Hedge ratio calculator
With a correlation of 0.9, a spot volatility of 4 and a futures volatility of 5, the optimal hedge ratio is 0.72: short 0.72 futures units for each unit of spot you hold. Size an overlay for grain, crude, an index or rates. Free in your browser.
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Worked example
- Correlation
- 0.9
- Spot std
- 4
- Futures std
- 5
- Hedge ratio
- 0.72
The optimal futures hedge ratio is the textbook answer to how many futures contracts offset one unit of a cash position when residual variance matters more than a one-for-one notional match. Risk desks, CFA candidates, and grain or energy merchants search that phrase when they already have those three statistics from a return window and need the minimum-variance overlay, not a futures profit-and-loss blotter and not Hedges' g. This hedge ratio calculator accepts the three finite numbers, returns the ratio, and rejects a futures standard deviation of zero because that denominator is undefined.
How the optimal futures hedge ratio is computed from correlation and volatilities
The optimal futures hedge ratio of a cash position is the number of futures units that minimizes the variance of the combined spot-plus-futures book. Both standard deviations must be in the same unit — daily percent, weekly log return, or annualized — because only the ratio of the two volatilities enters the formula.
A correlation of zero point nine with a spot standard deviation of four and a futures standard deviation of five yields zero point seven two: you short zero point seven two futures units for each unit of long spot. When the two series move in lockstep with correlation one and share the same volatility, the ratio is one. When futures are twice as noisy as spot you need only half a futures unit per cash unit.
A negative correlation flips the sign of the overlay, which means the hedge is a long futures position rather than a short. Zero spot volatility produces a hedge ratio of zero, which is honest: a cash book that does not move does not need an overlay. Zero futures volatility is not honest and is rejected, because dividing by a frozen futures series does not define a minimum-variance hedge.
You supply the three statistics; the calculator multiplies them and rounds the hedge ratio half-up so goldens compare byte-for-byte across runtimes. This is a hedge ratio from three published return statistics, not a closed-trade cash result, not an effect size, and not a weighted-average cost of capital.
Where a hedge ratio calculator earns its keep
Risk managers use a hedge ratio calculator to turn last month's estimated correlation and the two return volatilities into one overlay before they send a futures ticket against a cash book of grain, crude, equity index, or rates. CFA candidates and derivatives courses search the same phrase when an item set asks for the minimum-variance hedge ratio from correlation and the two standard deviations rather than for the profit or loss of a listed contract or for Hedges' g.
Treasury teams drop both standard deviations from an internal risk pack and compare the overlay with a naive one-for-one notional hedge rather than treating either figure as a substitute. This is a different search and a different job from a futures contract profit-and-loss calculator, from a Pearson correlation coefficient on two series, from Hedges' g, and from a contract-count sizer that needs portfolio value and futures multiplier: those tools price a closed ticket, measure association, report an effect size, or convert a ratio into lots.
The minimum-variance hedge ratio prices how much futures variance you need per unit of spot. Failed validation does not consume balance.
What you can do with it
Overlay ticket before the close
Turn last window's estimated correlation and the two return volatilities into one minimum-variance futures overlay before you send the ticket against the cash book.
CFA and derivatives item sets
Check the textbook hedge ratio from ρ, σ_S, and σ_F when an exam item asks for the minimum-variance overlay rather than futures P&L or Hedges' g.
FAQ
How is the optimal futures hedge ratio calculated?
A correlation of 0.9 with a spot standard deviation of 4 and a futures standard deviation of 5 comes back as 0.72. The ratio is rounded half-up to ten decimal places.
Can the spot standard deviation be zero, and can correlation be negative?
Yes. An unmoving cash book prints a hedge ratio of zero. Negative correlation prints a negative overlay, which is a long futures hedge rather than a short.
Is this the same as futures profit and loss or Hedges' g?
No. A futures contract calculator needs size and two prices to report cash P&L. Hedges' g is an effect-size statistic. This calculator returns the minimum-variance overlay from the three return statistics you send.
Does the hedge ratio tell me how many contracts to trade?
Not directly. It gives futures units per unit of spot exposure. To turn it into a number of contracts, multiply by the size of your cash position and divide by the size of one contract; the calculator does not do that step.
