The second way a Sharpe lies: a carry book with a Sharpe of 42.7
Stale closes inflate a Sharpe by shrinking measured volatility. A hedged carry book does the same thing for a different reason: measure only the coupon and you divide by 0.1%/yr, which is smoothness rather than risk. My first run returned +42.7 and −421. Adding the one missing return term tripled the denominator and moved BTC from −8.24 to −2.86 — and then the standard error, governed by the annualisation factor rather than the observation count, swallowed what was left.
A known failure, and its cousin
A Sharpe ratio inflates whenever the denominator understates risk. The familiar version is stale pricing: coarsen your bars, measure volatility off closes that have not moved, and a mediocre strategy acquires a Sharpe of 3 without anything real changing.
This is a different route to the same place, and it is specific to hedged carry. It produced a Sharpe of 42.7 in my first run, which is the kind of number that should stop you rather than please you.
What goes in the denominator
A delta-neutral funding carry book is long spot, short the perpetual, and collects a funding payment every eight hours. The obvious return stream is the funding payment. So:
pair window ret %/yr vol %/yr Sharpe
hyperliquid/HYPE OOS 8.95 0.12 42.70
hyperliquid/HYPE full window 9.60 0.24 23.76
binance/BTC OOS 2.71 0.16 -8.24
basket, $10M OOS 0.62 0.01 -421.27Look at the volatility column. 0.12%/yr. That is not the risk of a leveraged crypto position; it is the smoothness of a coupon. Funding rates are small, bounded by a venue cap, and heavily autocorrelated — so a series of funding payments has almost no dispersion, and dividing an excess return by it produces numbers in the hundreds in both directions.
The error is conceptual, not arithmetic. The funding payment is not the book’s return. A hedged position is long spot and short perp, so its equity change per period is:
R = funding − Δ(basis) × notionalYou earn the coupon and you mark the convergence. Measuring only the first term discards where the variance actually lives.
Adding the missing term
Recovering the basis was awkward in a way worth mentioning: my derived store kept mark_price but not index_price, so the basis was not reconstructible downstream. The raw venue objects carry both on the same rows. One backfill later:
binance/BTC, full window
income only funding − Δbasis
annual volatility 0.15% 0.47%
Sharpe -0.94 -0.27
binance/BTC, out of sample
Sharpe -8.24 -2.86One missing term, a three-fold change in the denominator. A second effect fell out that I had not anticipated: lag-1 autocorrelation flipped from +0.73 to −0.33. The funding coupon is persistent; the basis mean-reverts, and including it turns a strongly positively autocorrelated series into a mildly negative one. That raises the effective sample size and tightens every standard error below.
The third lie: the risk-free rate
With volatility this small the Sharpe becomes hypersensitive to a number nobody prints. Holding the measured return fixed at 3.87%/yr and varying only the assumed cash rate:
rf assumption Sharpe
4.0% -0.27
3.5% +0.79
2.0% +3.98
0.0% +8.23The same returns give −0.27 or +8.23 depending on one assumption. A published carry Sharpe without its rf stated is not a number you can use. And it explains how a positive return produces a negative Sharpe: BTC carry returned 3.87% against 4.00% cash, so the excess return is −13 bps. Positive return, negative excess return, negative Sharpe.
And then the standard error eats it anyway
Having fixed the denominator, the point estimate turns out not to be worth much either. Following Lo (2002), the standard error of a Sharpe measured over n periods and annualised by q is dominated by:
SE(SR_annual) ≈ √(q / n)My out-of-sample window is 438 eight-hour periods, which sounds ample. It is 146 days. √(1095/438) = 1.58.
The uncertainty is governed by the ratio of the annualisation factor to the sample size, not by the raw observation count. Sampling more finely within a short window does not help — it raises n and q together. A short window cannot produce a precise annual Sharpe, however much data it contains.
Which leaves, for the full 417-day window:
ret %/yr vol %/yr Sharpe SE 95% CI
perp binance/BTC 3.87 0.47 -0.27 0.66 [-1.57, 1.03]
perp binance/ETH 3.02 0.60 -1.63 0.62 [-2.85,-0.42]
dated BTC 4.30 1.74 +0.17 0.86 [-1.52, 1.86]
dated ETH 4.02 1.85 +0.01 0.89 [-1.74, 1.76]Three of four are not distinguishable from zero. The honest range across optimistic and pessimistic sub-windows is roughly −3 to +1, with a standard error of 0.6 to 1.3 that swamps the point estimate.
What this lets you do to other people’s numbers
Published Sharpes for funding-rate arbitrage include 3.53 for BTC at zero fees, 1.80 under retail costs — and, on two venues, 23.55 and 6.50.
The first two are defensible and reconcile with mine once you account for regime: that work attributes 8.64%/yr of BTC return to price convergence against 5.06%/yr from funding, a ~13.7%/yr total against my 3.87%, and the same literature documents the spread compressing ~11% a year. Richer era, bigger number, different `rf`.
The 23.55 sits precisely in the range my broken income-only computation produced, and so does anything else in that neighbourhood. Treat a carry Sharpe above roughly 10 as having an income-only denominator until the return stream is shown. It is a cheap and reliable filter.
The caveat that outranks all of it
Even the corrected Sharpe is an upper bound. The volatility of funding − Δbasis still excludes liquidation of the short leg when collateral is not unified — a liquidity event that never appears in a delta calculation — along with execution variance, forced exits, and counterparty failure. One of the trading firms whose desks serve this market cleared $61bn of volume in 2025 and filed Chapter 11 in March 2026.
A carry book with a high Sharpe and a fat left tail is the classic picking-up-pennies profile, and the Sharpe is the statistic least equipped to say so. Fixing the denominator makes it honest. It does not make it sufficient.
The one-line version
If a hedged carry strategy reports a Sharpe in the double digits, the most likely explanation is that somebody measured the coupon and called it the return. Add the mark-to-market term, state your risk-free rate, and put a standard error on it — and the number will usually turn out to be indistinguishable from zero.