Mean-Variance Optimization
Given the inputs (returns, standard deviations, and correlations), AllocationADVISOR determines the applicable range of possible returns by finding the return of the minimum variance portfolio (MinVarReturn) and the return of the asset with the greatest expected return (MaxReturn). AllocationADVISOR’s optimizer finds the combination of assets that minimizes the risk for each of 100 return points within this range. Thus, the efficient frontier is made up of 100 efficient portfolios. (If the user selects specific “Efficient Frontier Targets,” (see 8.1 SELECTING EFFICIENT PORTFOLIOS) the efficient frontier could contain as many as 105 efficient portfolios.)

For each E[R_p], minimize

subject to:

where:

p = 1 to 100
E[r_i] = Forcast return for asset i
w_i = weight of asset i
w_j = weight of asset j
correlation of asset i with asset j
standard deviation of asset i
standard deviation of asset j
n = number of assets

Note: Allocation Limits result in additional optimization constraints.