Terminology of key-rate exposures, Partial '01s, key rate 01s (KR01s)

[AUola2165]

Hi,

I am wondering what is terminolgy regarding key-rate exposures, Partial '01s, key rate 01s (KR01s)?

On page 168 of "Valuation and Risk Models", it is said that "...The impact of shifts, such as the ones shown in Figures 13.2 through 13.4, are sometimes referred to as partial 01s or key rate 01s (KR01s)." This, I think, implies that they are synonyms?

However, in the Bionic Turtle Mock Exam 1, question 40, in the answer it is said that:
"Partial ’01s are used for measuring and hedging the risk of portfolios of swaps or portfolios that contain both bonds and swaps in terms of the most liquid money market and swap instruments. As these instruments are almost always those whose prices are used to build a swap curve, the number of securities used in this methodology is usually greater than the number used in a key-rate framework."

So, is key-rate framework used for key-rate '01s? If no, what is key-rate framework used for? If yes, is GARP mistaken when they are referring to partial 01's as key rate 01's?

And finally, what is the key rate exposure? Per my experience, key rate exposure is used (maybe mistakenly) in real world as a synonym for key rate duration i.e. sensitivity of a bonds to a specific point along the yield curve.

 

[gsarm1987]

@AUola2165 , KRD are estimations, fixated on certain yield curve points. DV01 is a type of duration (discusses change per 1 basis point move in the rate), durations come in many shades: Effective, modified, DV01, PBV, etc. KR01 that you are referring to is key rate duration in context of 1bps movement in the rate. Key rates you can say are points on the yield curve for eg. duration at 5yr, 10yr, 20yr 30yr etc. so any duration specific to these points is KRD. and if you see it in the context of 1bps move on these points you see KR01s.

Key rate exposures are exposures to change in rates on certain key rates: 2yr, 5yr, 10yr, 20yr, 30yr. In CFA text, they discuss KRDs in the context of effective duration or empirical duration. here in GARP material they explain in 01 context too.

For note: PVBP vs DV01, They are closely related concepts, but the key difference is in the way they are expressed (PVBP in percentage terms, DV01 in dollar terms).

in conclusion, KRD can be interpreted in many ways, through effective duration, DV01, empirical, etc. Let me know if that helps.

 

[AUola2165]

Hi @gsarm1987 and thank you for your reply. Some things are still unclear:

1. Are partial 01s and key rate 01s (KR01s) synonyms?
2. Is key-rate framework used for key-rate '01s?
3. If we sum up all KR01's of a bond, do we get DV01?
4. If we sum up all Forward-buckets 01's of a bond, do we get DV01?

 

[gsarm1987]

Hi @gsarm1987 and thank you for your reply. Some things are still unclear:

1. Are partial 01s and key rate 01s (KR01s) synonyms?
2. Is key-rate framework used for key-rate '01s?
3. If we sum up all KR01's of a bond, do we get DV01?
4. If we sum up all Forward-buckets 01's of a bond, do we get DV01?

1. No, partial 01s and key rate 01s (KR01s) are not synonyms because they represent different interest rate risk measures.
2. Yes, the key-rate framework is used for key-rate 01s to assess the impact of specific key rate shifts.
3. No, summing up all KR01s of a bond does not give DV01 because KR01s only measure risk at specific key rates, not the overall interest rate risk.
4. Yes, summing up all forward-bucket 01s of a bond provides an estimate of its DV01 as it considers changes in interest rates across various maturity points.

re: 3, remember, sum of KRDs dont sum up to PF Duration, we have to use the PF cashflows as if its one mother of all cashflow bonds and then we calculate the duration based on timings and amounts of CF throughout. so thats totally different

 

[AUola2165]

1. No, partial 01s and key rate 01s (KR01s) are not synonyms because they represent different interest rate risk measures.
2. Yes, the key-rate framework is used for key-rate 01s to assess the impact of specific key rate shifts.
3. No, summing up all KR01s of a bond does not give DV01 because KR01s only measure risk at specific key rates, not the overall interest rate risk.
4. Yes, summing up all forward-bucket 01s of a bond provides an estimate of its DV01 as it considers changes in interest rates across various maturity points.

re: 3, remember, sum of KRDs dont sum up to PF Duration, we have to use the PF cashflows as if its one mother of all cashflow bonds and then we calculate the duration based on timings and amounts of CF throughout. so thats totally different

@David Harper CFA FRM could you please give some clarity to the questions raised in this thread?

@gsarm1987 thank you again for your answer.

English isn't my first language, not even my second, and I might be missing some subtleties of the FRM text, but on page 168 of 2023 version of "Valuation and Risk Models" it appears that partial 01's and key rate 01s (KR01s) are the same thing (red rectangle).
If they are not, what is the difference?

Also, according to FRM, the KR01's do sum up to DV01 (green rectangle).

 

[AUola2165]

@gsarm1987 @David Harper CFA FRM could you please advise if there is something unclear about my message above? My exam is closing fast and I would like to get some clarity in this isuse

 

[gsarm1987]

@gsarm1987 @David Harper CFA FRM could you please advise if there is something unclear about my message above? My exam is closing fast and I would like to get some clarity in this isuse

Kr01 is a type of partial duration . There are other types too, this is one of them. The thing you have highlighted in green, I can confirm with 100% conviction that it's an approximation and not exact equal. Here you see it's a quicker way to get to PF duration but not an exact one, rather an approximation. How to make it accurate? Well the more points of time your consider the more accurate it gets . K1 k2 k3 k4....... I hope it's clear? I'd also say follow your curriculum. That's the source.