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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

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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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  • $\begingroup$ I'm still kind of confused. The book states "The trade shorts about 2 face of the 77/8s of August 15, 2001, the 141/4s of February 15, 2002, and the 63/8s of August 15, 2002; shorts about 102 face of the 61/4s of February 15, 2003; and buys 100 face of the 103/4s of February 15, 2003." So it makes it seem like 1.899 is an amount of bonds. It says it shorted "about" 2 bonds. From your comment I started to think that maybe 2 bonds should be thought of as 1899 bonds which is close to 2000. Thinking it this way helped me grok the calculations but I'm not sure this is the right way. $\endgroup$ Oct 30 '20 at 6:39
  • $\begingroup$ 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. $\endgroup$ Oct 30 '20 at 12:43

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