Reading 21 - Duration of liabilities

Numerous times in reading 21 (managing for institutional investors) the DURATION of liabilities (e.g. 20 years) is mentioned in the context of the pension plan. Does anybody know how the term duration being defined here?

Should be relative to the duration of assets. (i.e. not in actual years, but in terms of interest rate sensitivity)… Recall, your position is manage your funded ratio (Assets/Liab).

That is what I would think too, but it is listed in years, but never defined anywhere I can see in the reading (kind of like the text is saying to me “you should know this already idiot”). Problems is that I don’t know it already.

Man, I can’t write very well this late at night. ^

mwvt9 Wrote: ------------------------------------------------------- > Numerous times in reading 21 (managing for > institutional investors) the DURATION of > liabilities (e.g. 20 years) is mentioned in the > context of the pension plan. Does anybody know > how the term duration being defined here? duration = weighted average number of years to receive cash flows. if you expect cash flows CF1 in 1 year, CF2 in 2 years, etc … -> calculate weighted average -> duration after you estimate duration, you can immunize your portfolio, etc … does that help?

I agree with maratikus. It is the weighted number of years to receive the cash flows. So if its 20 yrs, the weighted PV of cash flows ( liabilities in this case) will take 20yrs.

Duration of assets is really clear, yes? Use maratikus’ formula and you get something about interest rate sensitivity measured in years. Note that you get the usual sensitivity by saying if interest rates move by 1%/year * duration in years = % move of portfolio (so the units work out). Liabilities work the same way except that for an insurance company the cash flows of the liabilites are not as clear. Thus, if I have a bunch of life insurance policies on a group of people I can have some actuaries sit down and I tell them to estimate the weighted average of the cash flows on insurance payouts using maratikus’ formula. The estimate they give me is the duration of my liabilities. Clearly, it’s a guess but it’s not much worse than calculating the duration of a bond with optionality especially if the pool is big.

Durantion concept might have different meaning depend on what product we are talking about: For a zero coupon bond, duration is equal to the term to maturity because you do not have any cash flow come in. For coupon bond, durantion is different to term to maturity, it is less than the term to maturity. For Banks, assurance, duration is the average time it take to either hold an assets or a liabilities is due.

Thanks for all the input guys. I will revisit the reading and make sure I have this down.

sorry to bring this back up but in revisiting my historically crappy section, fixed income, this issue came up again… like joey says above, i always thought duration was the percent move in your portfolio per 1% move in interest rates. so i’ve always had problems with it being measured in years. then, to compound the problem, i’ve also seen maratikus’s definition used. which is it or are they the same? if someone tells me the duration of porfolio x is 5.2, which definition of duration are they using? would appreciate any feedback. thanks in advance…