30/360 Bond Accrual and the Limits of Calendar-Date Arbitrage
Summary
The note explains why the 30/360 day-count convention does not create a risk-free profit across January 30 and 31. Under the convention described, accrued interest is unchanged on those dates: a buyer owes the same accrued amount on either day, so holding the bond overnight does not add an extra day of interest income. The clean price is determined by market factors such as interest rates and credit spreads, not by accrued interest alone, and it can change from one day to the next.
The discussion allows that a relative-value opportunity might exist between otherwise similar bonds with different day-count conventions. Any such difference would represent only a small amount of interest and could be outweighed by bid-ask spreads and transaction costs. The answer does not analyze a specific bond quote, funding arrangement, or market scenario, so it is a conceptual explanation rather than an arbitrage test for an actual trade.
Key ideas
- The clean price reflects market valuation factors rather than accrued interest alone.
- Under the stated 30/360 convention, accrued interest is the same on January 30 and 31.
- Holding the bond across those dates does not generate an additional day of accrued-interest income.
- A day-count mismatch between similar bonds could create a small relative-value difference, subject to trading costs.
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Full text
# 30/360 convention on bond pricing # 30/360 convention on bond pricing I have a question regarding 30/360 convention on bond pricing. Say the bond starts trading Jan 1st, and on both Jan 30th and 31st, the bond will accrue 30 days of interest on both days. Since we calculate the clean price on the 30/360 day convention as well, the clean price will be the same on Jan 30th and 31st. So dirty price quoted for the bond will be the same for Jan 30th and Jan 31st. But if we know that prices on both days are the same, and we can short the bond on Jan 30ths and put it in a bank, and buy it back on Jan 31st for the same price, doesn't this mean there is an arbitrage? It is essentially an arbitrage? Apologies if I am missing something obvious and dumb. ## Answer by D Stanley (score 3) https://quant.stackexchange.com/a/81731 > Since we calculate the clean price on the 30/360 day convention as well, The "clean price" of a bond has nothing to do with the amount of interest accrued - it it much more related to underlying interest rates, credit spreads (for corporate bonds) and other factors. So there is absolutely no guarantee that the price of the bond will be the same on both days. > on both Jan 30th and 31st, the bond will accrue 30 days of interest on both days This may just be a poor choice of words, but a better explanation in my opinion is that no interest accrues on Jan 31. Whether you buy the bond on Jan 30 or Jan 31, you will owe the seller 30 days' of accrued interest. It also means that if you buy the bond on the 30th and sell it on the 31st, you do not get any additional "income" from interest - just from any change in the price of the bond. So there's not really an "arbitrage" with this bond in isolation - you could possibly find some very small arbitrage between similar bonds with different daycounts, but it would only be for a days' worth of interest (and it's generally hard to find completely identical bonds except for daycount), and may be totally offset by bid/ask spreads and other transaction costs.
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