hi there

A simple query:

BPV of asset is less than its BPV of liabilities and interest rate are expected to increase.

Manager wants to close the duration gap with future contracts.

Why should he underhedge? I do not understand this point.

Could it be that the liabilties are dropping faster due to the higher BPV and therefore not requiring 100%hedging as otherwise overhedging would occur, if interest rate rise indeed?

Regards

Say BPV of asset = $850 and BPV of liabilities = $1,000

Assume the BPV of a futures contract = $15, so you will need 10 futures contracts to close the duration gap.

BPV of asset + BPV of futures = BPV of liabilities

$850 + (10 × $15) = $1,000

**Scenario 1: Interest rate increases 10 bps, no hedge**

Asset value decreases by $8,500 (loss).

Liability value decreases by $10,000 (gain).

Net: Gain of $1,500

**Scenario 2: Interest rate increases 10 bps, duration gap closed**

Asset value decreases by $8,500 (loss).

Futures value decreases by $1,500 (loss)

Liability value decreases by $10,000 (gain).

Net: Gain of $0

**Scenario 3: Interest rate increases 10 bps, long 6 futures contracts (underhedged)**

Asset value decreases by $8,500 (loss).

Futures value decreases by 6×$15×10 bps = $900 (loss)

Liability value decreases by $10,000 (gain).

Net: Gain of $600

So when the manager underhedges, they still expect to profit when interest rates increase, but has less conviction in the view.

Many thanks, very good explanation. I am glad you took the time!

And in case of negative duration gap, the same thinking through logic helps! Awesome.

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