Modified Duration

jjj820jjj820
in CIA.Duration

Hi Graham

Could you please help me undersatand how dividing (Macaulay duration) by (1 + yield rate) measures the sensitivity of the cash flows to the interest rate?

Thank you.

Comments

  • grahamgraham

    Actually, any type of duration is a measure of the sensitivity of cash flows to the interest rate. The source text states:

    • Duration is a concept or tool that is used to measure both the average maturity of a series of fixed future cash flows, as well as to measure the sensitivity that interest rate changes have on the present value of a series of future cash flows.

    What it means is that the longer the duration, the more sensitive the cash flows are to interest rate changes. For example, if the duration of the cash flows is 0.5 years, the interest rate will have very little effect on the present value of the cash flows. But if the duration of the cash flows is 30 years (maybe a young person is totally and permanently disabled and requires payments for the rest of their life) then the PV of the cash flows will be very sensitive to the interest rate.

  • NycxBattleNycxBattle

    In one of the battle card the answer is
    modified duration is the approximate % change in PV(cash flows) from a 100 bps change in interest rate ASSUMING no change in cash flows

    Why does the modified duration approximate change % from a 100bps change?

  • Staff-T1Staff-T1

    That's because duration is a measure of interest rate sensitivity. This should have been covered in FM

  • NycxBattleNycxBattle
    edited April 16

    haha of course I understand that duration is a measure of interest rate sensitivity..... that like the most basic of concepts.

    What I meant was specifically was why dividing by (1+i) would equate to 100 bps change in interest rate. Dividing by (1+i) to me its just a shift of one period left.

    Like shifting from "t" to "t-1". How does that translate to 100 bps?

  • Staff-T1Staff-T1

    The battle card is saying modified duration approximates the % change in PV of Cash Flows. Where does it talk about the 1+i factor and how that specifically represents the 100 bps change in interest rates?

  • NycxBattleNycxBattle

    The formula for Modified duration is Mac/(1+i) right?

    So how is that related 100 bps (1%)?

  • Staff-T1Staff-T1
    Yes that's correct. Macaulay duration approximates the % change in CF and by extension so does Macaulay duration. The 1+ i is just an extension to it.
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