Interest Rates--Bootstrapping and spot rates, Duration

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hi David

i need your help-SOS.


1) please can you elaborate on how to use the bootstrapping methodolgy to compute zero rates and spot rates.

2) is there any difference between duration and macaulay duration or they just used interchangeably? can you pls state the formulars for both if they are different and when to use each formular?

thanks a lot

 

[David Harper CFA FRM]

Hi baffour,

Re bootstrapping, you can see a simple example in the XLS @ https://www.dropbox.com/s/9nio7ioppp0yhfb/3.b.5.irate_futures_chap6.xlsx
(tab = Hull Ex 6.5 Extend LIBOR)

The idea is (under continuous compounding)

1 year spot rate = 1.0%
1 year forward rate, f(1,1), = 3.0%
As exp(1%)*exp(3%)=exp(2*2yearspotrate);
this is the key: you should be indifferent, ex ante, to investing for 2 years at the 2 -year spot rate [right hand side] as compared to 1-year and "rolling over" into 1 year forward.
it follows that 2yearspotrate = (1% + 3%)/2 = 2%; we "bootstrapped" the 2 year spot rate based on the 1 year forward.

Re Mac versus Macaulay duration, this forum has literally dozens (hundreds?) of replies to the basic definitional question (search box above). Briefly:

* Macaulay duration is handy because an T-year zero coupon bond has Mac duration of T; e.g., 10-year zero has Mac duration of T
* Mod duration = Mac duration / (1 + yield/k) where k is compound frequency, such that under the special case of continuous, k --> inf, and Mac = Mod
* Mac duration has a somewhat intuitive, if tedious calculation (see https://www.dropbox.com/s/wnclo6zs272zggg/4.c.4.durations.xlsx) because Mac duration is the weighted average time to receipt of bond cash flows; even better is "weighted average maturity of bond" (weighted by PV of cash flows)
* But Mod duration, which is lower or only slightly lower, is the technically correct risk measure at it, being a function of the first derivative, is the SENSITIVITY of the bond price with respect to a parallel (one-factor) yield shift.
* In this way, to grossly simplify: both are denoted in years, Mac is the time (maturity) metric while Mod is the risk (sensitivity) metric.

Hope that helps, thanks, David

 

[raviekiran]

Hi,

Links are not working. Please update the links.

 

[Nicole Seaman]

Hello @raviekiran

Thank you for pointing out that these links were broken. They have both been fixed above, and I awarded you a star in our weekly forum contest!

Nicole