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Plan liability discount rate and liability duration

CFAI Mock 2017 Question 2B : How does a change in a DB plan’s liability discount rate affect the duration of the plan’s liabilities? 

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It doesn’t. Just think of Gordon Growth Model or a traditional DCF. The discount rate is always in the denominator, right? So when you’re discounting a cash flow, in this case liability, back to the present, a higher (lower) discount rate will produce a lower (higher) present value. If you have a Positive Funding Status (PVASSETS > PVLIABILITIES ), you’re asset portfolio of bonds has a larger value than that of your liability portfolio. If rates decrease, great! Your PVASSETS will appreciate more than the PVLIABILITIES…….but, if rates increase, your PVASSETS will fall in value compared to your PVLIABILITIES (depending on the duration of each, but all else equal). 

Bottom line: Rates moving only increases or decreases the surplus and whether a DB plan becomes overfunded or underfunded, but doesn’t affect its duration. Taking interest rate exposure through duration can help/hurt the VALUE of the bond portfolio, but whether interest rates move higher or lower, doesn’t affect your portfolio’s duration, in and of itself.