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) 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).


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