The Cross-Hedge Lab

Describe your exposure

Asset you need to hedge Hedge instrument (what actually trades)

Exposure quantity (units of the asset) Position

Hedge contract size (units per contract) Units must match between price columns and contract size

! A regression only gives the right hedge ratio when both price series are in the same unit. Mixing $/gallon against $/barrel silently scales your hedge ratio by the conversion factor — divide one series first if your two assets are quoted in different units. The contract size for the loaded Reliance sample (500) is backed out from your own file's turnover ÷ number of contracts ÷ price — NSE revises futures lot sizes periodically, so re-check it on nseindia.com before using this for a live hedge rather than a class exercise.

Upload price history

A CSV with a date column and one price column per asset — monthly, weekly or daily levels all work. Or start from the illustrative sample already loaded below.

Drop a CSV here, or click to choose a file

Columns: date, spot price, futures price — any header names, any order.

Using: real NSE data — Reliance Industries spot vs. its near-month futures, 29 Jun–25 Aug 2026 (42 trading days, supplied by the instructor from an NSE download).

Date column

Spot price column (asset to hedge)

Futures price column (hedge instrument)

! Direct hedge vs. cross-hedge. Reliance spot vs. Reliance futures is a direct hedge — the same asset against its own futures, so β sits near 1, R² is high, and basis risk is small. Reliance spot vs. Brent crude is a cross-hedge candidate — different asset classes, and the real 2026 data shows why you always check R² before trusting a hedge ratio: correlation comes out weak (R² ≈ 9%), meaning crude alone is a poor proxy for Reliance's price risk over this window. That sample also mixes ₹ and $ without conversion — a second, separate problem from the weak correlation, and worth having students untangle which is which.

Current hedge ratio — rolling

The number to actually trade on: β re-estimated on only the most recent window of data, the same way the backtest below re-estimates it at every step. This is the one figure to quote in class or in a workbook — never the full-sample average further down, which blends regimes that may no longer apply.

Trailing window (most recent periods)

Current hedge ratio (rolling β) — contracts of hedge instrument per unit of exposure

Correlation ρ (same window) — strength of the relationship

Fit in this window (R²) — share of price-change variance explained

Contracts to trade now (N*) — —

Window used — —

Full-sample regression — diagnostic only

Fitted across every period uploaded. Useful for reading the overall relationship and drawing the scatter below — not the number to size a live hedge with, since it averages across whatever regimes the data happened to contain.

Full-sample β —

Full-sample ρ —

Full-sample R² —

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Price-change relationship — full sample

Every point is one period's change. Gold points fall inside the current rolling window above; the line is the full-sample fit.

Current rolling window Earlier periods Full-sample fit line

Out-of-sample backtest: hedged vs. unhedged

The hedge ratio is re-estimated on the trailing window set in Step 3 and applied only to the next period — no lookahead. A negative number below means the hedge added risk instead of removing it, which can genuinely happen with a weak or unstable proxy — it isn't a display error.

variance reduction —

Unhedged cumulative P&L Hedged cumulative P&L

Beyond the static hedge

Three ways to turn the hedge ratio into an algorithm

Build a hedge gives you one hedge ratio at one point in time. An algo decides, period after period, whether to re-estimate it, how far to trust it, and — in one variant — whether to trade the gap it leaves behind. All three strategies share the same rolling-regression engine from the Build tab; they differ only in the decision rule layered on top.

Runs on whatever dataset and exposure are set in Build a hedge — load the sample above (it also resets Step 1's exposure to a 20,000,000-gallon short/consumer position and contract size to 42,000 gallons, 1,000 bbl), or configure your own there first. Currently loaded: —

Pick a strategy

How it works

iIn plain terms: think of this like getting your car's wheel alignment checked. You take it in on a fixed schedule (the Clock) — but you also go in early if the car visibly starts pulling to one side (Drift). Either is reason enough to recheck early; neither means you're betting on which way the market will move — you're only resizing the hedge. (The volatility-spike check below is Strategy 3's extra trigger, not this one — see that tab.)

The engine re-estimates β on the rolling window every single period, but it only applies the fresh number — actually resizes the hedge — when one of two triggers fires:

ClockPeriods since the last rebalance reach the check frequency set below (e.g. every 5 periods) — the baseline, time-based trigger. No calculation, just a countdown.

