Key rate duration Tuckman.

[Arka Bose]

Tuckman writes,
'Turning now to interpreting the results, the key-rate profile in Table 5.2 shows that the interest rate exposure of the 30-year C-STRIPS is equivalent to that of a long position in a 30-year par bond, a smaller, short position in a 10-year par bond, and even smaller short positions in 5- and 2-year par bonds. This accords with the intuition stated at the beginning of this subsection, that the 30-year par bond’s coupons create exposures at shorter terms that have to be offset by shorts of short-term par bonds'

I did not grasp the portfolio concept. Why does he say that the shorter term bonds have a short position.
Also, I would like to know why is the price of the 30 year old coupon increasing even if i shock the key rates by a positive 1 bp? Increasing the key rates should bring down the value?
Please help me on this.

 

[Dr. Jayanthi Sankaran]

Hi @arkabose,

I know that this is a tough one. I have read the above several times. I am going to hazard a guess here - what Tuckman is saying is that the 30 year par bond coupons do create interest rate exposures at the shorter end of 2 years, 5 years and 10 years, in addition to the interest rate exposure at 30 years. So, in order to delineate the interest rate exposure of only the 30-year C-STRIPS, we replicate it with a long position in the 30-year par bond and short positions in the 10-year, 5-year and 2-year par bonds. In other words the interest rate exposure at the shorter ends will be immunized against all possible interest rate scenarios....

Hope that helps somewhat
Thanks!
Jayanthi

 

[Arka Bose]

Yep, thats right, you are absolutely spot on! I figured that quite sometime ago, but phew! it took me a while!
Basically he way saying the C strips (the stripped ZCB's) will be equal to the portfolio that he mentioned. (so no interest rate risk if the bonds are ZCB)
The underlying concept there is portfolio replication.

Tuckman has to be the toughest author i read

 

[Dr. Jayanthi Sankaran]

Actually the first four chapters of Tuckman are pretty good, except for the equations of Modified Duration, DV01s and Yield Based convexity. However, these are intuitive too! But Chapter 5 is pretty tough

Jayanthi

 

[QuantMan2318]

This topic consumed most of my time as well while preparing for part I,

So, in order to delineate the interest rate exposure of only the 30-year C-STRIPS, we replicate it with a long position in the 30-year par bond and short positions in the 10-year, 5-year and 2-year par bonds. In other words the interest rate exposure at the shorter ends will be immunized against all possible interest rate scenarios....

, That was perfect; The 30 year par bonds had the coupons that needed to be corrected by the short positions in the 2, 5 and 10 year bonds

Why does he say that the shorter term bonds have a short position.
Also, I would like to know why is the price of the 30 year old coupon increasing even if i shock the key rates by a positive 1 bp? Increasing the key rates should bring down the value?

And again I also thought of it as a situation where the sum of all the Key rate shocks should equal a one basis point increase overall, necessitating a short position in the shorter end as the Bond Value increases with the shift and thus the negative sign and the long position at the maturity of the par bond equal to the C STRIP where we have the usual inverse relation, I presumed this relationship because of the fact that by pulling one Key rate string upward at the short end the value of the CSTRIP increased as the 30 year yields were unaffected. This is merely my conjecture, don't know if its correct

 

[Dr. Jayanthi Sankaran]

Will have to think through this one - I think (though I am not sure at all, about this) it has something to do with key rate duration and the non-parallel shift in the key rates. Will get back to you, on this, if in case I get a brainwave

Thanks!
Jayanthi

 

[Dr. Jayanthi Sankaran]

On second thought, since the shorter term bonds have a short position, as the key rates increase by 1 bp, their value will also increase. But as regards the 30 year bond, don't have the answer

Thanks!
Jayanthi