Upfront Cash Flow Conversion Using Duration & Fixed Income Primers in General
Siddhartha Jha's book, Interest Rate Markets, posits that one can convert an upfront cash flow into a running cash flow using duration. An example:
Eg.: an investment offers 20bps upfront (ie. .2% of notional). Over 30 years, this would not be 20bps/30, but rather 20bps/15 (15 being the duration of a 30 year bond at par).
What I don't understand is that he earlier claimed to use duration interchangeably with DV01. But clearly, the duration = 15 number he is using is not DV01. To perform this conversion, would we use Macaulay or modified duration?
(Aside: this book seems to have the incorrect formula for Macaulay duration as well--it differs from both Fabozzi and Investments by Bodie et al. I'm a beginner in fixed income, and am using Jha's book as an initial primer. Is this a bad idea?)
I have always used modified duration in the conversion, but I have a feeling it should be Macaulay. The difference never mattered to me that much. Duration is sorta interchangeable with DV01, but you need to keep the relationship between the two in mind.
I am not familiar with the book, so I can't offer any insight there. I am much more partial to Tuckman myself.
Implicitly you're referring to yield based measures of DV01 and Duration, which differ by approx. a factor of 100.
Specifically DV01 for yield to maturity is defined as (1/10,000) * dP/dy, where P = price and y = yield to maturity, and you're taking the derivative of P w/ respect to y.
Duration (or commonly modified duration) is defined as (1/P) * dP/dy
So for a par bond, Duration = (1/100) * dP/dy = 100*DV01
Whence, in the above example, Jha is basically saying 20 bps upfront is 20 bps / 15 = 1.33 bps running or equivalently, 0.20/0.15 = 1.33 bps running. If the price of the bond is far away from Par you will get different numbers. Tuckman goes into further detail about some of the differences.
If you believe that dimensionality matters (as I do), Macaulay duration should be used, rather than modified duration. I never thought about this until now.
Martinghoul: Thank you for the insight. I googled dimensionality in the context of rates, and read a paper on multi-factor polynomial vector models vs. macaulay duration: I still don't understand why Macaulay duration would better account for dimensionality, or what dimensionality you are referring to exactly (please excuse my ignorance).
Could you explain how dimensionality is better accounted for by Macaulay duration?
snipez--amazing. Thank you so much.
Do you have any advice on what an incoming analyst in rates can do to prepare, other than read books as primers? I am in particular trying to gain an in-depth knowledge of EM, but I'm not getting enough from reading the EM section in the WSJ.
Mmm, know nothing of EM, can't help sorry
USD Rates - if already working thru Jha, stick to it. Sometimes better to master material in 1 book rather hop around depends learning style. IR Swaps book by Sadr closest thing to training manual have seen. Tuckman more technical and requires more discipline to work thru, but good reference.
A good exercise is to build a yield curve from scratch in Excel/VBA. Doesn't need be fancy, don't re-invent the wheel. Take 1y T-bill, 2y, 3y, 5y, 7y, 10y, 30y yield and price quotes from WSJ or whatever and fit a curve thru those points (Youtube can actually help a lot). Then for a given maturity, obtain or assume an appropriate repo rate and compute carry. Compute roll-down. Back out the discount factor curve (zero coupon curve) from the yield curve. Compute DV01. Plot the spot yield curve and the forward yield curve, are there notable gaps between the two at different maturities? Does this mean anything?
I would only add, as I always do, a suggestion to take a look at Antti Ilmanen's papers.
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