# 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

• if you need to trade enough of this bond to get certain dv01 (or modified duration or whatever), then it's easier to see the dv01 of \$1 of face value and see how much face value is needed and round that (but this rounding is less material with large notionals) and eventually multiply by the current (dirty) price. Or, you could start with the (dirty) price, see how much dv01 you get for \$1 , how much \\$ you need to trade, and then get the rounded notional. Same end resut, except that the price fluctuates more. Oct 30 '20 at 12:43