Bonds

Reference: Lynch, John J. Jr. and Jan Mayle, Stanford Securities Calculation Methods, Securities Industry Association, New York, 1986.

A = accrued days, the number of days from beginning of coupon period to settlement date.

E = number of days in coupon bracketing settlement date. By convention, E is 180 (or 360) if calendar basis is 30/360.

DSC = number of days from settlement date to next coupon date. (DSC= E - A). M = coupon periods per year (1 = annual, 2 = semiannual).

N = number of coupon periods between settlement and redemption dates. If N has a fractional part (settlement not on coupon date), then round it to the next higher whole number.

Y = annual yield as a decimal fraction, YLD% / 100.

For one or fewer coupon period to redemption:

Note: coupon (CPN) is a percentage (CPN%) in both cases.

 

 

CALL + CPN

 

 

⎛A

 

CPN⎞

 

 

 

 

PRICE =

 

 

 

M

 

–

⋅

------------------------------------

⎛DSC

Y⎞

 

---

-----------M

 

 

 

 

 

⎝E

 

⎠

 

1

+ ⎝-----------E

⋅ Y--⎠

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

For more than one coupon period to redemption:

 

 

 

 

 

 

 

 

 

N

 

 

CPN

 

 

 

 

 

 

 

 

CALL

 

 

 

 

 

 

 

-----------

 

 

 

⎛A

 

CPN⎞

 

 

 

 

+

 

∑

 

 

 

M

 

 

–

⋅

----------------------------------------

 

 

 

 

 

 

-----------------------------------------

 

 

 

 

---

-----------M

⎠

 

N

–

1

+

DSC

 

 

 

 

 

 

----

K – 1 +

DSC

 

 

⎝E

 

 

 

 

-----------E

 

 

 

 

 

1 +

Y

-----------E

 

 

 

 

 

 

⎛

1 + Y--⎞

 

 

 

 

 

 

 

 

⎛

⎞

 

 

 

 

 

 

 

⎝

⎠

 

 

 

 

 

 

 

 

⎝

 

 

⎠

 

 

 

 

 

 

 

 

Y

 

 

 

 

 

 

 

 

 

 

M

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The end of month convention is used to determine coupon dates in the following exceptional situations. This affects calculations for YLD%, PRICE, and ACCRU.

•If the maturity date falls on the last day of the month, then the coupon payments will also fall on the last day of the month. For example, a semiannual bond that matures on September 30 will have coupon payment dates on March 31 and September 30.

•If the maturity date of a semiannual bond falls on August 29 or 30, then the February coupon payment dates will fall on the last day of February (28, or 29 in leap years).

IV Appendix B: More About Calculations