DriftWhat it means: how far today's freshly re-calculated hedge ratio has moved away from the one you're currently using, as a % change. Worked example: you're currently hedged at β=0.80; today's fresh number comes out to 0.92. That's (0.92−0.80)/0.80 ≈ 15% drift. If the drift threshold below is 10%, 15% crosses it — rebalance now, don't wait for the clock.

Whichever trigger fires, the fresh β is applied as-is — no blending (that's Strategy 3). This strategy never takes a view on direction; it only ever asks whether the hedge is still the right size. The volatility-spike trigger is Strategy 3's addition on top of this same clock-and-drift logic — it doesn't apply here.

!What to watch below: compare Variance reduction to a static hedge's — rebalancing only helps if it earns back its own transaction cost. The Note column in the signal log names which trigger fired each time.

How it works

iIn plain terms: picture the basis (how far the real relationship has strayed from what the regression predicts) as a rubber band. Stretch it too far and it usually snaps back — so this overlay bets on the snap-back: it enters when the band looks unusually stretched (Enter), takes the win once it snaps back to normal (Exit), and lets go rather than keep betting if it just keeps stretching instead (Stop). This is the one strategy here taking a directional bet — everything else is pure insurance.

Underneath, Strategy 1's hedge still runs unchanged. On top of it, this overlay z-scores the basis — the hedge residual, i.e. how far the actual relationship sits from what the rolling regression predicts this period — against its own recent mean and standard deviation, and trades the gap as a separate, small position:

|z|, the z‑scoreWhat it means: how unusual today's basis is, measured in "how many of its own typical day-to-day wiggles away from its recent average." Worked example: if the basis normally wiggles by about ₹2 (that's its standard deviation) and today it sits ₹3 away from its own recent average, |z| = 3/2 = 1.5. The thresholds below are just cutoffs on this number.

Enter|z| moves past the entry threshold (e.g. 1.5, from the example above) — the basis looks unusually stretched, so a small position (the overlay % of exposure set below) opens betting it reverts.

Exit|z| falls back below the exit threshold — the basis has reverted as expected; the position closes at a gain.

Stop|z| instead moves past the stop threshold — the bet was wrong; the position closes at a loss rather than risking more.

At most one overlay position is open at a time. This is the one strategy here making an active call on where prices go next — everything else on this page is pure risk management.

!What to watch below: Overlay P&L (alpha) is this bet's standalone result — read it separately from the hedge's own performance, never as proof the hedge worked. Scan the log's Note column for "overlay OPEN" / "overlay CLOSE" rows to see individual trades.

How it works

iIn plain terms: think of R² as a GPS signal-strength bar for the hedge — it just tells you how well "futures price" is currently explaining "spot price" (closer to 1 = explains it well, closer to 0 = barely explains it at all). Full signal (Full) and you follow the fitted β turn-by-turn. Signal's patchy (Medium) and you blend it with your general sense of the route (the long-run average). Signal's gone (Low) and you mostly fall back on the long-run average, because trusting this period's number alone would be like trusting a GPS with no bars.

Same rebalancing clock as Strategy 1 (plus the volatility override), but it adds one more question before applying a fresh β: how well is the proxy working right now? That's read off the rolling regression's own R², sorting every period into one of three confidence bands:

R², "R‑squared"What it means: a score from 0 to 1 for how much of the stock's recent price movement lines up with the futures' movement. Worked example: R²=0.6 means about 60% of the stock's recent moves are explained by the futures' moves — the other 40% is noise this hedge can't capture. Closer to 1 = tight fit; closer to 0 = barely related right now.

FullR² ≥ the high threshold (e.g. ≥0.6) — apply β as estimated. Identical to Strategy 1 in this period.

MediumBetween the two thresholds — blend β with its own expanding long-run average (the plain running average of every β ever estimated since the start, not just the recent window), at the moderate weight below.

LowR² below the low threshold (e.g. <0.3) — blend heavily toward that long-run average instead — a smaller, steadier bet on a relationship the data says is currently unreliable.

On a strong, stable proxy this strategy will often look identical to Strategy 1 — there's nothing to shrink away from. That's expected, not a bug: load a weaker cross-hedge pair in Build a hedge and switch back here to see the two strategies actually diverge.

