Identifier: C3T5L3 · Revision: 2026-10-26 · Classification: domestic

Decision and objectives

Size a supplied cross-hedge using regression sensitivity. The decision record must connect the exposure, cash dates and implementable contract, rather than stop at a favorable price forecast.

By the end, you can size a supplied cross-hedge using regression sensitivity; calculate realized residual when correlation changes; distinguish a statistical relationship from a contractual match.

Prerequisite: C3T5L2; completed Classes 1 and 2 and the Stock Market School foundation or Forex School foundation. All cases below are hypothetical; their prices, costs, rates, dates, contractual assumptions and collateral amounts are teaching inputs, not current offers.

Mechanics

A cross-hedge uses a related reference when no exact exposure contract is available or executable. A metal user may hedge one grade with a different standardized reference. Historical covariance can suggest a ratio, but no contract forces the two prices to keep moving together. Currency, region, timing, quality and business operating margins can all change the relationship.

Price and return drivers

A supplied minimum-variance teaching ratio is h = correlation × exposure volatility / hedge-reference volatility, using comparable return series and periods. Hedge notional = h × exposure value. This is a statistical estimate, not a guaranteed loss offset, and the ratio is inappropriate if the dataset or units are inconsistent. Stress actual outcomes rather than substitute correlation for cash.

Worked case

Hypothetical procurement exposure TRY 1,000,000, return volatility 12%, reference futures volatility 10%, correlation 0.75. h = 0.75 × 0.12/0.10 = 0.90. A long hedge of TRY 900,000 reference notional is indicated; with TRY 100,000 per contract, nine contracts. If procurement prices rise 10% and futures rise 8%, cost increases TRY 100,000 while hedge gains TRY 72,000. Residual TRY 28,000 plus execution TRY 1,800 and funding TRY 2,700 makes total incremental cost TRY 32,500 before tax. Matching a historical variance ratio has not fixed the invoice price.

Adverse case

If supply stress raises the business input by 15% but the futures reference only 2%, cost rises TRY 150,000 and hedge gains TRY 18,000, leaving TRY 132,000 before costs. If correlation falls to 0.25 with the same volatilities, a re-estimated ratio is 0.30, not 0.90. Automatically reducing the hedge after the break may crystallize losses or leave new exposure; decisions require fresh business context.

Practical use

Obtain synchronized, comparable observations without splicing unexplained maturities or mixing quote currencies. Confirm executable contract size, expiry, access, margin and physical cash needs. Include rebalance spreads, commissions, reserve financing, roll costs and tax. Historical confidence does not establish future borrow or liquidity.

Reconcile the confirmation, position register and cash statement separately. Costs include the quoted bid/ask spread, brokerage and clearing charges, collateral or principal financing, currency conversion, custody where relevant, and exit or termination charges. A mark is not a fill. Any amount explicitly excluded below remains outside the reported result. Tax is excluded from these teaching cases: an actual comparison requires income year, investor residence and individual/corporate status, contract and acquisition dates, settlement form and effective law. The GIB guide, checked 2026-10-26, covers 2025 individual investment income, so its publication date alone does not settle a 2026 derivative liability.

Decision boundaries

A cross-hedge is suitable when its residual is understood and better than alternatives under the objective. If the relationship breaks exactly when protection is needed, reducing the underlying exposure or accepting a smaller explicitly measured hedge can be preferable. Do not describe a high correlation as a probability of protection.

Practice and references

Exercise: hypothetical correlation 0.8, exposure volatility 15%, futures volatility 20%, exposure TRY 500,000. Calculate the ratio, notional and residual under a 12% procurement rise and 9% futures gain. Solution: h = 0.8 × 0.15/0.20 = 0.6, target TRY 300,000. At a 12% procurement rise and 9% futures gain, gross residual cost = 60,000 − 27,000 = TRY 33,000. Costs and margin cash are additional.

Takeaway: Distinguish a statistical relationship from a contractual match using the actual cash schedule, with every excluded cost and remaining exposure stated.

Reference card: viop-future. Formula: Supplied statistical cross-hedge ratio. Glossary: Cross hedge, Correlation. Next lesson: C3T5L4. Topic test.

Sources and verification date (2026-10-26):

Related product cards: viop-metal-future, viop-energy-future.

Shared reference guide