosByData`

function with the `'missingdata'`

flag set to
`true`

may fail with either too many iterations or a singular
covariance. To correct this problem, consider this:

If you have asset return data with no missing or

`NaN`

values, you can compute a covariance matrix that may be singular without difficulties. If you have missing or`NaN`

values in your data, the supported missing data feature requires that your covariance matrix must be positive-definite, that is, nonsingular.`simulateNormalScenariosByData`

uses default settings for the missing data estimation procedure that might not be appropriate for all problems.

In either case, you might want to estimate the moments of asset
returns separately with either the ECM estimation functions such as `ecmnmle`

or with your own
functions.

`cvar_optim_transform`

ErrorsIf you obtain optimization errors such as:

Error using cvar_optim_transform (line 276) Portfolio set appears to be either empty or unbounded. Check constraints. Error in PortfolioCVaR/estimateFrontier (line 64) [AI, bI, AE, bE, lB, uB, f0, f, x0] = cvar_optim_transform(obj);

Error using cvar_optim_transform (line 281) Cannot obtain finite lower bounds for specified portfolio set. Error in PortfolioCVaR/estimateFrontier (line 64) [AI, bI, AE, bE, lB, uB, f0, f, x0] = cvar_optim_transform(obj);

`estimateBounds`

to examine your
portfolio set, and use `checkFeasibility`

to ensure that
your initial portfolio is either feasible and, if infeasible, that you have
sufficient turnover to get from your initial portfolio to the portfolio set.
To correct this problem, try solving your problem with larger values for turnover and gradually reduce to the value that you want.

If you obtain efficient portfolios that, do not seem to make sense, this can
happen if you forget to set specific constraints or you set incorrect constraints.
For example, if you allow portfolio weights to fall between `0`

and
`1`

and do not set a budget constraint, you can get portfolios
that are 100% invested in every asset. Although it may be hard to detect, the best
thing to do is to review the constraints you have set with display of the
PortfolioCVaR object. If you get portfolios with 100% invested in each asset, you
can review the display of your object and quickly see that no budget constraint is
set. Also, you can use `estimateBounds`

and `checkFeasibility`

to determine if
the bounds for your portfolio set make sense and to determine if the portfolios you
obtained are feasible relative to an independent formulation of your portfolio
set.

`PortfolioCVaR`

| `checkFeasibility`

| `estimateScenarioMoments`

- Postprocessing Results to Set Up Tradable Portfolios
- Creating the PortfolioCVaR Object
- Working with CVaR Portfolio Constraints Using Defaults
- Troubleshooting for Setting 'Conditional' BoundType, MinNumAssets, and MaxNumAssets Constraints
- Asset Returns and Scenarios Using PortfolioCVaR Object
- Estimate Efficient Portfolios for Entire Frontier for PortfolioCVaR Object
- Estimate Efficient Frontiers for PortfolioCVaR Object