Basic Bond Math Interview Question
Hi all - I am expecting to receive an interview question on basic bond math that I was hoping someone here may have some insight into. The question will likely be as follows:
If you buy a bond at 80 (discount to par) with a 5% annual coupon, hold it for 5 years and sell it at par, what is your return?
Believe this will be a mental math question, so not expecting to be allowed to use a calculator. My simple brain assumes you take the 5% annual coupon and add the average annual return upon sale (20/100 = 20%/5 = 4%) to it to approximate a ~9% return, but I am almost sure that is oversimplifying it/just wrong in general. Any insight would be greatly appreciated!
Close. The growth of 80 to 100 should have 80 as the denominator, not 100.
That's a 25% return over 5 years = ~5%/year + the 5% coupon puts you at 10%. Actual math is 10.3%.
Semantics...this math is based on the bond "maturing" at par, not being "sold" at par.
Ah that makes sense. Thank you so much for the explanation - facepalm on using 100 instead of 80 as the denom.
It should be this: 5/80 = 6.25% from the coupon + (100-80)/5 = 4% from the yield = ~10.25% YTM
Total return (not annualized like YTM) is 100 (from principal) plus 25 from coupon (over five years) divided by 80 (what you paid for the bond) - 1 = 56.25%
Shouldn’t the actual be 11.25%? $5 per year coupon + $4 from discount ($20/5 years) so $9 of annualized yield (assuming $100 par). $9/$80 = 11.25%.
Yeah first comment is wrong, also for the 5% the denominator is 80, ie 6.25%
You arent getting the yield annually, thats the thing. You get it at EOP, which reduces IRR due to TVM
There we go, mixed up YTM / IRR with total annualized return
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