Duration of assets and liab and futures to close the gap

CFA Level III Fixed Income
#1

Jack Walsh manages the assets for a large European airline’s defined benefit (DB) pension plan. The DB plan is currently underfunded with a deficit of £3.5 billion. The DB plan’s projected benefit obligation (PBO) is currently £16 billion and has an estimated duration of 12.

The plan assets are split into two portions: return seeking and liability matching. The return-seeking assets (equity-based ETFs and alternative investments) are held to generate returns in excess of risk-free assets and comprise 56% of the plan assets. The liability-matching assets (UK government treasury bonds [gilts] and investment-grade corporate bonds) comprise the remaining 44% of plan assets and have a duration of 13.

Basis point value of plan liabilities (BPVL): BPVL = £16,000,000,000 × 12 × 0.0001 = £19,200,000
Basis point value of plan assets (BPVA)
Value of bond portfolio = £12,500,000,000 × (1 – 0.56) = £5,500,000,000
BPVA = £5,500,000,000 × 13 × 0.0001 = £7,150,000

Basis point value of CTD bond
BPVCTD = 14.95 × 0.0001 × [(£96.32/100 × £100,000)] = £144
BPV duration gap = BPVL − BPVA = £19,200,000 − £7,150,000 = £12,050,000

We are aiming to eliminate the duration gap. Since the BPVL > BPVA, the gilt futures will have to be bought (in effect, synthetically increasing the duration of the assets).

Um, excuse me? Duration of assets is higher than the one of liabilities, so you should SHORT futures, to decrease the duration of assets?

#2

I did not go through the calcs but you need to also consider the size of your positions, not only their durations (Money Duration or BPV). It looks like BPVL is greater than BPVA. This means you needs to increase your assets to match your liabilities. You do this by going long future contracts.

#4

Actually true, duration gap would be negative… thank you.
Do not attempt to do FI, or anything related to L3, at 9 PM in the evening after days of not sleeping…

1 Like
#5

:+1:

#6

Actually, no…
if duration of assets is beliw the one of liabilities, you need to buy.
Otherwise, sell.
Duration gap below is negative: BPV portfolio - BPV liab <0, and duration of assets below of liab, so you buy.

Here’s another example, which functions according to my point,
One of VAM’s clients is a defined benefit (DB) pension plan with a projected benefit
obligation (PBO) of $1.2 billion. The effective duration of the PBO is estimated to be
10.94. The plan assets of $1.55 billion are broken down into 70% equity and 30%
bonds. The bonds are highly illiquid and have a duration of 3.77. Espinosa notes that
the fund manager plans to use Treasury bond contracts to eliminate the duration gap.
The contract under consideration is based on $100,000 par, with a cheapest-to-deliver
(CTD) bond that has a basis point value (BPV) of $114.77, a duration of 9.86, and a
conversion factor of 0.9712

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The BPV of the liabilities (BPVL) is $1.2 billion × 10.94 × 0.0001 = $1,312,800.
The BPV of the assets (BPVA) is $1.55 billion × 0.30 × 3.77 × 0.0001 = $175,305.

To increase asset duration and close the gap, buy bond contracts.
The duration gap is $1,312,800 – $175,305 = $1,137,495.
The BPV of the futures contract (BPVfutures) is $114.77 / 0.9712 = $118.1734.
The number of contracts (Nf) for a 100% hedge is $1,137,495 / $118.1734 = 9,626.

#7

I may be wrong but I do not look at the duration gap being positive or negative, I just look to see whether my assets are greater than my liabilities. If my assets are greater than my liabilities = short. If my assets are less than my liabilities = Long. I believe both examples are the same, in both cases your liabilities are greater than your assets so you should go long.

#8

You have to think money duration (or BPV), not merely duration.

#9

Yes, now I see it… it is like this. Thanks.