Decision modelling · LP / ILP / NLP
Investment Portfolio Optimisation
Built three Excel Solver optimisation models — linear, integer, and nonlinear — to construct an ASX equity portfolio under real sector, risk, and allocation constraints.
10 ASX stocks · 5 sectors · 3 optimisation models
Executive summary
I modelled the same ten-stock, five-sector ASX universe three different ways to answer three different questions. A Simplex LP found the return-maximising proportional allocation (1.37% expected monthly return, 13 constraints on risk and sector exposure). A binary ILP found the best discrete 7-stock portfolio, consistently excluding the same three weakest performers the LP had already zeroed out — cross-validating the recommendation across two different optimisation approaches. A GRG Nonlinear model then flipped the objective, minimising portfolio variance via the full covariance matrix while guaranteeing at least 1.50% monthly return. Sensitivity analysis on the LP model showed the risk cap on the highest-risk assets was the single most expensive constraint, worth roughly 0.027% of return per 1% it was relaxed.
The problem
An investor holding ten ASX-listed stocks across five sectors needed a defensible way to allocate capital — maximising return under real constraints on sector minimums, single-stock exposure, and risk-category weighting — rather than picking stocks by feel.
The outcome
Built and solved three Excel Solver models: a Simplex LP for proportional allocation (1.37% monthly expected return under 13 constraints), a binary ILP for discrete stock selection (7 of 10 stocks, excluding the three weakest performers), and a GRG Nonlinear model minimising portfolio variance via the full covariance matrix. Sensitivity analysis then identified which constraints were actually costing the portfolio return.
Architecture
The actual Excel Solver LP model — objective function, decision variables, and all 13 constraints.