## Estimate Efficient Frontiers for Portfolio Object

Whereas Estimate Efficient Portfolios for Entire Efficient Frontier for Portfolio Object focused on estimation of efficient portfolios, this section focuses on the estimation of efficient frontiers. For information on the workflow when using `Portfolio` objects, see Portfolio Object Workflow.

### Obtaining Portfolio Risks and Returns

Given any portfolio and, in particular, efficient portfolios, the functions `estimatePortReturn`, `estimatePortRisk`, and `estimatePortMoments` provide estimates for the return (or return proxy), risk (or the risk proxy), and, in the case of mean-variance portfolio optimization, the moments of expected portfolio returns. Each function has the same input syntax but with different combinations of outputs. Suppose that you have this following portfolio optimization problem that gave you a collection of portfolios along the efficient frontier in `pwgt`:

```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 ]; pwgt0 = [ 0.3; 0.3; 0.2; 0.1 ]; p = Portfolio('AssetMean', m, 'AssetCovar', C, 'InitPort', pwgt0); p = setDefaultConstraints(p); pwgt = estimateFrontier(p); ```
Given `pwgt0` and `pwgt`, use the portfolio risk and return estimation functions to obtain risks and returns for your initial portfolio and the portfolios on the efficient frontier:
```[prsk0, pret0] = estimatePortMoments(p, pwgt0); [prsk, pret] = estimatePortMoments(p, pwgt); ```

or

```prsk0 = estimatePortRisk(p, pwgt0); pret0 = estimatePortReturn(p, pwgt0); prsk = estimatePortRisk(p, pwgt); pret = estimatePortReturn(p, pwgt); ```
In either case, you obtain these risks and returns:
```display(prsk0) display(pret0) display(prsk) display(pret)```
```prsk0 = 0.1103 pret0 = 0.0870 prsk = 0.0769 0.0831 0.0994 0.1217 0.1474 0.1750 0.2068 0.2487 0.2968 0.3500 pret = 0.0590 0.0725 0.0859 0.0994 0.1128 0.1262 0.1397 0.1531 0.1666 0.1800 ```

The returns and risks are at the periodicity of the moments of asset returns so that, if you have values for `AssetMean` and `AssetCovar` in terms of monthly returns, the estimates for portfolio risk and return are in terms of monthly returns as well. In addition, the estimate for portfolio risk in the mean-variance case is the standard deviation of portfolio returns, not the variance of portfolio returns.