Perps Discovery
[ 01 ] Safe leverage

How Much Leverage Can Your Perp Survive?

A perp lets you pick any leverage. The options market already prices how far each asset is likely to move.

We turn that implied vol into the most leverage you can hold — for an hour or for two years — and still have a 68%, 95% or 99.7% chance of never being wiped out.

Safe leverage for one asset

Asset
Confidence
Side
Funding

waiting for the engine

The line is the most leverage that survives the chosen move for that long; anything under it is safer, anything over it is wiped out more often than the band says. Hover or tab into the chart to read any holding period. The hatched stretch is past the last expiry in the chain the engine sent for this asset, so no vol is quoted there: the last expiry's is held flat and the lines go dashed. With funding on, the funding you pay comes out of your margin as you hold and the funding you receive goes into it; the dotted line is the same band without funding.

[ 02 ] Method

How the Chart Is Calculated.

Four steps, from each asset's options chain to the line on its chart. Nothing is fitted or tuned: the only input is the vol the market is quoting right now.

  1. Vol over the hold

    The engine sends each asset's at-the-money implied vol at every listed expiry. We read the vol for your holding period off that curve, interpolating in total variance (σ²T) between the two expiries either side — the rule the engine uses for its 30-day vol. Shorter than the first expiry we use the first one's vol; longer than the last we hold the last one's flat, and hatch that stretch of the chart.

    σ(T) from the ATM term structure
  2. The move

    Over T days the price moves about σ√(T/365) — one standard deviation. The band you pick multiplies it: 1σ, 2σ or 3σ.

    m = z · σ(T) · √(T / 365)
  3. The wipe-out line

    At L× a perp loses its whole margin when the price moves 1/L against it. Safe leverage is the largest L whose wipe-out price sits a full move m away.

    long L = 1 / (1 − e−m)
    short L = 1 / (em − 1)
  4. The odds

    A liquidation only has to touch the price once, at any moment of the hold. For a random walk that is twice as likely as ending beyond it, so surviving a z-sigma line is 2Φ(z) − 1.

    1σ 68.3% · 2σ 95.4% · 3σ 99.7%
  5. Funding, if ticked

    Funding is charged on the notional every 8 hours, so the wipe-out price moves as you hold: toward you if you pay, away if you receive. We solve for the leverage that still survives with the band's chance against that moving price, checked against a simulation to within 2.6 points.

    long b(t) = 1 − 1/L + f·t
    short b(t) = 1 + 1/L + f·t
What it leaves out
  • Fees, and funding that moves. Trading fees are not counted. Funding is, when you tick it, but at one steady rate you choose — real funding resets every 8 hours and can flip sign, so a short that counts on receiving it can end up paying.
  • Maintenance margin. An exchange liquidates a little before the margin is gone, so its liquidation price sits nearer than the wipe-out price drawn here.
  • Fat tails and gaps. Implied vol is the market's forecast, and real markets move 3σ far more often than a normal curve says — most of all over a weekend or an earnings print.
  • Drift and the far term. The walk is assumed to have no trend in log price: the median price stays where it is. Over days that choice barely matters. Over a year or two it does — assume instead that the average price stays put, and at 60% vol over two years a 1σ long survives about 54% of the time rather than 68%, a short about 80%. Past the last listed expiry the vol itself is an assumption too.