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## Validate the Portfolio Problem

In some cases, you may want to validate either your inputs to, or outputs from, a portfolio optimization problem. Although most error checking that occurs during the problem setup phase catches most difficulties with a portfolio optimization problem, the processes to validate portfolio sets and portfolios are time consuming and are best done offline. Consequently, the portfolio optimization tools have specialized methods to validate portfolio sets and portfolios.

### Validating a Portfolio Set

Since it is necessary and sufficient that your portfolio set must be a nonempty, closed, and bounded set to have a valid portfolio optimization problem, the method estimateBounds lets you examine your portfolio set to determine if it is nonempty and, if nonempty, whether it is bounded. Suppose you have the following portfolio set which is an empty set because the initial portfolio at 0 is too far from a portfolio that satisfies the budget and turnover constraint:

```p = Portfolio('NumAssets', 3, 'Budget', 1);
p = p.setTurnover(0.3, 0);
```

If a portfolio set is empty, estimateBounds returns NaN bounds and sets the isbounded flag to []:

`[lb, ub, isbounded] = p.estimateBounds`
```lb =

NaN
NaN
NaN

ub =

NaN
NaN
NaN

isbounded =

[]```

Suppose you create an unbounded portfolio set as follows:

```p = Portfolio('AInequality', [1 -1; 1 1 ], 'bInequality', 0);
[lb, ub, isbounded] = p.estimateBounds```
```lb =

-Inf
-Inf

ub =

1.0e-008 *

-0.3712
Inf

isbounded =

0```

In this case, estimateBounds returns (possibly infinite) bounds and sets the isbounded flag to false. The result shows which assets are unbounded so that you can apply bound constraints as necessary.

Finally, suppose you created a portfolio set that is both nonempty and bounded. estimateBounds not only validates the set, but also obtains tighter bounds which is useful if you are concerned with the actual range of portfolio choices for individual assets in your portfolio set:

```p = Portfolio;
p = p.setBudget(1,1);
p = p.setBounds([ -0.1; 0.2; 0.3; 0.2 ], [ 0.5; 0.3; 0.9; 0.8 ]);

[lb, ub, isbounded] = p.estimateBounds```
```lb =

-0.1000
0.2000
0.3000
0.2000

ub =

0.3000
0.3000
0.7000
0.6000

isbounded =

1```

In this example, all but the second asset have tighter upper bounds than the input upper bound implies.

### Validating Portfolios

Given a portfolio set specified in a Portfolio object, you often want to check if specific portfolios are feasible with respect to the portfolio set. This can occur with, for example, initial portfolios and with portfolios obtained from other procedures. The checkFeasibility method determines whether a collection of portfolios is feasible. Suppose you perform the following portfolio optimization and want to determine if the resultant efficient portfolios are feasible relative to a modified problem.

First, set up a problem in the Portfolio object p, estimate efficient portfolios in pwgt, and then confirm that these portfolios are feasible relative to the initial problem:

```m = [ 0.05; 0.1; 0.12; 0.18 ];
C = [ 0.0064 0.00408 0.00192 0;
0.00408 0.0289 0.0204 0.0119;
0.00192 0.0204 0.0576 0.0336;
0 0.0119 0.0336 0.1225 ];

p = Portfolio;
p = p.setAssetMoments(m, C);
p = p.setDefaultConstraints;
pwgt = p.estimateFrontier;

p.checkFeasibility(pwgt)```
```ans =

1     1     1     1     1     1     1     1     1     1```

Next, set up a different portfolio problem that starts with the initial problem with an additional a turnover constraint and an equally weighted initial portfolio:

```q = p.setTurnover(0.3, 0.25);
q.checkFeasibility(pwgt)```
```ans =

0     0     0     1     1     0     0     0     0     0```

In this case, only two of the ten efficient portfolios from the initial problem are feasible relative to the new problem in Portfolio object q. Solving the second problem using checkFeasibility demonstrates that the efficient portfolio for Portfolio object q is feasible relative to the initial problem:

```qwgt = q.estimateFrontier;
p.checkFeasibility(qwgt)```
```ans =

1     1     1     1     1     1     1     1     1     1```