# yield concept for a short maturity zero coupon bond

I am trying to clarify what is the more relevant and appropriate quantity for a discount security / zero-coupon bond, that is defined by a face value, FV, a present value, PV and a time to maturity, t, (in years)

1) the bond equivalent yield is defined as:

[(FV - PV) / PV] * (365 / # of days between maturity and today)

this rate can then be re-expressed in other terms, i.e. semiannual compounding, etc

2) the yield to maturity is defined as:

[FV/PV] ^ (1/t) -1

these numbers will be equivalent in the case where it is a 1 year security which counts as 365 days, but otherwise the 2 give different results, and it seems to be more of an issue when the security is less than one year

so, i am wondering, when is it correct to use either of these definitions?

## 1 Answer

(1) corresponds to simple interest and (2) to compound interest.

For instance, Canadian treasury bills are based on simple interest (see Broverman's book Mathematics of investment and credit).