HedgingSome background helps

A hedge does not remove risk. It exchanges a risk you did not choose for a smaller one you did — plus a cost, plus a basis, plus the possibility of being right and margined out anyway.

What a hedge is, stated honestly

Hedging means taking a second position whose losses tend to arrive when the first position's losses arrive, and vice versa. Three things follow that are usually left out of the sentence:

• The upside goes too. A symmetric hedge — a future, a forward, a swap — removes the good outcomes with the bad ones. If you only want the bad ones removed, that is an option, and options are paid for up front.
• The exposure is transformed, not deleted. After hedging you hold the difference between two things. That difference — the basis — is a new position, smaller but not zero, and it has its own behaviour.
• The cash flows change shape. A hedged position can be exactly right in economic terms and still demand cash daily in variation margin. Metallgesellschaft and LDI 2022 are the same story told forty years apart: correct hedges, fatal funding.

How much to hedge

If the hedge instrument is the same thing you hold, the answer is one for one. It usually is not — you hold a portfolio and hedge with an index, hold jet fuel and hedge with crude, hold a corporate bond and hedge with a government one. The ratio that minimises the variance of what is left is:

The second formula is the one that matters, and it is unforgiving. A correlation of 0.9 sounds like a good hedge and leaves 44% of the original volatility standing. A correlation of 0.7 leaves 71%. Hedging removes variance in proportion to ρ², so most of the risk survives anything short of a very tight relationship.

Basis risk: the position you are left holding

• Asset basis — you hedged a different thing. Refiners hedging with crude, airlines hedging jet fuel, a stock portfolio hedged with an index it does not resemble.
• Calendar basis — you hedged a different date. Hedging a twelve-month exposure with a three-month contract means rolling it four times at prices nobody has quoted yet, and each roll can cost or pay depending on the shape of the curve.
• Quantity basis — you hedged the wrong size, because contracts come in fixed lots or because the exposure itself moves. A hedge on an uncertain volume is a hedge on a guess.
• Location and quality basis — the physical commodity world's version: the right barrel, in the wrong place, of the wrong grade. LME nickel 2022 made the deliverable-grade version of that famous.

Static, dynamic, and the cost of each

• A static hedge is set once and left. Cheap in effort, and it drifts: the ratio that was right at inception is wrong after the exposure has moved.
• A dynamic hedge is rebalanced as the sensitivity changes — the delta hedge is the canonical case. It tracks far better and pays for it in transaction costs, which scale with how often you rebalance and how volatile the market is.
• The trade-off has no free side. Rebalance rarely and you carry tracking error; rebalance often and you pay the spread repeatedly. In a gap — a market that jumps rather than moves — the dynamic hedge does not get its chance to rebalance at all, which is exactly when it was supposed to earn its keep.
• An option hedge moves the cost forward. You know the premium on day one and nothing else can surprise you on the downside. That certainty is the product being sold, and the volatility risk premium is roughly what it costs on average.

The ways hedges actually fail

• Correlation breaks in the stress it was bought for. Relationships estimated on calm data are not the relationships that hold in a crisis, and the failure is one-directional: they break towards you being unhedged.
• The hedge is funded and the exposure is not. Mark-to-market on the derivative, no cash from the physical asset — a timing mismatch that has ended firms whose economics were sound.
• The counterparty is part of the risk. A hedge is a claim on someone. An uncleared hedge against a counterparty who fails in the same scenario is not a hedge, which is the argument for central clearing.
• The hedge outlives its reason. Exposures shrink, businesses change, positions are sold. A forgotten hedge is a naked speculative position wearing a prudent label.
• Hedging accounting diverges from hedging economics. Reported earnings can swing on a position that is economically flat, which creates pressure to unwind the right hedge for the wrong reason.

Questions worth asking before putting one on

• What exactly am I trying not to lose? A hedge without a stated exposure is a trade.
• What is left after it works? Compute the residual volatility, not the effectiveness percentage — the residual is what you will actually live with.
• What does it cost per year, in full? Premium, roll, spread, margin funding, and the upside forgone. The last one is a real cost, and it is the one never written down.
• Can I fund the worst path? Not the worst outcome — the worst path. They are different, and only one of them makes margin calls.