Duration of liabilities?

CFA Level III
#1

For example, when discussing pension plans, if the question states that the duration of plan liabilities is 15 years…what does that mean exactly?

Does that mean the liabilities will start being paid in 15 years, the bulk of the liabilities will start being paid in 15 yrs, or what? With a pension, you’re already paying some of the liabilities out to currently retired employees, so what exactly does the 15 year timeframe mean? Especially if the plan is perpetual, won’t there be liabilities after 15 years.

Thanks in advance.

#2

I thought duration of liabilities could be interpreted similarly to duration of assets, which is a weighted average of time of cash flows (in years), where PV of CFs make the weights? It would suggest that unless the future liability is a single payment, duration is just an average… And actual payments (e.g. pension plan CF outflows) are in fact spread around the moment in time equal to duration (15 year point in this case).

#3

the duration of a portfolio is the market value weighted average of the duration of its components.

#4

Thanks. Perhaps this is a silly follow-up question, but when the text refers to the general sense of ‘duration’, are they referring to duration as it pertains to fixed income securities (ie price sensitivity to interest rate changes) or more simply the time period itself.

I know that fixed income duration is largely based on time (maturity) and is often stated in years, but it takes a more exact meaning than just talking about time in general. Further, if the portolio or liability is fixed income based, then clearly the former can apply as we are dealing with FI securities.

That said, I know it’s blurry, but I just wanted to make sure i wasn’t over thinking it and thinking along the lines of a very specific term when really it should just be viewed as a simple length of time?

Thanks much

#5

you are overthinking. duration is - as you said - the price sensitivity to interest rate changes. this is very much related to when payments are due. for zero coupon securities it is the same as time.

#6

So when they talk about duration, are we meant to think along the fixed income lines and the impact of interest rate changes or, more simply, just the amount of time when payments come due?

I know they’re related, so it’s probably tough to truly differentiate, but duration in the fixed income sense takes on a very specific meaning with consideration for interest rates, whereas generally speaking, duration can just mean a period of time.

#7

Duration commonly refers to the interest rate sensitivity of a financial instrument. However, it is expressed in “years” and is generally related to payment timing. Payments with longer maturity are generally more sensitive to changes in interest rates.

#8

Duration can meaure 2 things. one is interest rate sensitivity. the other is weighted average of maturity of the coupon payments.

but what does weighted average of maturity of coupon payments mean?

#9

It’s not only about coupons but also about the principal. So I would say rather about cash flows than just coupons, and it means more or less the same as every average - a man and a dog have on average 3 legs each…

#10

you have short term payments due + long term payments in 10-15- 20 years)that will occur int the future, I guess it’s the average maturity of all plan payments

#11

I think duration of liabilities = %change in PV of liabilities / 1% change in discount rate used for liabilities. No?

#12

In most examples CFA Institute uses the time until the liabilities are paid as their duration. Thus, they are implicitly using Macaulay duration.

Unfortunately, they then try to equate it to the duration of the assets, but for assets they’re using price sensitivity; i.e., modified duration.

It’s a contradictory treatment, but that’s what they’re teaching, so that’s what you should use on the exam. You don’t have to like it. i don’t.