How Coupon Accrual Affects a Bond’s Holding-Period Return
Summary
The document compares holding a high-coupon bond bought just after a coupon payment with buying it shortly before the next payment. With the same clean price and a hold to maturity, the earlier purchase also pays accrued interest, while the next coupon arrives soon after purchase. The worked example shows a lower return for that second cash-flow comparison because the accrued amount earns no return over the short holding period.
The explanation expresses the effect algebraically: when an investment with a positive return is combined with an additional amount earning zero, the combined return falls. It cautions that the two cases are not equivalent comparisons of invested capital. The example assumes no default, foreign-exchange risk, or coupon reinvestment and holds the bond to maturity; it does not establish a general advantage from waiting to buy after a coupon. Accrued interest, clean price, and the timing and reinvestment of all cash flows must be handled consistently when comparing returns or yield to maturity.
Key ideas
- Accrued interest raises the buyer’s cash outlay when a bond is purchased between coupon dates.
- A coupon received soon after purchase contributes little or no return if it is treated as cash earning zero.
- Adding an amount with zero return to an investment with a positive return lowers the combined return percentage.
- Comparisons should account consistently for accrued interest, cash-flow timing, and coupon reinvestment assumptions.
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Full text
# Impact of accrual on bond total return
# Impact of accrual on bond total return
A bond pays 30% annual coupons, the next coupon is in 1 month and the bond will mature in 13 months, reimbursement at maturity is 100.
Assuming the same clean price in both scenarios (90), no FX risk, no reinvestment of coupons, and the bond is held until maturity.
2 scenarios
1) I buy bond immediately after the coupon
cash flows until maturity:
OUT: clean price only = 90
IN: Notional+coupon in 13 months = 130
at maturity total return = (130-90)/90 = 44%
in this case the YTM will be very close to the total return of the bond
2) I buy the bond immediately,
cash flows until maturity:
OUT: clean price + accrual for 11 months = 90 + 30 * (11/12) = 117.5
IN: coupon in 1 month and Notional+coupon in 13 months = 30 + 100 + 30 = 160
at maturity total return = 160/117.5 - 1 = 36%
in this case the YTM will be above the total return of the bond because YTM doesn't keep into account the the accrual?
==> Based on the above it seems it's better from buying after the cpn. Does this make sense and how to derive a general rule for the impact of accrual on the total return of a bond?
## Answer by Attack68 (score 5, accepted)
https://quant.stackexchange.com/a/80730
If you break down your question into its respective components it reads like this:
- I pay 90 and get back 130, so my return is $\frac{130}{90}-1$=44%.
- I pay out 117.5 (and get back 30 almost immediately which accrues no interest going forward) and get back another 130 at maturity. I evaluate my return as $\frac{160}{117.5}-1$=36%.
So yes option 1) will always look better because of the mathematical fact:
$$ \frac{b}{a} \ge \frac{b+k}{a+k}; \quad b>a>0, k>0 $$
I uphold the view that the comparison is meaningless, because you have introduced an additional 30 (which is $k$) which accrues at 0% so the overall return has to be lower.
But the overall answer is, yes it is better (assuming no default) to invest all of your money returning 40%, than to invest part of it returning 40% and some of it returning 0%.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.