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2017 AM Exam - 2B (Discount Rate and Duration)

I don’t think this is needed for full credit on the question, but anyways…

“Scenarios 1 and 2 would have no effect on the plan’s time horizon (these scenarios would, however, change the duration of the plan’s liabilities).” 

How does increasing or decreasing the discount rate applied to plan liabilities impact duration?

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Is it possible it means dollar duration? Decreasing rates = increasing liabilities and therefore = increasing liability duration.


If you're the first out the door, that's not called panicking

Increasing/Decreasing rates doesn’t affect Duration. When you take on duration/interest rate risk, with either your Asset Bond Portfolio or the Liability Bond Portfolio, the value of those portfolios will fall (rise) with increasing (decreasing) interest rates. 

ex) Just for the sake of argument, let’s say you have a BPVA of $100 with a 4 duration and you have a BPVL of $95 with a 4 duration. If rates go up by 100 bps/1% then, both portfolios will drop by 4%, right? So the BPVA is now worth $96 and the BPVL is worth $91.20. 

Beginning Funding Status = BPVA - BPVL = $100 - $95 = $5 surplus

Ending Funding Status = BPVA - BPVL = $96 - $91.20 = $4.8 surplus

The duration of the BPVA or BPVdidn’t change, but the funding status did. 

The same were to happen if you’re valuing the BPVA or BPVL and you increase/decrease the discount rate (think GGM or DCF), a higher (lower) discount rate means a lower (higher) present value. All that changes is the value of the BPVA or BPVL and subsequently the difference between them (funding status). Their duration doesn’t change however. 

The duration uses the present value of the individual cashflows and the present value of the portfolio to weight the times at which cashflows are received. The duration of liabilities/assets is bound to change if the discount rate changes.