Do both standard deviations need the same units?
Yes. Use daily percent, weekly returns or annual figures, but the same for both, measured over the same window as the correlation. Only the ratio of the two volatilities enters the result, so mixed units give a wrong hedge.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/fin/hedge-ratio \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"correlation":0.9,"spot_std":4,"futures_std":5}'const res = await fetch("https://api.kit.forhosting.com/fin/hedge-ratio", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"correlation": 0.9,
"spot_std": 4,
"futures_std": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/fin/hedge-ratio",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"correlation": 0.9,
"spot_std": 4,
"futures_std": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/fin/hedge-ratio", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"correlation":0.9,"spot_std":4,"futures_std":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"correlation":0.9,"spot_std":4,"futures_std":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/fin/hedge-ratio", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"correlation": 0.9,
"spot_std": 4,
"futures_std": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "fin.hedge_ratio",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
It is the product of the correlation between spot and futures returns and the ratio of their standard deviations: hedge_ratio equals correlation times spot_std over futures_std.
How the optimal futures hedge ratio is computed from correlation and volatilities
Hull, CFA curriculum notes, and every exchange-traded overlay primer write that number as the product of the correlation of spot and futures returns and the ratio of their standard deviations: hedge_ratio equals correlation times spot_std divided by futures_std. Correlation is Pearson's r between the two return series over the window you chose, bounded in minus one to plus one. spot_std is the standard deviation of the spot cash returns over that same window; futures_std is the standard deviation of the futures returns. This endpoint does not estimate correlation or either standard deviation from raw ticks, does not pick a lookback, does not convert the ratio into a contract count from notional and multiplier, and does not mark a futures ticket to profit or loss.
Input contract, response shape, and error behaviour
A correlation outside minus one to plus one fails because it is not a Pearson coefficient. A negative standard deviation fails because a standard deviation cannot be negative. POST a JSON body with three required finite numbers. correlation is Pearson's r between the spot return series and the futures return series, and must lie in the closed interval from minus one to plus one; aliases rho, corr, and correlation_coefficient map to the same field so a spreadsheet can keep its column names. spot_std is the standard deviation of spot returns in the same unit as futures_std; aliases sigma_s, spot_sd, sigma_spot, and spot_stdev are accepted. futures_std is the standard deviation of futures returns; aliases sigma_f, futures_sd, sigma_futures, and futures_stdev are accepted. Each numeric field may arrive as a JSON number or a numeric string. Missing fields, empty strings, and non-finite values fail with invalid_input naming the field. A zero spot_std is allowed and returns a hedge ratio of zero. On success the body echoes correlation, spot_std, and futures_std, then reports hedge_ratio as the rounded overlay, plus a formula string restating the identity. Example: correlation zero point nine, spot_std four, and futures_std five yield a hedge ratio of zero point seven two. Pair the JSON with your own note for the window and the return convention you used — simple versus log, daily versus weekly — because this endpoint multiplies the three numbers you send; it does not rebuild a covariance matrix, annualize mixed frequencies, or size the book in contracts. Keep futures_std strictly positive and finite, pin the rounded hedge_ratio in tests, and you get a reproducible minimum-variance hedge ratio for worksheets, LMS plugins, and edge workers without standing up a regression engine of your own.
Where a hedge ratio calculator earns its keep
Merchants and desk assistants re-run the same three fields when a new window closes or a basis regime shifts either volatility, then pin hedge_ratio in a blotter so every conversation starts from one number. Keep futures_std strictly greater than zero, pin the rounded overlay in tests, and you get a reproducible hedge ratio for teasers, LMS plugins, and edge workers without standing up a covariance engine of your own.
Integration use cases
Basis regime after a new window
Re-price the overlay when a week closes or a basis shift moves either volatility: same calculator, new inputs, one shared hedge_ratio.
Technical questions
What happens if the futures standard deviation is zero?
The task fails with invalid_input. The hedge ratio is undefined when the futures standard deviation is zero, so futures_std (aliases sigma_f, futures_sd, sigma_futures, futures_stdev) must be a finite non-zero number. That failure is not billed.
What does the hedge ratio calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.