View Full Version : Key Rate Duration

Tristanjade

03-30-2009, 12:50 AM

Objective (5i): calculate effective duration and key rate durations of a portfolio.

Anyone has come across a calculation example of key rate duration in the readings? I know to see price sensitivity relative to non-parallel yield curve change, we have to use KRD. What is the formula?

In Carmody practice essay #16, the solution stated KRD = maturity / (1+yield) for zero-coupon bonds. But I thought Modified Duration = Macaulay Duration (or Duration for zero-coupon bond) / (1+ yield)?

Any help is appreciated. Thanks.

Size17

03-30-2009, 03:26 PM

There's some stuff in SN-130.

I don;t have a formula memorized for KRD, just know that it is the change in the portfolio based on a change on a 'key rate' hence the name.

Simple formula - (price Change)/(2*1%*Face)

Assume $100M bond portfolio consiting of 2-yr and 5-yr bonds.

If 2-year rate changes by 1% and my portfolio changes by $4m, then KRD(2) is 2

If 5-year rate changes by 1% and my portfolio changes by $8m, KRD(5) is 4

Duration of portfolio should equal weighted sum of KRDs.

FrankieY18

04-02-2009, 11:02 PM

In Carmody practice essay #16, the solution stated KRD = maturity / (1+yield) for zero-coupon bonds. But I thought Modified Duration = Macaulay Duration (or Duration for zero-coupon bond) / (1+ yield)?

For zero-coupon bond, macaulay duration = maturity.

Allacalander

04-13-2009, 10:34 PM

There's some stuff in SN-130.

I don;t have a formula memorized for KRD, just know that it is the change in the portfolio based on a change on a 'key rate' hence the name.

Simple formula - (price Change)/(2*1%*Face)

Assume $100M bond portfolio consiting of 2-yr and 5-yr bonds.

If 2-year rate changes by 1% and my portfolio changes by $4m, then KRD(2) is 2

If 5-year rate changes by 1% and my portfolio changes by $8m, KRD(5) is 4

Duration of portfolio should equal weighted sum of KRDs.

Some clarifying questions. Why is the factor of 2 in there? I thought duration was the resulting percent change when the interest rate changed by 1%. Since the first example causes a 4% change in the portfolio, doesn't that mean the duration (KRD) is 4?

Also, wouldn't they actually be negative KRDs? I think they work the same way as regular durations, that they are defined as negatives, so a positive duration indicates a rate increase causes a value decline. Am I using too many negatives?

Car'a'carn

04-13-2009, 11:53 PM

Some clarifying questions. Why is the factor of 2 in there? I thought duration was the resulting percent change when the interest rate changed by 1%. Since the first example causes a 4% change in the portfolio, doesn't that mean the duration (KRD) is 4?

Most often the change in value is:

V_{-}-V_{+}

in this case the denominator is multiplied by 2 to account for the fact that rate goes up and down.

Also, wouldn't they actually be negative KRDs? I think they work the same way as regular durations, that they are defined as negatives, so a positive duration indicates a rate increase causes a value decline. Am I using too many negatives?

You are mixing it up here. Durations are not defined as negative, the change in price is defined as "minus" duration times other stuff. There are however few instruments, e.g. IOs, with a negative duration. Some of the key rate durations can be negative, the important fact to remember is that their sum is the regular duration.

Allacalander

04-14-2009, 10:50 AM

Dragons are the smartest!

Car'a'carn

04-14-2009, 11:24 AM

:tup:

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