Quick questions about duration

[wrongsaidfred]

Hi David,

First of all, I appologize for all of the emails and sincerely thank you for all of the questions you have answered for me already.

Will the test specifically say Macaulay duration or modified duration? If it just says duration, is one the default?

Does the formula for the price change of a bond use delta y in terms of continuous compounded YTM or discretely compounded YTM?

Thank you,
Mike

 

[David Harper CFA FRM]

Hi Mike,

No need to apologize. Rather, THANK YOU for speaking with Josh to give us valuable feedback so we can seek improvements!

Re: "Will the test specifically say Macaulay duration or modified duration?" Yes, GARP is well aware the difference must be specified.
If, for some unlikely reason, it is not specified, you should assume modified duration as modified duration (not Macaulay) is the SENSITIVITY metric (the % price change per unit of yield change); e.g., it is used to compute the price change. The most fundamental building block in risk measurement is the first partial derivative; and modified duration (not Mac) is this first partial derivative in the bond class (analogous to delta in options; marginal VaR in portfolio VaR; risk contribution in credit). For our purposes, Mac duration is a "means" to the end of Mod duration (b/c it's easy for a zero and because it is the time-weighted receipt to calculation, so it's a more intuitive calculation)

Re: "Does the formula for the price change of a bond use delta y in terms of continuous compounded YTM or discretely compounded YTM?"
Either. Just as the price of a bond can be discounted discretely or continuously (yet it matters: they give a different price!), as the modified duration is a first derivative of this price function, so too can its frequency as an input into the price change. Please note the input is a delta Y, as you suggest, so the technically correct delta y is the same frequency (e.g., semiannual) used to to get the modified duration. (however, as this is already a first order approximation with built-in bias, I'm not sure we worry about the frequency of the delta Y, as an input. What i mean is, unlike our other threads, I frankly would not expect GARP to write "given a 20 basis point shock with [continuous | semiannual] compounding" ... the difference is overly precise for what is an approximation anyhow).

I hope that helps, David

 

[David Harper CFA FRM]

Hi Mike,

on that last point, sorry to append, what i mean to say is:

the exam can rightfully ask you to "estimate the price change of a bond, given a duration of 7.0 years, for a 10 bps increase in yield."

While you have studied enough to spot the two technical imprecisions in the request (1. it does not explicitly say modified duration; if it were Mac duration, technically it would need to multiply by 1/(1+y/k); 2. esoterically but related, compound frequency is not specified [but it never would be]), we have quite enough to answer: approximately 7 * 0.10% = a decrease of approximately 0.70%.
(Where "approximately" is the key: we want to further know why this linear answer necessarily overstates the decrease. A better answer is "by less than 0.70%")

 

[wrongsaidfred]

Works for me.

Glad I could help out with the survey.

Thanks,
Mike