!What to watch below: Time in full-confidence regime vs. low-confidence regime tells you how often this strategy actually differs from Strategy 1 on your loaded data. The chart above lets you compare the two runs directly — switch strategies without reloading data.

Strategy settings

Shared — every strategy's rebalancing clock

Rolling estimation window (periods) Rebalance check every N periods

Also rebalance early if hedge ratio drifts more than Transaction cost per contract (same currency as exposure)

Results

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Cumulative P&L: unhedged vs. static hedge vs. strategy

Static hedge sets the ratio once, at the end of the first window, and never touches it again — the baseline every rebalancing rule has to beat net of its own transaction costs.

Unhedged Static hedge (set once) Strategy

Signal / rebalance log

Every period the strategy acted — rebalanced the hedge, opened or closed an overlay, or (strategy 3) switched regime. Most recent first, capped at 60 rows.

In practice

What a "Contracts" number above would mean as a real order

Everything on this page is a paper backtest — it never touches a real market. Worth walking through what the gap between this model and an actual trade looks like, before anyone mistakes the log above for a trading signal.

iIn plain terms: this tool outputs a number of contracts the same way a recipe outputs grams of flour — it tells you the right quantity. It says nothing about the five real-world steps between that number and an actual position: which contract, how big a lot is, how much cash you need to put down upfront, how you'd actually place the order, and why the price you'd really get is never quite the clean closing price used here.

MarketA number in the log's "Contracts" column means a position on NSE's F&O segment (its futures & options market, separate from the cash/equity market where you'd simply buy the shares), in whichever single contract this tool is configured for. The near-month contract (the one nearest to expiry) is the market convention and what this tool assumes, but liquidity sometimes sits in a further-out contract instead; a real hedger checks volume and open interest before picking which one to trade, not just time-to-expiry.

Lot sizeFutures aren't traded one share at a time — they come in a fixed bundle size (the "lot") set by the exchange, not chosen by the trader. The contract size set in Build a hedge, Step 1 is that lot — it's why N* gets rounded to a whole number of contracts rather than the exact hedge ratio.

MarginA futures position isn't paid for upfront like a share purchase — you put down a deposit instead. That deposit is the SPAN margin (the exchange's own estimate of the position's one-day worst-case loss) plus a smaller exposure margin on top as a buffer. The position is then marked to market daily — meaning gains and losses are settled into or out of your account every single day it's held, not just when you close it. Nothing on this page models that day-to-day cash flow.

ExecutionAn order doesn't place itself because a spreadsheet says 503 contracts. In practice it's entered on a broker's trading terminal, as a limit or market order against that contract's live order book, during market hours — and a large order can itself move the price before it's fully filled.

TimingThis backtest rebalances at each period's closing price with no slippage and a flat cost per contract. A real fill happens at whatever price is live the moment the order reaches the exchange — routinely worse than the model's clean closing-price number, especially for a large position or a volatile instrument.

!This is market-mechanics education, not trading instructions. Nothing on this page is a recommendation to open any position, and the figures above assume frictionless, idealized execution that a real account will never quite get. Treat every "Contracts" number here as a teaching device for sizing a hedge, not as an order ready to place.

Concept explainer

Why you sometimes have to hedge with the wrong asset

Most exposures a firm actually carries — jet fuel, a regional crude grade, a basket of inputs — don't have a liquid futures market of their own. Cross-hedging is what you do instead: hedge the exposure you have with the closest instrument that actually trades.

The problem

A consumer or producer has a real exposure to an asset's price. If that asset trades on an exchange, hedging is direct: take the opposite futures position, one-for-one. If it doesn't — no market, or a market too thin to move real size through — you need a proxy: a correlated, liquid instrument that moves with your exposure most of the time.

The catch

A proxy is never a perfect substitute. The two prices can drift apart — this is basis risk. Cross-hedging doesn't eliminate risk; it trades price risk on an untradeable asset for a smaller, more measurable risk: the gap between the proxy and the real exposure.

Finding the right hedge ratio

You don't hedge one-for-one with a proxy — you hedge in the ratio that has historically minimized the variance of your combined position. That ratio, h*, is:

h* = ρ · (σ_S / σ_F) correlation × (volatility of the asset to hedge ÷ volatility of the hedge instrument)

ρCorrelation between period-to-period price changes in the asset to hedge and the hedge instrument.

