What each hedge size actually buys you
Portfolio volatility for a hedge of size k, where k is the short notional as a fraction of the bag: σ² = σa² + k²σb² − 2kρσaσb. The minimum sits exactly at k = β, and both under- and over-hedging cost you.
| Hedge | Short notional | Resulting vol | Risk cut | Carry over period |
|---|
Where this sits next to the other hedging tools
This calculator answers how big the short should be. Once you have the notional, the hedge calculator takes it and plays the position out across price moves, and the funding rate calculator prices the carry in more detail. If you are estimating the volatility and correlation inputs rather than reading them off a terminal, derive them from real candles with the historical volatility calculator and the correlation calculator — a hedge ratio is only as good as the two numbers underneath it.
The hedge that leaves you long
The standard move when a portfolio of altcoins starts to feel heavy is to short an equal dollar amount of bitcoin perpetuals and call the position flat. It is not flat. A basket of mid-cap alts routinely carries somewhere between 1.3 and 2 times bitcoin's volatility, which means that when bitcoin falls 10%, the bag falls 13% to 20% — and a dollar-for-dollar short only ever returns the 10%. The correct size is the minimum-variance hedge ratio, which finance has known as beta for a century: the correlation between the two assets multiplied by the ratio of their volatilities. At a correlation of 0.82, a 90% volatility bag against 55% volatility bitcoin gives a beta of 1.34, and a $100,000 portfolio needs roughly $134,000 of short notional to be genuinely neutral. Everybody who shorted $100,000 instead has spent real funding to remain, on net, a third long into a drawdown they were trying to sit out.
The mirror-image error is more expensive and less discussed. Hedge a bag of large-cap majors — beta well below one — with a 1:1 short and you are no longer hedged, you are net short the market with someone else's money at risk. The table above makes the shape of this visible: portfolio volatility as a function of hedge size is a parabola, minimised exactly at beta, and rising on both sides. Overshooting beta by 50% costs you almost as much variance as not hedging at all. There is no zone where "more hedge" keeps helping, which is the single most counterintuitive thing about sizing one.
Then there is the part no ratio can fix. Correlation of 0.82 sounds like most of the risk is bitcoin's, but variance scales with the square: 0.82² = 0.67, so bitcoin explains two thirds of your bag's movement and one third belongs to the coins themselves — unlocks, listings, a protocol exploit, a sector rotating out. Even at the perfect hedge ratio the residual volatility is σa√(1−ρ²), which at these inputs is still 57% annualised on a bag that started at 90%. A hedge is a reduction, never a removal, and the more idiosyncratic your holdings the less of it you get. Set against that the running cost — funding on the full beta-weighted notional every eight hours, which is more than 100% of the portfolio value, plus the round trip — and the honest test is simple: if the expected carry over your holding period is larger than the drawdown you fear, selling some of the bag is the cheaper hedge, and this calculator gives you both numbers side by side to make that call.