Simple Interest and Compound Yield for Discount Bonds

Summary

The document compares two annualized yield measures for a short maturity zero-coupon security. Bond equivalent yield scales the return relative to the purchase price by the fraction of a year represented by the days to maturity, reflecting simple interest. Yield to maturity instead computes the annual compound rate implied by the face value, present value, and time to maturity.

The two measures coincide for a one-year term measured as 365 days, but can differ for shorter maturities because simple and compound interest treat elapsed time differently. The answer notes that the appropriate convention depends on the instrument’s market practice, giving Canadian Treasury bills as an example of securities quoted using simple interest. The discussion is brief and does not provide a general survey of market conventions or address day-count variations beyond the stated 365-day basis, so users should check the convention applicable to the security being valued.

Key ideas

• Bond equivalent yield expresses a discount security’s return using simple interest.
• Yield to maturity expresses the implied return using compound interest.
• The two measures agree for a one-year term on a 365-day basis but can diverge for shorter terms.
• Instrument market convention determines which yield definition is appropriate.
• Canadian Treasury bills are cited as an example of simple-interest quoting.

Tags

# yield concept for a short maturity zero coupon bond


# 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?

## Answer by Bjørn Kjos-Hanssen (score 3)

https://quant.stackexchange.com/a/37617

(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).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.