key rate and bucket exposures-table7.2

[ckyeh]

Hi! David,

I have a question about Tuckmen's textbook, in the table 7.2,

I don't understand why the 2-Year,5-year,and 30-year bond, which are

all sell at par can only be affected by the interest rate change of their own tenor,

while the premiun 10-year bond will be affected by 2-year, 5-year, and 10-year

interest rate change?

I have read the explanation below page 138, but I still can't figure out why.

Would you please explain why sell at par or premium would make difference ?

And what if 10-year bond is sold at discount?

Thank you very much !!

 

[David Harper CFA FRM]

Hi ckyeh,

I can't explain because I think it's a mistake in Tuckman. I absolutely could be wrong (e.g., it took me a few tries to figure his table 7.1), but this issue has been raised several times; nobody has been able to explain to me why he can make those assumptions. It is true he assumes par yields but that doesn't explain it for me either.

The 2- and 10-year make sense to me: they are each exposed to all key rates within their cumulative tenor.

But (eg) the 30-year par bond: by definition, it pays a coupon at the 2-, 5- and 10-year tenor. So, a 5-key rate shock (eg) would alter the PV of the cash flow at 2-years...his footnote does not change that, IMO.

If the hedging instruments were instead 5-year ZERO coupon bond and 30 year ZERO coupon bonds, then i would understand the isolated exposures, but obviously zeros aren't used. Otherwise, i cannot figure it either (it's the only Tuckman table in 7.2 i haven't been able to replicate).

David

 

[David Harper CFA FRM]

Hi ckyeh,

I think I just figured this out, I think.
(Seriously, it only took three or four years, this question has come up every year). Here is what i think he means:

He is using par yields, which is the yield-to-maturity for a bond priced at par.

So (eg) his 30-year 5% coupon, as the yield is 5%, is priced at par.

Now, if we shock (eg) the 5-year SPOT rate, that will impact the price of the bond, clearly. Hence all the confusion...

But i think he means: shock the par yield, which is this case, is the same thing as shifting the "yield" (YTM; at par) from 5.00% to 4.99%. Because it's not a spot/zero or forward rate, shocking the 30 year par yield is tantamount to shifting the whole yield curve down 1 basis point.
... if i have that right, he leans on the fact the 30-year par yield is a single-factor proxy for all the spot rates before it
... further, if i have that right, a big if, then shifting 30-year par yield by one basis point is really the same thing as shocking the yield (YTM) of a par bond, in which case the 30-year KR01 is really a DV01 in disguise
... i am not sure that is the correct interpretation. Even if it is, i have no idea why it is superior to using zero coupon bonds for the hedging instruments which would leave no confusion as to why (eg) a 30-year zero has no exposure to a 5-year spot.

David

 

[David Harper CFA FRM]

... and to append, I *finally* found the sentences in Tuckman that confirm and settle this "mystery:" (page 140-141):

"Second, computing the sensitivity of a par bond of a given maturity with respect to the par yield of the same maturity is the same as computing DV01. In other words, the key rate exposures of the hedging securities equal their DV01s"

(seriously, every year this question has come up and i did not understand. yippee!) let me know if i can help clarify, on the assumption you don't have three years like me to figure this out

 

[ckyeh]

Hi ! David,

Thank you very much!

 

[turtle2]

David,

Do you think GARP will assume that DV01 is same as KR01 in exam for hedging question and we can do this in the exam ?

Turtle2

 

[David Harper CFA FRM]

Hi ckyeh,

No, I do not think GARP will assume that (nor, to my knowledge, ever has) because:
1. it's not unconditionally true (Tuckman does it for convenience), and
2. It is too esoteric from an exam perspective

…. I am glad we figured out why T 7.2 has more zeros than we'd expect, but for exam purposes, it might be too much knowledge: for convenience's sake, Tuckman selected par yields for the hedge instruments so that the KR01s (where key rates are par yields; i.e., YTM when price = par) = yield-based DV01.
So, KR01 (if par yield) = DV01 but the converse is not necessarily true: DV01 does not imply, is not = KR01 (par yields)

If I could just avoid the detail of 7.2, IMO the following are exam relevant:
* DV01 is generally the dollar change for a one basis point drop in some needs-to-be-defined interest rate
* For exam purposes, we so far have always assumes a yield-based (YTM) DV01; i.e., the $change for a parallel 1 bps drop across the entire maturity
* The KV01 is initially relevant because, as opposed to the single factor DV01, we can refer to the $change for a 1 bps drop in a key rate, as opposed to the whole maturity (and notice we are now into multi-factor, as we are breaking up the maturity into multiple key rates)
… like the DV01 and KV01, we always have this technical issue of "what rate do we mean?"; spot, forward, YTM, par (special case of YTM)

Hope that helps, David