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.