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Yield of zero-coupon instruments given price

computes
the yield of zero-coupon instruments given price. `Yield`

= zeroyield(`Price`

,`Settle`

,`Maturity`

)`zeroyield`

calculates
the bond-equivalent yield for a portfolio of general short and long-term
zero-coupon instruments given the price of the instruments. In other
words, if the zero-coupon computed with this yield is used to discount
the reference bond, the value of that reference bond is equal to its
price

adds
optional arguments for `Yield`

= zeroyield(___,`Period`

,`Basis`

,`EndMonthRule`

)`Period`

, `Basis`

,
and `EndMonthRule`

.

To compute the yield when there is zero or one quasi-coupon
period to redemption, `zeroyield`

uses the formula

$$Yield=\left(\frac{RV-P}{P}\right)\times \left(\frac{M\times E}{DSR}\right)$$

.

*Quasi-coupon periods* are the coupon periods
which would exist if the bond was paying interest at a rate other
than zero. The first term calculates the yield on invested dollars.
The second term converts this yield to a per annum basis.

When there is more than one quasi-coupon period to the redemption
date, `zeroyield`

uses the formula

$$Yield=\left({\left(\frac{RV}{P}\right)}^{{}^{\frac{1}{Nq-1+\frac{DSC}{E}}}}-1\right)\times M$$

The elements of the equations are defined as follows.

Variable | Definition |
---|---|

| Number of days from the settlement date to next quasi-coupon date as if the security paid periodic interest. |

| Number of days from the settlement date to redemption date (call date, put date, and so on). |

| Number of days in quasi-coupon period. |

| Number of quasi-coupon periods per year (standard for the particular security involved). |

| Number of quasi-coupon periods between the settlement date and redemption date. If this number contains a fractional part, raise it to the next whole number. |

| Dollar price per $100 par value. |

| Redemption value. |

| Annual yield (decimal) when held to redemption. |

[1] Mayle, Jan. *Standard Securities Calculation Methods.* 3rd
Edition, Vol. 1, Securities Industry Association, Inc., New York,
1993, ISBN 1-882936-01-9. Vol. 2, 1994, ISBN 1-882936-02-7.

`bndyield`

| `cdyield`

| `tbillyield`

| `zeroprice`