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);

[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);

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.