If market rates decline: - the value of bonds (asset) increases (i.e. gain) - the value of liabilities also increases (i.e. loss) - the value of receive-fixed IRS also increases (i.e. gain)
When Asset BPV < Liability BPV, the liability value will increase more than the increase in the asset value (i.e. plan surplus declines).
To hedge the plan liabilities, the plan manager will use receive-fixed IRS (positive BPV) to match the Asset BPV towards the Liability BPV.
When hedging the plan liabilities using receive-fixed IRS, the equation is as follows:
Asset BPV + (Notional x BPV of receive-fixed IRS per $1 notional) = Liability BPV
Case 1: Allowable hedging range is between 25% to 75% when Asset BPV < Liability BPV
So, if the plan manager expects market rates to decline, the plan manager will hedge 75% of the liability BPV using the receive-fixed IRS. In this case:
Asset BPV + (Notional x BPV of receive-fixed IRS per $1 notional) < Liability BPV where:
Asset BPV + (Notional x BPV of receive-fixed IRS per $1 notional) = 75% x Liability BPV
When market rates decline, the increase in the value of (Assets + Receive-fixed IRS) will offset 75% of the increase in the liability value, so this minimises the decline in the plan surplus.
Case 2: Allowable hedging range is between 25% to 125% when Asset BPV < Liability BPV
So, if the plan manager expects market rates to decline, the plan manager will hedge 125% of the liability BPV using the receive-fixed IRS. In this case:
Asset BPV + (Notional x BPV of receive-fixed IRS per $1 notional) > Liability BPV where:
Asset BPV + (Notional x BPV of receive-fixed IRS per $1 notional) = 125% x Liability BPV
When market rates decline, the increase in the value of (Assets + Receive-fixed IRS) will be 125% of the increase in the liability value, so this maximizes the increase in the plan surplus.