# Modified Duration of Liability

How to calculate the “modified” duration is of oof liabilty (single or multiple ) )) ? Is it calculated in the same way as that of the “modified” duration is of oof bonds?

modified duration is simply the macaulay duration divided by 1+r where r is the effective interest rate. macaulay duration is the weighted average of cash flows incurred in the liability i.e. the time period weighted cash flows to the total cash flow.

Assumptions are that the yield curve is flat, the cash flows do not depend on prevailing interest rate i.e. they’re independent of the interest rate and that any interest rate changes are parallel .

Liabilities are assumed to be like the other side of investing in bonds i.e. being short the bond.

Also, take a look at the footnotes of the CFA reading on duration it shows Modified Duration roughly equal to Macaulay Duration which is (the percentage change in price for a percentage change in yield).

vs the traditional definition of duration as the percentage change in price for a 100 basis point change in rates.

Looks like Macaulay duration is used often with immunization strategies.

Also, take a look at the footnotes of the CFA reading on duration it shows Modified Duration roughly equal to Macaulay Duration which is (the percentage change in price for a percentage change in yield).

vs the traditional definition of duration as the percentage change in price for a 100 basis point change in rates.

Looks like Macaulay duration is used often with immunization strategies.

I understand that the Modified Duration shall be valid only if the cash flows do not depend on prevailing interest rate. But why the yield curve shall be flat and any interest rate changes shall be parallel ?

Furthermore, which duration (Macaulay or Modified) shall be applied in ALM ? The text does not specify clearly.

another factor has also not been specified explictiy… small parallel changes of rate ONLY.

those are the basic requirement of duration.

for a bigger change of rates - duration simply does not cut it. you need to use convexity as well, and even that does not work for twists … so you go to the other things - such as PV Dist of Cash flows and the Key Rate Duration concepts.

I have so many questions regarding ALM (CFAI Text P.25~42 of Vol 4) ! Very much confused ! It seems that some concepts are introduced roughly/vaguely.

but in curriculum they have used these terms interchangeably i.e. Effective duration ~ Modified duration ~ Macaulay duration. Do we need to get into their definitions?

Before this I did not pay any heed towards this & only got into the flow of understanding duration the same way.

Since duration and dollar duration play an important role in ALM, so I can not have a good understaning without clear definitions.

Besides the definition of duration, guranteed rate of return/assured rate of return/target return/imminization target rate of return are used in text. I am very much confused by these terms.

Also, it seems to me that this section is not written systemmatically/logically/consistently. I can not capture the whole picture, only trying to piece together.

I know I shouldn’t post it here, but it seems that this is the latest discussion on modified duration, I share what I just found on wiki.

Strictly speaking,Macaulay duration is the name given to the weighted average time until cash flows are received, and is measured in years. Modified duration is the name given to the price sensitivity and is the percentage change in price for a unit change in yield.

Modified duration is usally slightly lower than Macaulay duration. One mock question provide both durations at the same time.

tulkuu,

I agree with the definitions of Macaulay and Modified Durations mentioned by you. But which ones shall it be when the duration of the liability (liabilities) is mentioned in Reading 23 ?

At the bottom of P.28, it is stated that : a manager shall invest in a bond or a bond portfolio whose (1) duration is equal to the investment horizon (here the unit shall be in “year”).

In the middle of P.41, it is stated that : 1. (for multiple liability) The (composite) duration of the portfolio must equal to the (composite) duration of the liabilities. And the equation in footnote 27 shall for “Macaulay Duration”.

However, Modified Durations shall be used to calculate the "Dollar Duration (as in Example 6). My question : Which duration (Macaulay or Modified) is referred to in the text ?