Key Rate

[sipanivishal]

Hi David,

I cannot find the key rate spreadsheet where you are calculating the Key rate duration all.

Thanks
Sipani

 

[sipanivishal]

Hi David,

One more thing,it seems you have changed the calender now but have not updated till date.if you can update it we can plan better.

Thanks
Sipani

 

[David Harper CFA FRM]

Hi Sipani,

Re key rate, you mean Tuckman's example - yes? See here, I think i need to dress up for member page still:
http://forum.bionicturtle.com/viewreply/390/

Re calendar, the movies will always be on schedule. The Credit notes are delayed b/c GARP has published now three AIM versions and still the latest is *filled* with problems (i have a list of 20+ issues with the Credit; nevermind re: Ops they have forgotten at least two dozen AIMS !?). I will update the calendar as soon as i can be realistic. But I do still plan to "catch up" with the notes by investment (i.e., july 7th per original). We should be pretty good about meeting July 7th for all notes.

Thanks David

 

[David Harper CFA FRM]

Sipani,

Re the movie calendar, I see your point: I will update it (We are actually running a bit *ahead* of the original calendar schedule). To recap:

* I'll update the movie calendar; it is currently running a little bit ahead schedule. I may just add an additional cram session/webinar at the end since i might finish the regular a week early
* Notes should all publish (per shedule) by July 7th
* Questions will publish as currently

Thanks, David

 

[sipanivishal]

Hi David,

They have updated the AIM !!!!!!!!.... :O.........shocked......why dont they convey it to us (Thanks we have you to look after us). Plus even I am finding Tuckman AIM redundant so many time. Multifactor has been talked about in two AIMs which I feel is same.
a ) Describe the key rate shift technique in multifactor hedging applications.
b ) Explain how key rate and bucket analysis may be applied in estimating portfolio volatility.

Anyway I would restrain myself from these discussions.
David, I am finding the Bucket Analysis a bit tough to grab.Do we need to just know the difference between bucket and Key rate or the complete thing as it appear the Tuckman.The example with swap as mentioned is very confusing.If possible can you explain it with a spreadsheet or possibly a 5-6 minutes screencast.

Plus,

1. page number 135 Tuckman "the fact that the shifts ............." What is he trying to convey in this paragraph.......
2. Pg. No. 138....foot note two.......unable to visualise it. Your intuition will help certainly.
3. In tables 7.2 (in your lecture appears as KR2,2 etc) ......are key rates mentioned ?

Thanks, Sipani

 

[David Harper CFA FRM]

Hi Sipani,

Re: bucket analysis, I admit i gave that short treatment in movie. Yes, I will make it a one of the daily screencast in the next few days. Good idea, thanks for the request!

1. page number 135 Tuckman “the fact that the shifts .............” What is he trying to convey in this paragraph.......
See graphic below. You can choose the rule as to how rates in between the key rates shift (i.e., if we shock up the yield at 5 years, what happens to the 4.5 year rate? How will it be shocked since it is not a key rate?). His example is maybe the simplest idea: linear interpolation. His point is: yes, this linear interpolation is unrealistically simple, but attempts to imbue the curve with more realism (curve) do not give much better accuracy. Linear is "good enough"

2. Pg. No. 138....foot note two.......unable to visualize it. Your intuition will help certainly.
Yes, good notice. It has come up before. http://forum.bionicturtle.com/viewreply/685/
I continue to think Tuckman is wrong. He implies a 10 year par bond (coupon = yield) is a good hedge instrument b/c it is only sensitive to the 10-year rate. I disagree: shock the 5 year rate and the coupon paying in five changes value. If he said the hedge instruments were ZERO coupon bonds, i'd agree (but then they wouldn't be par).

But still: it does not really matter. It is not the point here. The point is the hedging portfolio contains an array of key rate sensitivities. I think his array should contain values in a triangle (ie., 2 impacted by 2, 5 impacted by 2 and 5), but it doesn't matter for his point. His point is: you want to solve for a hedge portfolio that sums to the same key rate '01s as the instrument being hedged.

3. In tables 7.2 (in your lecture appears as KR2,2 etc) ......are key rates mentioned ?
KR2 is just me abstracting the numbers. I'll try to give better help it some specific screencasts and i'll link bank.

