Duration mismatch

Hi Guys,

In the CFAI book 4, Question 23, I’m a litle confused here. The pension liabilities duration is 10.2, the assets average duration is 60.2. the plan should be more concerned about:

  1. Flattening yield curve, 2. steepening, or 3.parallel upward shift.

Can anyone shed a light on this one?


Sorry, assets duratoon is 6.2 not 60


I believe so.

The correct answer cannot be a parallel upward shift; the value of the assets would decline by about 6.2 times the shift while the value of the liabilities would decline by about 10.2 times the shift; that’s a good thing.

To decide between a flattening or steepening yield curve it would be helpful to know the average maturity of the assets and liabilities. As we don’t know those numbers, we have to make the reasonable assumption that the average marturity of the liabilities is greater than the average maturity of the assets (to account for the duration difference). Given that, flattening is bad - the shorter-maturity assets will drop in value while the longer-maturity liabilities would increase in value - and steepening is good - the shorter-maturity assets will increase in value while the longer-maturity liabilities will decrease in value.

So they should be concerned about a flattening of the yield curve.

My pleasure.

no assumption is needed. duration is longer on the liabilities so the average maturity must be longer.

never the less, very well explained!

Not necessarily: if the liabilities are zero-coupon and the assets pay coupons (or worse: are amortizing securities), the duration of the assets will be shorter than those of the liabilities even with the same (or longer) average maturity.


The shorter maturity assets will increase in value while the longer maturity liabilities will decrease in value: This is a good thing for investor right (as liabilities decrease) ? Why would he be concerned?

Question asked is which one should he be concerned about . Not why should he be concerned .

Obviously the 3 scenarios are distinctly different.

And only flattening is worrying to him since the assets rise / decline/whatever by a small amount ( given smaller duration ) while the liabilities RISE by a large amount . Only way for flattening to happen from a initial upward sloping curve is when the long declines appreciably ,example circa spring 2010 , which makes tghe liability look horrible

That _ isn’t _ the only way flattening could happen; it’s one way flattening could happen. Another way is for the short end of the yield curve to rise while the long end remains unchanged. Or the short end could rise a lot while the long end rises a little. Or the long end could decline a little while the short end rises a little, or a lot.

There are many ways that the yield curve can flatten. And all of them are bad.

Thanks S2 , you are correct , my bad.

Usually the volatile end is the short . The rising short end , with the long changing very little , is the normal way flattening happens.

The yield could get inverted too ( rarely happens ) , when the market anticipates that rates in general will drop a lot. Or if investors crowd the long end , causing yields to drop at the long end.

My pleasure.

It happens . . . rarely.

Don’t give it another thought. We’ve all made our fair share of mistakes here.


Hello Magician, to answer this question so we are basically assuming that initially the yield curve is upward sloping? Is that a correct?

I would have answered flattening too. But based on just the fact that its bad anyway… Steepening is a positive result and so is the upward shift. But not sure if thats the right way to answer it…



The problem is that the language of yield curve changes only makes sense for upward-sloping yield curves. The term “steepening” means that the difference (long-end yield – short-end yield) increases, and the term “flattening” means that the difference (long-end yield – short-end yield) decreases. Think of “steepening” as “long end moves up relative to the short end” or “short end moves down relative to the long end”; think of “flattening” as “long end moves down relative to the short end” or “short end moves up relative to the long end”.

If the yield curve is inverted, then “steepening” will actually make it look flatter, and “flattening” will make it look steeper (down). That’s unfortunate, but it’s the language we’ve been given, so we have to work with it.

As Victor Borge used to say, “I can’t stand sitting. (It’s _ your _ language; I’m just trying to use it.)”

Then you’d have gotten it right.

I have bookmarked your response and anytime I have a trouble (praying I dont get that anymore) with duration & yield curve movements, I am going to refer this :slight_smile:

Thanks a ton Magician :slight_smile: You really are a star!

I blush.

In regards to this - assuming that a flattening of the yield curve involved short term rates coming down and the subsequent rise in asset and liability values (inverse relationship between yield and values) longer duration liability values would rise by more than shorter duration asset values due to increased interest rate sensitivity… Correct?