Leverage cannot beat the funding rate: why the whole range is worth exactly 2x

The intuition, and why it misleads

A delta-neutral carry book is long spot and short the perpetual. The spot leg costs its full notional in cash. The perpetual leg costs only margin. So if you raise the leverage on the perpetual, you free up capital, buy more spot, and earn more funding.

That is all true, and it is not leverage. It has a hard ceiling that arrives faster than people expect, and the arithmetic is four lines.

The arithmetic

capital    C = S + M            S = spot notional, M = perp margin
leverage   L = S / M       →   M = S/L
           C = S(1 + 1/L)  →   S = C · L/(L+1)

RoC        = f · S/C = f · L/(L+1)       f = funding rate on notional

Leverage sets what fraction of your capital is earning rather than sitting as margin. That is the whole of its effect. It is not levering the carry; it is reclaiming idle collateral.

At f = 3.86%/yr, the measured BTC funding rate over my study window:

leverage   S/C     RoC %/yr   vs 1x      step    liquidating move
    1x     0.500      1.93      1.00x       —          ~100%
    2x     0.667      2.57      1.33x     x1.333          ~50%
    3x     0.750      2.90      1.50x     x1.125          ~33%
    5x     0.833      3.22      1.67x     x1.111          ~20%
   10x     0.909      3.51      1.82x     x1.091          ~10%
   20x     0.952      3.68      1.90x     x1.048           ~5%
 infinite   1.000      3.86      2.00x       —             0%

Two columns, two different quantities, and conflating them is the trap. The step column chains multiplicatively: 3× earns 1.333 × 1.125 = 1.50× what 1× earns, not 1.33 + 0.125.

S/C runs from 0.5 to 1.0, so the entire range of leverage is worth exactly 2× and not one basis point more. Infinite leverage buys you double the 1× case. Meanwhile the adverse move that liquidates you falls from 100% to 5%.

Why the funding rate is a hard ceiling

The spot leg is bought with cash at 1:1, so total notional can never exceed capital however thin the perpetual margin becomes. To genuinely lever the carry you would have to lever the spot leg too — borrow to hold more coin than your cash supports:

RoC = f · (notional/C) − borrow_rate · (borrowed/C)

Crypto borrow rates sit well above a 2–4%/yr carry, so that trade is negative before it opens. The carry ceiling is the carry. Every financing structure available to you redistributes it; none manufactures more of it.

The measured curve is the formula

I swept leverage as a free parameter — never fitted — across a backtest with reconstructed order books, real fee schedules and venue margin ladders. At the $10M tier, out of sample:

leverage   measured RoC   predicted S/C   predicted ratio   measured
  1.0x          1.14%           0.50            1.00       1.00
  1.5x          1.69%           0.75            1.50       1.48
  2.0x          2.20%           0.99            1.98       1.93
  3.0x+         2.20%      saturated              —          —

Predicted 1 : 1.50 : 1.98 against measured 1 : 1.48 : 1.93 — inside 3%. And note where it saturates: 2×. Past that point the binding constraint stops being leverage and becomes the capital budget, because you cannot buy more spot than you have cash for. More leverage buys nothing once the margin requirement is already small relative to capital.

What you pay, and the asymmetry nobody prices

Liquidation on the short leg arrives at roughly a 1/L adverse move. Crypto moves 10% in a day routinely, which makes 10× a short fuse for a gain of 82% over the unlevered case.

With non-unified collateral the exposure is asymmetric in the worst direction. When price rallies, the spot leg gains and the perpetual leg loses — but the gain sits in a different account and cannot defend the margin call. You are liquidated on the short while holding a profitable spot position you cannot reach in time.

This is a liquidity risk, not a price risk, which is why it never appears in a delta calculation. The book is perfectly hedged and still dies. It is the same mechanism that destroys hedged locked-token positions.

So the return gain decays — +33%, +12.5%, +11%, +9%, +5% — while liquidation risk grows linearly in L. The risk-adjusted optimum is low, somewhere around 2× to 4×, and the measured curve saturating at 2× agrees with that from a completely different direction.

The lever that actually matters

Measured capital required per 1.0 of notional, from venue margin ladders:

unified margin     (both legs, one venue)     1.013
non-unified        (legs on two venues)       1.200

Splitting collateral across venues costs 18.4% of return on capital. That is more than going from 3× to 10× buys you — and it comes with no additional liquidation risk rather than a great deal of it.

If the spot can be made to collateralise the perpetual on a single venue, that is worth doing before leverage is touched at all. It is the only move in this structure that improves return and risk simultaneously.

The one-line version

Leverage in a spot-perp carry book is a plumbing optimisation, not a return multiplier. It is worth at most 2×, it is capped by the funding rate, it saturates around 2× in practice, and it is paid for with a liquidation threshold that shrinks as 1/L. It moves 1.93% to 3.86%. It does not move 2.90% to 8%, and no arrangement of margin will.