Fixed Income: Key rate shift technique (FRM T4-43)

The key rate shift technique overcomes the key limitation of duration and DV01 which is that they must assume a parallel shift in the yield curve because they are single-factor risk measures. The key rate shift technique, on the other hand, is multi-factor: the term structure is carved into a limited number of "key rate regions;" in this illustration, four key rates are selected, 2-year, 5-year, 10-year, and 30-year.
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[@rachnapriyanka]

Thank you, David! I am learning so much from your videos!

[@bionicturtle]

Thank you @Rachna very grateful for your support!

[@abhishekbal399]

Fantastic ...as ever. David is GOD.

[@bionicturtle]

Aw shucks, you are TOO kind but thank you

[@prasadkamath1205]

nice video, where can I get the excel for this?

[@janghyuk2466]

Hi David, since we have a positive key rate, 0.1133 for 30 year shift, does it means that as factor increase by 1 basis point, the dollar value increase by 0.1133? Why does the price decrease to 26.20152?

[@bionicturtle]

Hi @Jang No, a positive value signifies that the bond's value will gain if the key rate drops; the price decreases to 26.20152 because the key rate profile assumes a one basis point increase. The KR01 is analogous to the DV01; KR01(k) = -1/10000 * ∂P/∂y(k); i.e., a positive (negative) KR01 implies that the position's value increases (decreases) when the rate drops by one basis point. The key rate duration, D(k) = -1/P * ∂P/∂y(k), is also similar to plain-old duration, a positive (negative) key rate duration implies that the positions value increases (decreases) when the rate drops. But the key rate profile assumes UPWARD shifts of one basis point. Thank you!

[@citizenobserver7066]

Hi-So all other things remaining same the price of bond would increase if the yield increases by 1bps for 2/5/10 year key rate? Also how to interpret the duration of -43 for 30 yr key rate?

[@qkameryun5427]

Hi, thanks for your excellent video. I am confused why there are positive KR01 and KR durations? I think as a bp increase, the bond price will always fall. Isn’t it?

[@bionicturtle]

Of course you are correct about a LONG bond position: a (key) rate increase implies a drop in value; just as a rate increase implies a drop in (vanilla) bond price. However, key rates (KR01) are much similar to duration and DV01: the formulas include a negative that negates. KR01(k) = -1/P*∂P/∂y[KR]. In this way, a positive key rate (like a positive key rate duration) implies an inverse relationship: if the key rate goes up (down), the position decreases (increases) in value. Equivalently, a positive key rate is said to be "equivalent to a LONG position in the X-rate par bond" while a negative key rate is said to be "equivalent to a short position ...". The only minor nuanced difference between a DV01 and a KR01, strictly speaking, is that a DV01 measures the price change associated with a one basis point drop, while the key rates are shocked up, so the DV01 is measuring -1 bps versus +1 bps, but that doesn't change the positive outcome for a typical long vanilla position as DV01 = -1/10,000*∂P/∂y = -1/10,000*∂P/-0.01% has the two negatives canceling into a positive Δp. Hope that clarifies how you being correct is consistent with positive key rates.

[@qkameryun5427]

Thanks man! I think I am getting there~ Can I say if we consider only the key rates of a single zero coupon bond or treasury, all the kr01s and durations for different key rates must be either all negative or all positive. Only a portfolio with longs and shorts can have positive or negative or both.

[@bionicturtle]

@@qkameryun5427 For a single zero, if the key rates are spot rates (or forward rates, arguably the most logical), then I think you are correct. But if the key rates are par rates, this is not true; Tuckman's example is famously just such a case. Key rates can be various "interest rates." A zero with par rate key rates will have a mix of signs. More here on our forum if you want to follow-up further www.bionicturtle.com/forum/threads/t4-43-fixed-income-key-rate-shift-technique.22781/

[@qkameryun5427]

Bionic Turtle Thank you so much! You are genius

[@TheBartlord]

Hi David, thanks for the video, it's very clear. One question though: Since the bond only has one cash flow, that is, after 30 years, why do shifts earlier on in the curve result in a change in present value of the bond in the 2/5/10 year cases wrt the initial present value? A shift in the 30 year par yield leads to a different discount factor for the (only) cash flow, and thus in that scenario we indeed get a different present value, but if I understand it correctly, in the other cases we should find the same present value every time since we don't shock the par yields affecting the discount factor to be used for the cash flow. Hope that made sense. Thanks!

[@bionicturtle]

Hi Bart, yes this is easily the most challenging aspect. I followed Tuckman, as mentioned who illustrates/selects PAR YIELDS as the key rate. We do not need to choose par yields; e.g., if we use spot rates, then of course the 30-year spot rate will be unaffected by (e.g) the shift of the 10-year spot rate. But par yields are advantageous as the key rate WHEN the hedging securities are (approximately) par bonds; i.e., the hedging solution is easier. The downside to par yields (mostly) is what you are pointing out: a shift in the 10-year par yield (even as it implies no shift in the 30-year PAR YIELD per the interpolation) DOES INDEED impact the 30-year spot rate (and therefore of course the 30-year discount factor). This is counterintuitve but is explained (somewhat) in Tuckman, can be discussed further in my forum, or if you like here is my XLS where I perform the actual calculations and you can see why it must be true www.dropbox.com/s/1w22978jn7pkobp/071719-fixed-income-key-rates.xlsx?dl=0 Thanks,

[@TheBartlord]

Bionic Turtle Hi David, thanks for your reply. Is there any way you could give some more intuition about the formula used to compute the “alternative” discount factors which take into account the fact that these are par bonds? I would move this discussion to the forum if not for the fact that understanding this to me seems like a key aspect of getting the entire picture, and other viewers might be interested in this as well.

[@bionicturtle]

@@TheBartlord I assume you mean: what is the intuition behind how shocking a 10-year (or 5-year) par yield, as the selected key rate, will impact the 30-year discount factor (or equivalently, the 30-year spot rate)? More generally, how can shocking an X-year par yield impact zero rates that are outside (greater than) its own region? That calculation is shows in the XLS but I can attempt an intuitive explanation by building on Tuckman's, but i'll prefer to do that in our forum and then share the link from here ... let me know if that's the right question (because the other hard question is maybe: why are par bonds better for hedging?)

[@TheBartlord]

@@bionicturtle I posted my question to the VRM youtube section but the post was deleted after a comment by Nicole Seaman asking why I posted the question where I did. Please tell me if I should post it elsewhere. So indeed, I am interested in how shocking an X-year par yield can impact zero rates that are outside (greater than) its own region, and more specifically, the calculation (in your spreadsheet, for example cells K34:K92 in the main sheet). How did you derive this formula for discount factors constructed from par yields? But aside from that, I'm also interested in your last point, why par bonds are better for hedging.

[@bionicturtle]

@@TheBartlord Nicole did not delete you post (we would never do that to you!), she MOVED it under the thread devoted to this video (the same link that's in the description), where I will respond when I get a chance (probably tomorrow b/c i am recording today), please see here at www.bionicturtle.com/forum/threads/t4-43-fixed-income-key-rate-shift-technique.22781/

[@dangharaa]

Could you share the excel file?

[@arjavjain5671]

nuh uh