Rule of thumb to calculate bond price change from IR move

Is there a quick rule of thumb to calculate the change in value of a bond based on an interest rate move? For example, if the 10-yr yield goes from 1.75% to 1.00%, is there a quick way to find the new price based on current price and relative interest rate move? TIA

Comments (14)

Oct 12, 2016

Very roughly, yes...

If you're long 100MM of a 10y bond, your DV01 should be roughly 100k/bp (this is v approximate). On a 75bp rally, your PNL should be 7.5MM. From there it's easy enough to get the change in price.

This is obviously, a VERY approximate calculation. This might help with the understanding:
https://www.cmegroup.com/trading/interest-rates/fi...

Oct 12, 2016

Multiply the yield change by the modified duration. This works for small yield changes. To get a better result make a convexity adjustment.

    • 1
Oct 12, 2016

If they are otherwise identical bonds, with the same coupon payments, default risk, etc. it's probably a liquidity premium that would cause the more recently issued bond to demand a higher price. This is typically seen in US Treasuries. Unless I'm missing the point of your question...

Oct 12, 2016

Thanks for the replies. I got the question from a friend so I'm not completely sure what the crux of the question is. I would've guessed that it might be to do with the fact that bonds (which tend to be issued at a fixed coupon rate) from 2005 have a higher coupon (as the interest rate was higher back then)?

If so, it would be priced higher, correct? Otherwise, if the maturity, coupon, risk (discount rate) and principal are the same, the bonds would be priced the same (except for the liquidity premium wishuponastarr mentioned)?

Oct 12, 2016

Tax exempt or taxable? Taxable relatively the same priced at 100 or slight oid, exempt would have higher price now assuming the market standard coupon for both years

Oct 12, 2016

BUMP

Oct 12, 2016

I would agree that the main answer is that 2005 bonds most likely had a higher coupon in a higher rate environment so as rates have gone down, that bond becomes more valuable. This is assuming nothing material has changed with the business. The business could have dropped from IG to HY and now be printing a higher coupon.

As mentioned, you could bring up other points like the new bond will be more liquid but that really only applies to bonds in the last few years where rates have been similar. Same remaining life so you are likely issuing a 20-year tenor to match the 30-year (assumed) of the first one so that presents some issues. The new bond could have some call features or be subordinated to the old bonds. The old bond might be a private placement. The size of the offerings come into play.

The basic answer is, holding all else equal, the old bond is worth more because of the higher coupon. But this seems more open ended just to see what you can come up with. I'd just be careful about how you bring this up in an interview because the interviewer might press you and if you don't understand, you might come off looking worse.

Oct 12, 2016

Thank you so much for the additional clarification and for everyone for your input!

Oct 12, 2016

Most banks have their internal sources (ie trading desks)for bond pricing.

I think the only public place for prices is Bloomberg.

Oct 12, 2016
Oct 12, 2016
BrokenIncome:

TRACE

http://www.finra.org/RegulatorySystems/TRACE/Corpo...

Oh wow, I dind't know you can pull TRACE quotes online. TRACE should only be used as a source though if it's a high volume trade. Then again, since there's no other public sources, and it's not like you're quoting these prices to clients, TRACE should be fine.

Oct 12, 2016
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