Selection and allocation are separate decisions
A portfolio can select exactly the same stocks and produce different behavior under different weights. Capitalization weighting emphasizes larger companies; equal weighting assigns the same initial capital to each selected name; score weighting emphasizes a chosen descriptor. S&P Dow Jones Indices' mathematics reference distinguishes these construction families. None is a neutral wrapper around an otherwise unchanged stock-selection result.
Specify whether capitalization means total equity value or free-float-adjusted value, and whether caps apply to securities or issuers. Several share classes of one company should not bypass an issuer limit. For a long-short strategy, also state gross exposure, net exposure and the capital denominator. Weights summing to zero do not mean the portfolio has no market or financing risk.
Count concentration, not just constituents
Consider three fictional holdings weighted 60%, 30% and 10%. The sum of squared weights is 0.46, so the inverse-concentration measure 1 divided by that sum is approximately 2.17. The portfolio has three names but the weight concentration of roughly 2.17 equally weighted positions. Equal weights would give a value of three.
Now impose a 50% issuer cap and redistribute the excess proportionally to the uncapped positions. The resulting weights are 50%, 37.5% and 12.5%. Their squared-weight sum is 0.40625 and the inverse is about 2.46. This improves capital dispersion in the illustration, but it does not establish better risk diversification because correlations and individual volatilities have not been supplied.
Make the constraint system executable
Capping once and renormalizing can push another name above its cap. A reproducible allocation routine must repeat redistribution or solve the stated constrained problem, then verify all limits. Some specifications are infeasible: three holdings cannot be fully invested if each is capped at 30%. Choose a documented response, such as holding residual cash or rejecting the proposed portfolio, rather than silently violating the cap.
Store target weights, pre-trade drifted weights and actual or simulated post-trade weights separately. Market moves alter concentration between reviews; a target cap is not necessarily a continuous exposure guarantee. Transaction costs, rounding and unfilled orders can also leave holdings away from targets. State which version is used in risk reporting and which one generates returns.
Evaluate the allocation choice on its own terms
If the purpose is to assess a signal, begin with a transparent weighting rule and hold it fixed across candidate comparisons. If the purpose is to study weighting, keep the signal and eligible universe fixed. Simultaneously changing both makes attribution difficult. Include turnover, liquidity demand and sector exposure so an attractive gross result is not mistaken for a costless improvement.
The inverse-concentration measure is a descriptive capital statistic, not an independent-bet count or a loss forecast. Two unrelated companies can be highly correlated, while several share classes can be one economic issuer. Use risk estimates and business exposure alongside weight statistics. All allocations here are illustrative, and no return evidence supports preferring the capped portfolio over the alternatives.
Inspect the example
| Weighting illustration | Holding N | Holding O | Holding P | Inverse squared-weight concentration |
|---|---|---|---|---|
| Capital weights supplied | 60% | 30% | 10% | 2.17 |
| 50% cap, proportional redistribution | 50% | 37.5% | 12.5% | 2.46 |
| Equal capital | 33.3333% | 33.3333% | 33.3333% | 3.00 |
Sources & reproduction
Primary references support the definitions and method. Numerical examples are illustrative unless a source record is explicitly identified.