View Full Version : Duration Questions

mikeman

12-03-2009, 09:17 PM

I was wondering if there are any tricks to two problems I had in regards to Macaulay and Modified Duration. I will give general questions as I am looking for a formula that could be applied to the ideas.

(1) If you are given the Macaulay Duration of an n-period annuity, how can you find the Macaulay Duration of an n+1-period annuity? You are not given the interst rates and my initial approach was to solve for the interest rate of the annuity with the given Macaulay duration and than proceed accordingly with the second duration.

(2) If you are given the Macaulay and Modified duration of the same cash flow series, how can you find the number of periods in that cash flow? I solved for the interest but I couldn't figure out a quick means for going about solving for the periods.

Thanks.

I havent thought too hard about this so it could be wrong but I'll give it a stab.

(1) I don't know

(2) Sorry I thought I had an idea but it was wrong

Do you have any specific examples, it doesn't seem like enough info is given to solve anything, or I'm just not smart enough to solve anything

Veckatimest

12-04-2009, 12:02 PM

I havent thought too hard about this so it could be wrong but I'll give it a stab.

(1) I don't know

(2) Sorry I thought I had an idea but it was wrong

Do you have any specific examples, it doesn't seem like enough info is given to solve anything, or I'm just not smart enough to solve anything

Agreed. I read the post, thought about his questions for a few moments and decided either the thread starter is withholding information or it's an impossibility. One of the two.

mikeman

12-04-2009, 12:34 PM

No that is all the information I recall from the questions. Sorry and thanks for your help.

ndruo

12-04-2009, 12:55 PM

Definitely doesn't seem like OP is giving us all the information we need. However, we can still make our guesses.

If you are given the Macaulay Duration of an n-period annuity, how can you find the Macaulay Duration of an n+1-period annuity? You are not given the interst rates and my initial approach was to solve for the interest rate of the annuity with the given Macaulay duration and than proceed accordingly with the second duration.

Are you given the coupon rate? par value? indication as to whether or not the bond is priced at par?

If you are given the Macaulay and Modified duration of the same cash flow series, how can you find the number of periods in that cash flow? I solved for the interest but I couldn't figure out a quick means for going about solving for the periods.

Again, any indication of whether or not the bond is priced at par?

From what limited information is presented, with a BIIIIG dose of me assuming things about these problems, it sounds like you're progressing to the type of situation in which you're one crazy algebra trick away from getting the exact answer. That is to say, you do enough to work to set up a single equation with the single unknown variable. Problem is, you can't simplify that equation any further since it's got that single variable spread out all over the place and it's difficult to isolate into a "variable = ~~~~~~~~~~" statement.

It's a pretty unsavory workaround, but when you get to a point like this just plug and chug. You've got what amounts to THE EQUATION and only five answer choices to pick from.

OR you're not quite aware of all of the information the problem is giving you, so neither are we.

Wolf Follower

12-04-2009, 01:53 PM

when you get to a point like this just plug and chug.

Love the expression! And it's a good thing to remember too. Sometimes I forget to even look at the answers until after I've solved the problem.

I don't have any other insight into these problems. Where did they come from, and were there no solutions attached?

WF

ndruo

12-04-2009, 02:29 PM

I forgot to explain something in the earlier post:

If the bonds are priced at par, you can use the annuity-due trick with Macaulay Duration.

For example:

A bond with n years to maturity is priced at par and pays semi-annual coupons at a nominal annual rate of 10%. You are given that the duration of the bond is 5.19679. Find the duration of a similar bond with n+1 years to maturity.

Key word: priced at par.

MacD = a-due (upper 2)-n at 10%

5.19679 = a-due (upper 2)-n at 10%

5.19679 = (.5) * a-due-2n at 5%

^^^ That is the annuity-due trick. The MacD of a bond priced at par is the PV of an annuity-due with a payment of 1, with the same number of payments and the same interest rate as the bond. This becomes much more usable when you understand the following:

a-due (upper x)-n at y%

with y quoted as a nominal rate of interest compounded x times yearly is the same as

(1/x) * a-due-(x * n) at (y/x)%

Using your calculator, you'll get 2n = 14. n = 7 years. n+1 = 8, and the rest of the solution to my made-up problem is pretty cut and dry.

mikeman

12-04-2009, 02:47 PM

Thanks ndruo it is very possible I may have overlooked the fact that is was priced at par and that MacD of a par bond is a-due(n) @ i. I wish I could remember all of the details of the question but I haven't seen the problem since August.

Thanks to all for your help, I take the exam on Monday and I wanted to avoid making the same mistake twice.

lloopy

12-04-2009, 03:12 PM

I was wondering if there are any tricks to two problems I had in regards to Macaulay and Modified Duration. I will give general questions as I am looking for a formula that could be applied to the ideas.

(1) If you are given the Macaulay Duration of an n-period annuity, how can you find the Macaulay Duration of an n+1-period annuity? You are not given the interst rates and my initial approach was to solve for the interest rate of the annuity with the given Macaulay duration and than proceed accordingly with the second duration.

(2) If you are given the Macaulay and Modified duration of the same cash flow series, how can you find the number of periods in that cash flow? I solved for the interest but I couldn't figure out a quick means for going about solving for the periods.

Thanks.

Once you have the interest and some combination of present value, future value, and payment amount, your calculator will solve for n for you.

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