I have seen Bond Durations both stated in years and % loss for a 100bps increase in yield. Is there a conversion that can get you from % loss to duration in years and vice versa?
For example, if I said the Portfolio’s Duration is 7.6%, can I tell what the Portfolio’s duration is in years?
Duration is measured in years.
Period.
CFA Institute has recently stopped showing the units, so a bond with a 4.5-year duration will be described as having a duration of 4.5. That’s wrong (or, at best, sloppy), but that’s what they do.
Never would anyone (who has a clue what they’re doing) write that a portfolio’s duration is 7.6%. If they mean that for a 100bp increase in yield the price would drop 7.6%, then they should write that the portfolio has a duration of 7.6 years (but CFA Institute will call it a duration of 7.6).
My understanding is that duration is both of those things so no conversion is necessary. It is both the time (in years) that the average dollar of principal will be repaid based on discounted cashflows, and it’s also the % change in the bonds price for a 1 point move in yield. So, 7.6 would be both the duration in years and the % change in price for a 1 point yield move.
The duration, by itself, is measured in years, not percent. Modified duration and effective duration can be used to calculate the (approximate) change in the value of a bond (or portfolio of bonds) using the formula:
% Δ price ≈ -Dur × ΔYTM
Note, however, that the (modified or effective) duration is only the first factor on the right side, not the entire right side.
Duration may be measured in years, but the practical application of duration is an estimate of the % change in price for a 1 point move in yield. They harp on this extensively in L1 and discourage investment managers from expressing duration as a measure of years to a client.
I’m not questioning the practical use to measure interest rate sensitivity.
However you use it, the units are still years.
^(This is my personal preference on the matter. What the “true” right or wrong is, I do not know.)
I understand that Macaulay duration is the weighted average cash flows stated in number of years, so when you think about it that way, duration makes sense when stated in years.
Personally, I don’t like thinking of it in years because, in my early days in finance, I confused “duration” with “maturity”. I just like to think of it as a sensitivity measure these days, kinda like beta or delta. And I think the CFA formula for effective duration lends to this, since nowhere in the formula do you see any time measure. (I guess it’s embedded in the YTM formula somehow.)
The units on YTM are %/year, so when you divide by ΔYTM, you end up with years in the numerator.