The Lab

Where the idea comes from

• Gold as a shelter. Dirk Baur and Brian Lucey (2010) split the idea in two:
  • a hedge moves unlike the rest of your money on average;
  • a safe haven holds up, or rises, in a crash.
  • We ask the same of gold and stock funds beside crypto.
• Mixing to cut the swings is Harry Markowitz's portfolio idea (1952): two things that don't move together swing less as a pair than alone.
• A trap: in a crash, almost everything moves together for a while. Kristin Forbes and Roberto Rigobon (2002) showed that measuring correlation in turmoil overstates it. So for crashes we read what the assets did, not their correlation.
• The costs of a token against the real thing come from our parts 1 and 2: "Stock perps while the stock market is shut" and "Gold on crypto exchanges".

How we tested

• The assets:
  • gold as the PAXG token (Binance), from September 2020;
  • the S&P 500 fund (SPY) and the Nasdaq-100 fund (QQQ), the real funds from Yahoo, the reference only;
  • Bitcoin and Ether on Binance.
• The window: September 2020 to September 2026, 73 months, split in halves of 36 and 37 months.
• The crypto book: half Bitcoin, half Ether, set back to half and half at each month's start, paying 0.1% on what is traded.
• The mix: the same, with 10, 20 or 30% moved into gold or a fund.
  • The funds are charged the stock perps' funding (8.2% a year, from part 1), as a perp holder would pay it.
• The bar, fixed before the run:
  • pick the share with the best Sharpe ratio in the first half;
  • in the second half, the mix's worst fall must be smaller, with the band of the difference above zero;
  • and its Sharpe ratio must be no worse.

The maths, step by step

1. The worst fall. The deepest drop from a high. A book at 100 that rises to 150 and then falls to 60 has a worst fall of 1 − 60 ÷ 150 = 60%.

2. Why a mix falls less. Two assets, each with a yearly swing σ, and a correlation ρ between them. Half and half swings by

σ × √((1 + ρ) ÷ 2).

• With ρ = 1 (they move together), it swings by the full σ.
• With ρ = 0.15, it swings by σ × √0.575 = 0.76 σ: a quarter less.

3. The Sharpe ratio. The average daily return over its spread, times √365: the return for each unit of swing.

What we found

1. What a token costs and gives, against the real thing.

• Tokenised stocks held as tokens (xStocks on Bybit) tracked their stocks within 3.0% to 6.2% a year, from about July 2025. On average they sat 0.0% to 0.17% over the stock's close.
• Their issuer's own page says xStocks are not available to residents of the US, the UK, Canada or Australia.
• PAXG's issuer (Paxos) says it charges no storage fee, and PAXG can be redeemed for gold bars or for dollars at the gold price. XAUT's terms page could not be read without a browser, so it isn't quoted.

2. What a market order costs, beyond the middle price. Bybit's public order books, 10 readings 30 seconds apart, the middle of them:

• The perps are cheap to trade, like the big coins.
• The tokenised stocks held as tokens are thin. A 100,000 USDT order in TSLAX cost about 0.47%. In AAPLX, one side of the book didn't hold 100,000 at all.

3. Beside the crypto majors, September 2020 to September 2026.

• Gold barely moved with Bitcoin (0.15). The stock funds moved with it more (0.36–0.37).
• The correlation drifts: gold's ran from −0.43 to +0.65 over 90-day stretches, the funds' from about −0.05 to +0.65.

4. On Bitcoin's worst days, all three fell, but far less. Bitcoin's worst 5% of days, against the rest:

• None was a safe haven in Baur and Lucey's sense: none rose when Bitcoin fell hard.
• Gold came closest, with a small fall. In Bitcoin's worst weeks gold fell 1.0%, against +0.3% in other weeks. The band of that difference (−2.9% to +0.3%) reaches above zero, so over weeks a fall isn't shown.

5. Moving 30% of a crypto book into gold or a fund cut its worst fall.

The second half, September 2023 to September 2026.

• All three passed the bar. The fall saved: gold 15 points (band 8 to 24), the S&P 500 fund 15 points (8 to 17), the Nasdaq-100 fund 16 points (7 to 17).
• Gold also raised the Sharpe ratio clearly (by 0.27, band 0.09 to 0.45). The funds' gain (0.11 and 0.14) has a band that reaches just under zero: "no worse", not "better".
• 30% was the largest share tried, and it won the first half for all three. A larger share might have done better still; it wasn't tested.

What it means

• Gold, beside a crypto book, September 2020 to September 2026:
  • it moved little with Bitcoin (correlation 0.15);
  • it fell least of the three on Bitcoin's worst days (−0.28% on average);
  • a book with 30% in it had a smaller second-half worst fall than half Bitcoin and half Ether (45% against 60%), and a higher Sharpe ratio (0.81 against 0.54).
• The stock funds also gave a smaller second-half worst fall (45% and 44%). They moved more with crypto (0.36 and 0.37) and fell about 1% on Bitcoin's worst days. Their Sharpe gain was not shown beyond its band.
• The cost of the form: a perp long paid about 3–13% a year in funding, which holding the token, or the real fund, did not. That was about as much as gold or the S&P 500 fund returned in a year in this window. The real funds also paid dividends (1.40% and 0.58% a year) that a perp does not.
• Tokenised stocks held as tokens tracked their stocks within 3–6% a year. Their books were thin: 0.47% to buy or sell 100,000 USDT of TSLAX. Their issuer does not offer them in the US, the UK, Canada or Australia.
• All of this is one six-year window in which gold, stocks and crypto all rose. A window where they fall together could show less.

Credits

• Dirk G. Baur and Brian M. Lucey, "Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds and Gold", The Financial Review, 2010.
• Kristin J. Forbes and Roberto Rigobon, "No Contagion, Only Interdependence: Measuring Stock Market Comovements", Journal of Finance, 2002.
• Harry Markowitz, "Portfolio Selection", Journal of Finance, 1952.
• William F. Sharpe, "Mutual Fund Performance", Journal of Business, 1966: the Sharpe ratio.
• Dimitris N. Politis and Joseph P. Romano, "The Stationary Bootstrap", Journal of the American Statistical Association, 1994: the bands.
• Paxos (PAXG) and xStocks: their own published terms, as quoted.
• Our own: the costs side by side, the sell-off reading and the mix test.
• Data: Binance's public archive; Bybit's public market data; Yahoo's public fund and gold prices, as the reference only; our parts 1 and 2.
• PerpGremlin and Claude, Tokenised gold and stocks: are they worth it?, TerminalGremlin, 2026: the tests, the code and the words.