σ_SStandard deviation of the asset-to-hedge's price changes.

σ_FStandard deviation of the hedge instrument's price changes.

This is algebraically identical to the slope β of a simple regression of the asset's price changes on the hedge instrument's price changes — which is how this tool actually computes it. Regress instead of computing ρ, σ_S, σ_F separately and you get the same number with one calculation.

Sizing the position

Once you have h*, convert it into an actual number of futures contracts:

N* = − Q_A × h* ÷ contract size Q₀ is the exposure, signed: negative for a short/consumer exposure, positive for a long/producer exposure

Hedger's rule. A short/consumer exposure (you will need to buy the asset later) is hedged by going long futures. A long/producer exposure (you will need to sell later) is hedged by going short futures. The payoff on the futures leg offsets the payoff on the underlying exposure either way.

Basis risk: direct hedge vs. cross-hedge

Basis risk is whatever risk survives after you've applied the optimal hedge ratio — R² (hedge effectiveness) is a direct read on how much of it is left. It shows up very differently depending on what you're hedging with, which the two real samples loaded in the Build tab make concrete:

Direct hedge — Reliance spot vs. its own futures R² ≈ 94% Basis risk is small and structural: the only reason spot and futures ever diverge is cost-of-carry mechanics (interest, dividends, time to expiry), and that gap is forced to zero at expiry by arbitrage. ~6% of the risk survives the hedge.

Cross-hedge — Reliance spot vs. Brent crude R² ≈ 9% Basis risk is large because they're not the same asset: Reliance's price moves on refining margins, retail, Jio and market sentiment that crude prices never see. Even the best-fitting β only captures the ~9% of Reliance's risk that happens to move with crude — the other ~91% survives the hedge regardless of sizing.

The general rule: basis risk isn't something a better hedge ratio fixes — h* is already the best available ratio. Basis risk is a ceiling set by how strong the relationship is in the first place. A direct hedge starts with a low ceiling almost by construction; a cross-hedge's ceiling depends entirely on the economics linking the two assets, which is exactly why R² is worth checking before trusting one.

Why hedge ratios drift

Correlation between an asset and its proxy is not constant — supply shocks, storage bottlenecks and demand shifts can decouple them for months or years at a time. Split your history into a high-correlation and a low-correlation stretch and re-run the regression on each; a hedge ratio that moves a lot between the two is telling you the relationship itself is unstable, and that basis risk is larger than a single full-sample number would suggest.

Why backtest out-of-sample

Fitting β on the whole sample and then testing the hedge on that same sample flatters the result — you're using information you wouldn't have had in real time. A proper backtest re-estimates β on a trailing window and applies it only to the period right after that window, then rolls forward. What's left is a fair read on how much variance the hedge would actually have removed.

Worked mini example

This is a classic textbook illustration, kept because the numbers are clean enough to follow by hand — it isn't one of the loadable samples in the Build tab. For a worked example using the real data this tool ships with, see the R² ≈ 94% vs. R² ≈ 9% comparison above.

An airline has a short exposure of 20,000,000 gallons of jet fuel — it will need to buy fuel over the coming months and loses if the price rises.
Jet fuel isn't liquidly traded, but WTI crude futures are. Regressing monthly jet fuel price changes ($/gallon) on monthly WTI price changes ($/gallon-equivalent) over the last few years gives β ≈ 1.02, R² ≈ 0.85.
Contract size for the WTI proxy is 42,000 gallons (1,000 barrels). N* = −(−20,000,000) × 1.02 ÷ 42,000 ≈ 486 contracts, long.
Because the exposure is short (needs to buy), the hedger's rule says go long futures — buying 486 WTI contracts now locks in most of the airline's fuel-cost risk, leaving only the basis risk between jet fuel and WTI.

Quick glossary

Basis risk: The risk that the proxy and the real exposure don't move together exactly, so the hedge is imperfect even after sizing it correctly.
Minimum-variance hedge ratio: The hedge ratio that minimizes the variance of the combined (exposure + hedge) position, given historical price behavior.
Hedge effectiveness (R²): The share of the asset's price-change variance that the hedge instrument's price changes explain — a rough read on how much risk the hedge actually removes.
Walk-forward backtest: A backtest that only ever uses data from before the period being tested, avoiding lookahead bias.