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# How are bond prices quoted?

The price at which a quoting dealer is prepared to buy prepared to pay for an amount of a bond at a particular time is the bid, it representing the demand side of the transaction.  The price at which a quoting dealer is willing to sell an amount of a bond at a certain time is the ask, it representing the supply side of the transaction.  Taken together, a quoting dealer’s bid price and ask price are a quotation (quote).

In most markets, the quoted price of a bond is stated as a percent of the principal value of the bond.  If, for example the ask price of a fixed-coupon bond is 105.13, it will sell at a 5.13% premium to its principal value.

US Treasury notes and bonds are quoted in dollars and fractions of a dollar, where the normal fraction used for Treasury security prices is 1/32.  A decimal point separates the full dollar portion of the price from the 32nds of a dollar at the right of the decimal.  With a quote of, say, 105.08 - 105.12, a dealer is bidding \$105.25 (\$105 + 8/32 of a dollar) and asking for \$105.375 (\$105 + 12/32 of a dollar) per \$100 face value.  Very active issues are commonly quoted in 64ths of a point, which is indicated by a plus sign (+) at the right of the price, for example:

104.07+ = 104 + 7/32 + 1/64 = 104 + 15/64 = 104.234375%

The money market instruments in all markets are quoted either on a discount rate or add-on basis.  Unlike T-notes and -bonds, bills are quoted at a discount to their face value, with the discount expressed as an annual rate based on a 360-day year.  An investor's return on a bill is the difference between the purchase and subsequent sale price or the face value if held to maturity.  With a quote of 5.08-5.06, for example, the T-bill could be sold to the dealer at a yield of 5.08% or bought at a yield of 5.06%.  The pricing formula for discount and add-on instruments is as follows, where PV is the present value, FV is the expected future value paid at maturity, t is the number of days between settlement and maturity, T is the number of days in the year, DR is the discount rate stated as an annual percentage, and AOR is the add-on rate, respectively:

PVDiscount Instrument = F x (1 – (t/T) x DR
PVAdd-On Instrument = F/(1 + t/T) x AOR