Indian households have a variety of investment options, ranging from fixed deposits and government small savings schemes to equity index funds, gold ETFs and REITs. However, most tend to be guided more by habit and imitating their surroundings rather than rational allocation. This paper uses linear programming (LP), a classic operations research methodology, to determine the optimal allocation of a budget of ₹10,00,000 across ten investment options available to an Indian retail investor as of October 2026. Expected returns were calculated using official and established sources and a risk score was assigned to each option (on a scale of 1 to 10).

 

The LP model was formulated to maximise expected annual return subject to thirteen constraints: a weighted average risk ceiling of 5, a 30% floor in government-backed instruments, a 25% cap on lock-in schemes, the statutory PPF limit and minimum and maximum holdings for each asset class. The model was solved using Excel Solver (Simplex LP). The solution was verified by a hand-worked simplex tableau and by the graphical method for a reduced two-variable form.

 

All three methods give the same optimum: ₹4.5 lakh in the Nifty 50, ₹2.5 lakh in NSC, ₹1.5 lakh in gold, ₹1 lakh in G-Secs and ₹50,000 in a fixed deposit. This earns an expected ₹1,04,895 a year (10.49%) at an average risk score of exactly 5.0. Sensitivity analysis shows that each 0.1-point increase in risk tolerance adds about ₹720 a year, and that the allocation stays unchanged for any equity return between 8.4% and 14.3%. Benchmarked against an all-FD saver, equal weighting, EPFO-style, NPS lifecycle and multi-asset fund allocations, the LP portfolio earns the highest return of all allocations that are constrained to respect the investor's constraints. The paper concludes that LP implemented in a ubiquitous Excel provides a transparent and verifiable basis for asset allocation for retail investors and advisers.