So- I THINK I understand the concept that the LIBOR curve is quoted as annualized rates so if given like a 180 day libor rate quoted at 5% we simply divide by 2 to get the discount factor to use in discounting cash flow in the future. But why then in the fixed income section - if we are discounting a bond with a coupon payment in say 180 days, the discounting factor would be calculated differently right?
To discount a payment using LIBOR: looks something like 1/(1 + 5%/2)
But with bonds - it’s 1/(1 + 5%)0.5
I’m super confused about when and why to use the various conventions…don’t we use the 1st for derivatives and the second for regular bonds? I assume I’m missing something with regards to weather or not the rate given is a LIBOR rate or just a non-annualized rate?
thnx
The convention that you use is the convention that applies to a specific rate quotation, not to a specific type of security.
LIBOR is quoted as a nominal rate, so you multiply the (quoted, annual) rate by n/360 to get the effective rate for the payment period.
The YTM on bonds is usually quoted as BEY, which is also a nominal rate. You divide the annual rate by 2 to get the semiannual effective rate.
You would use (1 + r)1/2 only when the annual rate is quoted as an effective annual rate. They should tell you that that’s how the rate is quoted.
(By the way: I edited your post to make it easier to read. Please use parentheses and superscripts; they help immensely.)
Will do. And super helpful, thank you!
You’re quite welcome.
The superscripts, subscripts, and underlining are recent additions, but they make for much more readable posts here.