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.
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);
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);
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.
estimatePortMoments
| estimatePortReturn
| plotFrontier
| Portfolio