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"Obviously, the bond offers a CAGR of something close to 6.09% and a YTM of something close to 9.99%"

A bit of semantics: It's a CAGR of 6.09%, YTM of 6.09%, and an annualized HPR of 9.99%.

YTM is well defined - you can't redefine that term (at least not without expecting a lot of disagreement and confusion). YTM is calculated with PV=F/(1+r)^T (or a summation of those terms for a bond with coupons)

Therefore, for a zero, there is only one PV (present value) required (rather than a summation across all the payments), so YTM=CAGR

As you've pointed out, the errors between 6.09 to 6.17 you are encountering are related to the 360 day year assumption (and based on your use of 15.8172, likely a small error since you need to account for the 3 days between purchase and settlement)

What you are calculating is a an annualized Holding Period Return (HPR). HPR is calculated as:

(End Price - Beginning Price + Dividends) / Beginning Price

Dividing the HPR by the holding period produces the annualized HPR, and matches your 9.99%

Tom

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