PerpetualDiscount Duration Calculation

Very simple.

Given that the yield is “r” per period and that the first payment is received exactly one period hence:

Macaulay Duration = (1+r) / r

Modified Duration = 1 / r

And here’s the proof (TIF file).

Note that, strictly speaking, these are the durations of a perpetual annuity; the assumption of perpetuity gets shakier as redemption becomes more likely.

This entry was posted on Monday, August 11th, 2008 at 6:40 pm and is filed under Primers. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

4 Responses to “PerpetualDiscount Duration Calculation”

  1. PrefBlog » Blog Archive » Research: The Swoon in June says:
    September 24, 2008 at 11:56 am

    […] The algebra is linked in the post PerpetualDiscount Duration Calculation. […]

  2. PrefBlog » Blog Archive » December 1, 2008 says:
    December 1, 2008 at 11:07 pm

    […] Readers will instantly recognize this as highly suspicious, at best. The duration of a perpetual annuity is the inverse of the interest rate. Long Gilts are currently yielding about 4.5% … assuming that the Gilt Perpetuals are trading […]

  3. PrefBlog » Blog Archive » Research : Modified Duration says:
    February 15, 2009 at 3:31 pm

    […] Update, 2009-2-15: Note that the Modified Duration of a PerpetualDiscount is dependent solely upon its yield. […]

  4. PrefBlog » Blog Archive » How to Hedge Interest Rate Risk? says:
    February 18, 2009 at 5:14 pm

    […] be aware that the Modified Duration of a PerpetualDiscount is simply the inverse of its yield (see http://www.prefblog.com/?p=2582). With yields at about 7%, this means a MD of about 14 years. Many investors will blithely purchase […]

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