Thanks,
David

http://learn.bionicturtle.com/images/forum/keyrate_interpolate.png

 

[sipanivishal]

Hi David,

Ya your intuition helped. "Infact It was great "
I might sound stupid but how did he calculate the KR2,2 ; KR5,2 etc...

Thanks, Sipani

 

[David Harper CFA FRM]

Hi Sipani,

No, good question, your sequence reminds me of how i learned it, this is the maybe the last hard part of it

He has four hedging bonds, so (this is why the disagreement over point 2 above is not critical) he will always be solving for four unknowns with four equations. The unknowns are the amount (the face amounts) of the hedging bonds. He wants to find the correct amount of 2-, 5-, 10-, and 30-year hedging bonds that nullifies (hedges, offsets) the Key Rate 01s in the matrix (table 7.2).

He got the cells in Table 7.2 (KKR2, ...) the same way he got the key rates for his mortgage bond (the thing *being* hedged): shock the key rate and find the dollar price difference of the bond; e.g., his 0.043375 under 5-year means the 5-year *hedging bond* drops by 0.04... when the 5-year rate increases by 1 basis point. (see my disagreement: if you shock the 2 year rate by +1 bps, then the 2-year coupon on the 5-year bond will drop slightly, and this has tiny impact on the 5 year bond price, so i think to left of 0.04 should be non-zero. But no matter)

So, the four hedging instruments constitute a VECTOR of key rate '01s. And the whole point of solving for the four unknowns is find the right blend of hedging instruments such that the total, for example, key rate 01 at 2 years approximately equals the key rate 01 at 2 years for the bond *being* hedged. Then, under a 2 yr rate shift, the changes in value should offset. So, it is good to see these key rates as a vector which together approximate the DV01 (i.e., the DV01 implicitly assumes the whole curve shifts by 1 bps, so the key rate is trying to improving by breaking up the curve into "pieces")

David

 

[dtammerz]

So, the four hedging instruments constitute a VECTOR of key rate '01s. And the whole point of solving for the four unknowns is find the right blend of hedging instruments such that the total, for example, key rate 01 at 2 years approximately equals the key rate 01 at 2 years for the bond *being* hedged. Then, under a 2 yr rate shift, the changes in value should offset. So, it is good to see these key rates as a vector which together approximate the DV01 (i.e., the DV01 implicitly assumes the whole curve shifts by 1 bps, so the key rate is trying to improving by breaking up the curve into "pieces")

David

This might be very basic.. but generally what is meant by a "vector of key rate 01s" / "vector of key rate durations" / "vector of sensitivities"? (some of the phrases taken from the notes VRM Ch.13, p.6 &7)

 

[David Harper CFA FRM]

Hi @dtammerz In this context, a vector is a list of numbers; a matrix has rows and columns, but we can refer to a single row or a single column of the matrix as a vector and this vector is just a set of numbers. It's a good question in this context because it speaks to the essential difference between a key rate '01 and a DV01: just as duration is a single-factor, the DV01 of a position is captures by a single value (in algebra, we call this a scalar https://en.wikipedia.org/wiki/Scalar_(mathematics)). But the key rate approach has a different KR01 for each key rate, so the position's key rate profile is described by a vector of key rates, for example: {KR01(2-year), KR01(5-year), KR01(10-year), KR01(30-year)}. The use of "vector" is deliberate as it means to convey that the key rate shift technique is multi-factor. I hope that's helpful!

 

[dtammerz]

Hi @dtammerz In this context, a vector is a list of numbers; a matrix has rows and columns, but we can refer to a single row or a single column of the matrix as a vector and this vector is just a set of numbers. It's a good question in this context because it speaks to the essential difference between a key rate '01 and a DV01: just as duration is a single-factor, the DV01 of a position is captures by a single value (in algebra, we call this a scalar https://en.wikipedia.org/wiki/Scalar_(mathematics)). But the key rate approach has a different KR01 for each key rate, so the position's key rate profile is described by a vector of key rates, for example: {KR01(2-year), KR01(5-year), KR01(10-year), KR01(30-year)}. The use of "vector" is deliberate as it means to convey that the key rate shift technique is multi-factor. I hope that's helpful!

thank you!