# TS-GMRI Methodology v1.3 Addendum — Equal-Weight Formula Correction

**Effective:** 28 June 2026
**Status:** Live
**Applies to:** TS-GMRI-EW (and any future equal-weighted family member)

## Summary

The equal-weighted variant **TS-GMRI-EW** is changed from a market-cap-ratio average to a **price-return average**. The formula now matches academic and industry standard (S&P 500 Equal Weight, MSCI Equal Weighted) and is immune to supply-side noise on small constituents.

## Rationale

The original formula computed
\[ \text{EW}_t = \frac{1}{N} \sum_i \frac{M_{i,t}}{M_{i,0}} \times 100 \]
where \(M\) is market cap. Market cap = price × circulating supply. A token that mints new units (supply emission) sees its mcap-ratio jump without any change in token value.

On 26 June 2026 the microcap token **TGLD** (Tenbin Gold, base mcap $74,886) experienced a +450.91 % mcap change driven entirely by a ~5.4× supply expansion (price moved only +1.46 %). With N = 18 active constituents, this single token contributed +25.05 percentage points to TS-GMRI-EW, pushing the published value to 122.73 against a true price-only move of ~95.90.

This violates the index's stated economic meaning ("the average return of an equally-weighted portfolio rebalanced to 1/N at base date"), since a passive 1/N portfolio does not buy newly minted tokens — it holds the base-date allocation and only earns price returns.

## Corrected formula

\[ \text{EW}_t = \frac{1}{N} \sum_i \frac{P_{i,t}}{P_{i,0}} \times 100 \]

where \(P_{i,0}\) is the constituent's price on the base date (22 June 2026) and \(P_{i,t}\) is today's price. Both prices are taken from CoinGecko (same source feeding the cap-weighted flagship TS-GMRI).

If a price field is unavailable for a given day, the implementation falls back to the mcap-ratio for that constituent only. This fallback is expected to never trigger after 28 June 2026; it exists strictly to keep the index computable if upstream data ever degrades.

## Backfill

All historical TS-GMRI-EW values from base date (22 June 2026) through 28 June 2026 have been recomputed using the corrected formula. The previously published series (which spiked to ~122 on 26 June) has been retired and replaced with the corrected series, which moves coherently with TS-GMRI cap-weight:

| Date | Old EW | New EW | TS-GMRI (cap) |
|------|-------:|-------:|--------------:|
| 2026-06-22 | 100.00 | 100.00 | 100.00 |
| 2026-06-23 | 99.72  | 97.72  | 98.50 |
| 2026-06-24 | 99.58  | 97.13  | 96.78 |
| 2026-06-25 | 97.03  | 94.82  | 94.52 |
| 2026-06-26 | 122.26 | 94.50  | 95.03 |
| 2026-06-27 | 124.63 | 96.52  | 96.89 |
| 2026-06-28 | 122.73 | 95.90  | 96.75 |

## No impact on other members

TS-GMRI, TS-GMRI-CAP20, TS-GMRI-AU, TS-GMRI-PRE, and TS-GMRI-AG remain unchanged. They are all market-cap-weighted (cap-weight is the correct definition for an mcap-weighted index — supply changes a token's weight in the portfolio, which is the intended economic exposure).

## Implementation

- `scripts/gmri-family.js` → `computeEW(records)`
- `fetch-gmri.js` → top-level `gmri_ew` field
- `scripts/run-gmri-once.js` → CLI flagship/EW computation
- `scripts/backfill-family-history.js` → historical record builder

All four call sites now use `today_price / base_price` per constituent. Records carry both `base_price` + `base_mcap` (and their today counterparts) so the cap-weighted variants are unaffected.

## OTSFA note

This is a methodology bug-fix, not a data revision. The underlying CoinGecko prices are unchanged. The published TS-GMRI-EW values from 23 – 27 June were mathematically internally consistent given the old formula, but the old formula did not match the index's stated definition. We treat this the same way a regulated benchmark administrator would treat a formula correction: full backfill, full disclosure, no quiet edit.