Why Bond Arbitrage Trades Use Fractional Face Amounts

Summary

The exchange explains why a bond arbitrage example can show a fractional face amount even though a bond’s coupon is quoted as a rate on par. The key distinction is between the denomination and trading increment of an individual bond and the aggregate face amount used to describe a portfolio or arbitrage position. An institutional trader can combine many eligible bond units into a large short position whose total face amount is not a round multiple of one hundred or one thousand.

The answer illustrates this by noting that bond markets impose minimum trade sizes and increments, while those constraints become small relative to institutional notionals. A fractional amount in an arbitrage table should therefore be read as the scaled quantity of bonds in the position, with coupon cash flows calculated proportionally from that aggregate face amount. The response gives examples of minimum amounts for different bond sectors, but these are recalled market conventions and may vary by issue or over time. It does not address settlement, accrued interest, or the mechanics of borrowing a specific bond.

Key ideas

• Coupon rates apply proportionally to the total face amount of a position.
• An aggregate bond position can have a non-round face value even when individual units trade in set increments.
• Minimum denominations matter less to institutional trades with large notionals.
• Trading increments vary across bond sectors and may change over time.

Tags

# How can the face value of a bond not be a round number?


# How can the face value of a bond not be a round number?












I'm reading Bruce tuckman's "fixed income securities" and I'm at the section that is explaining arbitrage. In the chart below, the cash flows are based off the biannual interest rates * the face amount of the bond.

For example, a short of 2.114 of the 6.(3/8)s of August 15, 2002, incurs an obligation of 2.114×6.(3/8)%/2 or .067 on November 15, 2001, and May 15, 2002, and an obligation of 2.114×(100%+6.(3/8)%/2) or 2.182 on November 15, 2002.

My question is, why are the cash flows based off face values that are not round numbers like 100, 1000? How can it ever be the case like in the third column where the face value of a bond is a ratio 2.114?

I realize the price of a bond can change but the interest payments should be based on par so I'm not understanding how par can be anything but 100, 1000 etc

## Answer by Dimitri Vulis (score 3, accepted)

https://quant.stackexchange.com/a/58958

Almost all bonds have a "minimum amount" and "minimum increment", in the thousands of dollars, which is a lot if you're a retail investor working with thousand-dollar notionals, but is effectively zero if you're an institutional investor working with million-dollar notionals. As I recall, U.S. treasury is now USD 100 minimum, most corporate bonds are USD 1,000 minimum, and most munis are USD 5,000 minimum.

E.g., shorting USD "18,990,000" of some bond is not a problem, but shorting USD "18.99" would be.

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