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…

i was glad to see this thread because i had the same issue while getting thru reading 21. good points JDV and maratikus. i wasn’t thinking about how duration was measured, just as whether it was high or low. this simple thinking seems to work for me so far: i think about asset/liability duration as the timing of the cash flows. eg, as an insurance company with a shorter liability duration relative to assets, you will have policies (liabilities) that demand payment sooner than you will receive the cash flows from your investments (assets). that’s a problem. this thinking also fit with LADG: shorter time to receive cash flows = shorter duration = lower interest rate risk. so if you have neg LADG (duration of assets < duration of liabilities), then the duration effects of your liabilities dominate your portfolio. so, interest rates go up, liabilities decrease more than equities decrease, so mkt value of equity increases. the caveat being that i’ve only read through this once, so this thinking may work so far but may have issues later. happy to hear criticism…

cfasf1 Wrote: ------------------------------------------------------- > 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… There are several equivalent definitions of duration. http://en.wikipedia.org/wiki/Bond_duration “In finance, the duration of a financial asset measures the sensitivity of the asset’s price to interest rate movements, expressed as a number of years. The reason for expressing this sensitivity in years is that the time that will elapse until a cash flow is received allows more interest to accumulate. Therefore the price of an asset with long term cashflows has more interest rate sensitivity than an asset with cashflows in the near future. Because of this relationship, duration is sometimes calculated as the weighted average number of years to receive each cashflow. Thus the duration of a zero coupon bond with a maturity period of n years is n years, since the only cashflow will occur in n years. If there are coupon payments, the duration will be less than n years. This measure is closely related to the derivative of the bond’s price function with respect to the interest rate (in terms of the Greeks, this is referred to as the Ä or Delta, where the underlying is the interest rate), and some authors define the duration to be this derivative divided by the price (in terms of the Greeks, this ratio is referred to as the ë or Lambda). This ratio is the weighted average term, with appropriate weightings for a non-callable bond.” Because you know that there are several equivalent definitions, you can choose which one to use.

done… thanks maratikus.