The Lab

Where the idea comes from

• Gold tokens are crypto tokens, each backed by real gold held by its issuer. PAXG (from Paxos) and XAUT (from Tether's gold company) are each one troy ounce of gold, by the issuers' own documents.
• Gold perps follow the gold price without any token being held: some follow a token (a PAXG or XAUT perp), others gold itself (an XAU perp).
• How far a tracker strays from what it follows is how funds that track an index are judged. Antti Petajisto (2017) measured it for exchange- traded funds.
• How fast a gap closes is the half-life of a pull back to normal, from the model of George Uhlenbeck and Leonard Ornstein (1930).
• Whether a grid suits gold is our own question: our paper gold bot runs a grid 12% either side of its start.

How we tested

• The tokens and perps:
  • PAXG on Binance and XAUT on Bybit, the tokens themselves;
  • perps on PAXG, XAUT and gold on Bybit and Binance;
  • Hyperliquid's PAXG perp and its xyz market's gold perp.
  • Each from 23 October 2024 (or its listing) to 16 October 2026.
• Real gold: gold futures, Yahoo's public prices, the reference only. Each price is read at 16:00 New York time, on the days both trade.
• The grid: our engine's own backtest on Bybit's 15-minute candles:
  • each month, a fresh grid bought from the month's first price, held to the month's end, then sold;
  • 3, 6, 12 and 20% either side, with 6, 12 or 20 rungs;
  • 10,000 USDT, no leverage, real order steps, fees and funding;
  • on the PAXG perp over 54 months (April 2022 to September 2026), and on the XAUT perp over 17 months (May 2025 to September 2026).
• The bar, fixed before the run: pick the best setting on the first half of the months. In the second half it must make money and beat 95% of 100 shuffled copies, in which each month's hours are dealt at random.

The maths, step by step

1. Tracking error. Each day, the token's move minus gold's. Gold up 1.0% and the token up 1.2%: a gap of 0.2%. The spread of those daily gaps over a year (times √252, the trading days) is the tracking error.

2. The premium. The token's price over gold's, as a percentage.

• Futures sit above the gold price for delivery today, by about the interest rate until they expire. So a premium to futures is not a premium to gold itself.

3. The half-life. If a gap keeps a share φ (phi) of itself each day, it halves in ln 2 ÷ −ln φ days. With φ = 0.8, that is 0.693 ÷ 0.223 = 3.1 days.

What we found

1. Every gold token and perp tracked gold closely.

Against gold futures, at 16:00 New York.

• The tracking error was 2.3% to 4.6% a year. For comparison, gold futures themselves moved about 26% a year over the same days (the spread of their daily moves). So a token follows gold, with a little noise.
• All sat about 0.4% to 0.9% under the futures. That is about what futures' carry would explain: an interest rate near 4% for one to two months. It is not a discount to gold itself.
• The biggest single-day gaps fell on 30 January 2025, 30 July 2025 and 29 July 2026. Those are when gold futures roll to the next contract. They come from the reference, not the tokens.

2. The two tokens of the same metal differ a little.

• PAXG sat 0.22% over XAUT on average (band 0.18% to 0.27%).
• The gap itself varied by about 0.23%, and any departure from its average halved in about 3 days.

3. Each perp sits right on its own token.

• The perps sat 0.03% to 0.05% under their tokens.
• Any gap halved in under a day.

4. Holding a gold perp long costs funding, paid to the shorts:

• Holding the token itself costs no funding. A perp long costs about 4.6–13% a year. It is roughly the interest rate, as futures' carry is.

5. No grid setting beat chance on gold.

• PAXG: the first half's best was 6% either side with 20 rungs. In the second half it made +0.19% a month, beating only 44% of the shuffled copies. Not shown.
• XAUT: the first half's best was 3% with 6 rungs. In the second half it lost 0.38% a month (beating 83% of shuffles). Not shown.

6. Is 12% sensible? On PAXG, 12 rungs:

• 12% rarely runs out on gold, in 15% of months, against 65% for Bitcoin. So it is a survival shape: it stays in range.
• But it barely trades: about 3 round trips a month, and about +0.1% a month after costs.
• In XAUT's 17 months, when gold rose about 27% (from about 3,280 to 4,160 dollars), 12% ran out in 35% of months.
• A 3% grid trades 9 times as often, but runs out in nearly 9 months of 10.

Credits

• Antti Petajisto, "Inefficiencies in the Pricing of Exchange-Traded Funds", Financial Analysts Journal, 2017: judging a tracker by its premium and its tracking.
• G. E. Uhlenbeck and L. S. Ornstein, "On the Theory of the Brownian Motion", Physical Review, 1930: the pull back to normal behind the half-life.
• Dimitris N. Politis and Joseph P. Romano, "The Stationary Bootstrap", Journal of the American Statistical Association, 1994: the bands.
• Paxos (PAXG) and TG Commodities, Tether's gold company (XAUT): what each token is backed by, by their own documents.
• Our own: the comparisons, the grid test and the range table.
• Data: Bybit's public market data; Binance's public archive; Hyperliquid's public data; Yahoo's public gold futures prices, as the reference only.
• PerpGremlin and Claude, Gold on crypto exchanges: how close, and does a grid suit it?, TerminalGremlin, 2026: the tests, the code and the words.