Epistemica · Decision Instrument

Aid fell 23% in 2025 — the steepest contraction on record

Make the same capital
work twice

Official development assistance fell to 174 billion dollars in 2025, a second consecutive annual decline, and grants — the form development finance leans on hardest — fell nearly three times faster than loans. Donor envelopes, concessional guarantees and shareholder recapitalisation are all tightening at once.

One lever stays fully inside your control: how hard the capital you already hold is made to work. A well-run institution can roughly double the development its existing capital finances over a decade, without a single new dollar. This instrument computes by how much — on your balance sheet, not a stylised one.

−23%
aid in 2025
steepest on record
48%
of capital genuinely
freed per cycle
1.9×
the lending, same
capital, one decade
Run it on your numbers
Live Tool Deterministic No Data Retained

Why velocity, and why now

Development finance has always measured itself by stocks: capital deployed, and the health of the loan book. Both matter, and in an era of replenishment both were sufficient. They are not sufficient now. An institution that lends a rand once and holds the exposure for twenty years, and one that lends the same rand, recovers it through disciplined recycling and lends it again, report almost identical numbers on today's conventions — and finance very different amounts of development. What is missing from the measurement is a flow: how many times a unit of scarce capital can be put back to work before it retires.

The catch is that the arithmetic is usually done dishonestly. A board approving a securitisation is told how much of the loan pool is being sold, and assumes the capital follows. It does not. Selling 85 per cent of a pool does not release 85 per cent of the capital behind it: prudential rules charge the deepest retained layer close to dollar for dollar, and the guarantee on the layer above does not remove that charge — it substitutes the guarantor's own risk weight, lower but not zero. Counted properly, roughly half the capital stays locked. That gap is the difference between a multiplier a board can defend to its supervisor and one it cannot.

Enter your institution's own capital, prudential and structural parameters below and the tool recomputes the net capital release, the annual velocity ratio, the cumulative multiplier over your horizon, a set of constraint tests, and a sensitivity grid across retention thickness and guarantor quality. It also shows what a placed-share calculation would have claimed, so the overstatement is visible rather than buried. Every figure is computed from the inputs by fixed formulas — nothing estimated, forecast or generated. The defaults reproduce the stylised illustration in the working paper.

Capital velocity
Capital multiplier
Cumulative origination
Net capital release, ρ

1 · Institution

2 · Securitisation structure

3 · Retained first loss

4 · Guarantee pricing

5 · Recycling

6 · Board attestations

Cycle-by-cycle build-out

Origination financed per recycling cycle, and the cumulative total (US$ m).

Origination in cycle Cumulative

Honest versus naive accounting

Cumulative origination over the horizon (US$ m). The naive figure ignores retained-position capital charges.

Constraint tests

Every test must pass before the multiplier means anything.

TestValueResult

Sensitivity — capital multiplier

Rows: funded junior sublayer retained. Columns: protection provider risk weight. The outlined cell is nearest your current inputs.

Engine detail — all intermediate values

Method

Why this is deterministic

Every output is a fixed function of the inputs. The same parameters always produce the same figures, and each can be traced by hand: capital intensity is the capital ratio times the average risk weight; capital consumed is the funded junior sublayer in full plus the protected sublayer at the guarantor's substituted risk weight; the release fraction is what remains of usable capital; and the multiplier is the geometric sum of the effective redeployment ratio over the number of cycles the horizon allows.

There is no model, no estimation, no forecast and no generated content. The page makes no network requests, draws no random numbers, and stores nothing — the calculation runs entirely in your browser, and the figures you enter never leave it.

Limits

What it does not claim

The tool computes the capital arithmetic of a structure you describe. It does not read financial statements, verify that your inputs reflect your balance sheet, or substitute for supervisory judgement. Capital relief is not automatic: it depends on the supervisor accepting that the transaction achieves significant risk transfer, and the applicable regime — Basel or a rating agency's model — determines which charge actually binds.

Two of the constraint tests are declarations you make, not computations the tool performs: whether the senior notes are genuinely placeable, and whether your institution has adopted the sequencing rule. A pass on either reflects what you entered.

Working Paper · July 2026

The Developmental Capital Velocity Framework

The full framework behind this tool: the capital mechanics, the split first-loss treatment, the guarantee pricing, the prudential tests, the risks turnover introduces, and the implementation pathway. Opens in a reader on this page — no download.

Cite as: Sarpong, P. (2026). The Developmental Capital Velocity Framework: Repositioning Securitisation as an Instrument of Capital Recycling for African Development Finance Institutions. Working paper, Sarpong Strategia.