Rate Duration

Hi, all:

I need your help since I am very much confused by the definition of “Rate Duration”. The defintion of “Rate Duration” at the bottom of Page 363 on CFAI Text Vol 5 is :

The percentage change in the value of a (bond) portfolio if only one maturity’s yield changes while the yield for all other maturities is unchanged.

Referring to practice question 6.A. on the same page and the solution to this question on Page 390, my question is:

What will be the change in the portfolio’s value if there is a 50 basis point change in the yield for “all maturities” (i.e. a parallel shift of the yield curve, similar to that in Exhibit 1.a. on Page 360) ?

First of all you shouldn’t be worried about Rate Duration, Key rate Duration and Parallel or Nonparallel shifts in Yield curve in Level 1. Its clearly written that These topics will be covered in Level II that’s why there is not much explaination about them.

Yield curve is a series of yields for each marurity. “Rate” is an interest rate/ yield for a particular maturity. If you have a portfolio of having maturities up to 20 yrs then the yield curve of your portfolio will have 20 yields (every maturity has a seperate yield) and each single yield is called “Rate”

If “10 yr rate duration is 4”, then it means if 10 year interest rate / yield changes by 100 bps then the portfolio value will be changed by 4%. As mentioned earlier yields are different and seperate so 10 yr rate duration is related only with 10 yr yield and other yields remains unchanged…

Now talk about duration. Duration is an approximate percent price change measure. Approximation mean that duration assumes (by default) that 100 bps change is same for all maturities (Parallel shift in yield curve.) Parallel shift means if interest change by 2% then one yr rate is changed by 2%, 10, 15 and 20 yrs are also changed by 2 %, which does not happen in reality because of embedded options, cap, floor, put call options, credit risk etc etc with bonds and most inportant, the relationship of yield and maturity is not linear it is covex (which you learn in reading 59 page 613). So there are other types of duration (effective duration etc) which measure nonparallel changes.

and what is meant by this , (What will be the change in the portfolio’s value if there is a 50 basis point change in the yield for ”all maturities) is that, here change in interest rate affecting all maturities in same way so change is Parallel (Parallel yield curve shift). and this type of changes can be measured by (simple) duration.

Hi, Raza Syed :

Thank you for your response ! But I still have following questions :

  1. If a bond portfolio has a duration of 6 (which is calculated by weighting the duration of each maturity, please refer to Page 632 of CFAI Text Vol 5) and the duration of a bond of 10 years maturity in the portfolio is also 6.

What is the difference in the change of a bond portfolio’s value between the following two scenarios ? Is it that the change in the portfolio’s value same (both are 0.5% x 6 = 3%) ?

A. Only the yield of one maturity (e.g., 10 years) in a bond portfolio changes by 50 basis points.(As in practice question 6.A. and the solution to this question on Page 390).

B. A 50 basis points change in the yields for ”all maturities” (i.e. a parallel shift of the yield curve, similar to that in Exhibit 1.a. on Page 360).

  1. Where (in CFAI text) can I find that it is written these topics will be covered in Level II ?

Thank you very much !

Sorry for late reply, I was busy

  1. Where (in CFAI text) can I find that it is written these topics will be covered in Level II ?

Page 360 6th line, changes in yield curve will be covered in Level II.

Page 363 2nd Para, Last line, Key duration will be covered in Level II.

portfolio examples are same on pages 632 and 360. either individual bond or a portfolio duration assumes parallel yield curve shift which is drawback of duration because in reality it doesn’t happen.

A. Only the yield of one maturity (e.g., 10 years) in a bond portfolio changes by 50 basis points.(As in practice question 6.A. and the solution to this question on Page 390).

I mentioned earlier this is not duration. Here Rate duration is asked because its only related with one maturity (just think its a spot rate of specific maturity). In rate duration only one maturity is affected but in duration all maturities are affected by same change.

Hi, Raza Syed :

Thank you for your response ! It seems that you have a very good understanding about “fixed income” and I will like to take this opportunity to learn more from you even thogh these topics will be covered in Level II.

My further question :

Will the change in market value (in %) of the portfoluio will be same for the two scenarios in my previous message ?

If the changes in the market value of the portfolio are same (both are o.5% x 6 = 3.0%), why the 0.5% change in yield of only one maturity (the 10-year maturity in my example, as in my previous message) in the portfolio has the same impact as the 0.5% changes in yields of “all maturites” of the bonds in the portfolio ?

Your further response will be much appreciated !