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Learn / Risk & ALM

Interest-rate hedging

A hedge is a position added so that a market move hurts the book less. Hedging is not the same as guessing the next move in rates. You name the exposure, pick an instrument that offsets it, measure how much of the exposure closed, and keep watching what is left.

The classroom book is the same one as the insurance lesson. Assets $100 million, duration 6. Liabilities $100 million, duration 12.

01

Why the gap is the exposure

If assets and liabilities had the same dollar sensitivity to a parallel rate move, a parallel move would change both sides by about the same number of dollars. Surplus would barely move. They do not match. Assets move about $60,000 per basis point. Liabilities move about $120,000 per basis point. The book is short about $60,000 per basis point of parallel duration.

Who moves more per basis pointAsset dollar duration is $60,000 per basis point. Liability dollar duration is $120,000 per basis point. The gap is $60,000.Who moves more per basis pointTeaching sketchAssets$60,000 per bpLiabilities$120,000 per bpGap to close with a receive-fixed swap: $60,000 per basis point
Both sides are $100 million. Assets have duration 6. Liabilities have duration 12. The longer liabilities move about twice as much when the curve shifts in parallel.

A rate decline is the painful parallel case for surplus. Liabilities, being longer, rise in value by more than the assets. Surplus shrinks. A rate rise does the opposite: the liabilities fall in value by more, and surplus grows. The hedge below is aimed at the shortfall of asset duration, not at a view that rates will rise.

From a gap to what is left overName the exposure, identify the risk, select a hedge, measure how well it offset, then watch what remains.From a gap to what is left overTeaching sketchExposureIdentifySelectEffectivenessResidual
Effectiveness here means how much of the parallel gap the hedge closed. Residual is the risk that is still open, such as a twist.

02

Matching, immunization, and the swap

Duration matching means choosing assets, or a hedge, so the dollar duration of the assets lines up with the dollar duration of the liabilities. Cash-flow matching is stricter: the asset cash arrives in the same periods the liability cash is due. Immunization is the classic name for setting duration so a small parallel move leaves surplus about unchanged, with convexity watched as the second-order leftover.

A receive-fixed interest-rate swap lengthens the asset side. You receive 4% fixed and pay floating, on a notional sized so the swap’s dollar duration is about $60,000 per basis point. After that, a small parallel move changes the swap and the old gap by offsetting dollars. The notional itself is not a loan. The swap lesson shows why the $100 million stays put and only the interest nets are paid.

03

When the team reaches for something else

The receive-fixed swap obligates both sides for the remaining life. If the liability might change, or the hedge might not be wanted yet, that obligation is the wrong tool. A payer swaption is the right to pay fixed later. It spends a premium and keeps the choice. That is the swaption and the insurance ALM lessons. It does not lengthen assets today. It is a different job from the receive-fixed swap.

Five tools, five jobsA receive-fixed swap lengthens assets. A payer swaption is the right to pay fixed later. A cap pays when a rate rises through a strike. A floor pays when a rate falls. A Treasury future is a listed rate hedge.Five tools, five jobsTeaching sketchReceive-fixed swap — Lengthens assetsPayer swaption — Right to pay fixed laterCap — Pays if a rate rises through a strikeFloor — Pays if a rate falls through a strikeTreasury future — A listed rate hedge
The swap closes today's parallel gap. The swaption keeps a later choice. Caps, floors, and futures are other ways to take a rate view without copying the swap.

A cap pays the holder when a stated rate rises through a strike. A floor pays when a stated rate falls through a strike. A collar is a cap and a floor together. A Treasury future is a listed contract on a government bond, useful when the team wants a rate hedge that trades on an exchange. Each one changes rate exposure. None of them is a substitute sentence for the others.

04

Effectiveness and what remains

Hedge effectiveness, in this classroom, is how much of the $60,000 per basis point the hedge offset. A receive-fixed swap sized to $60,000 per basis point closes the parallel gap. Effectiveness against a parallel move is high. Effectiveness against a twist can still be poor, because the 2-year and the 30-year did not move together and the swap was not built as a set of key-rate hedges.

Dynamic hedging means adjusting that size as the book and the curve change, instead of setting one trade and walking away. Residual risk is the list of what the hedge did not cover: curve shape, credit, equity, volatility, liquidity, and the chance the liability cash flows change. Economic effectiveness is also not the same thing as the accounting result. That split is the economic risk and GAAP page.