(1+r)^(T/360) vs. (1+r*(T/360))

CFA Level II
#1

Hey guys,

Am confused on how to convert annualized rates to per-period rates. For example, when you are finding discount factors to calculate the price of a fixed rate swap, you would multiply each annualized rate by T/360 instead of taking it to the T/360 exponent.

For example, if 90-day annualized Libor is 3.13%, then Z1 is 1/[1+.0313(90/360)] instead of 1/[1.0313^(90/360)]

This doesn’t end up making that big of a difference, but does anyone have an easy way to remember which method to use when?

#2

LIBOR is a nominal interest rate; that’s why you multiply by (days/360). Similarly for Eurobor.

Virtually everything else in Level II will be given as an effective annual rate, so you raise it to the power (days/365). Bond yields will be given as BEY, a nominal rate with semiannual compounding, so you divide by 2, then compound for the appropriate number of semiannual periods.