Fixed-Income Toolbox™

zeroyield - Yield of zero-coupon instruments given price

Syntax

Yield = zeroyield(Price, Settle, Maturity, Period, Basis, 
EndMonthRule)

Arguments

`Price`	Scalar or vector containing prices of instruments.
`Settle`	Settlement date. A vector of serial date numbers or date strings. `Settle` must be earlier than or equal to `Maturity`.
`Maturity`	Maturity date. A vector of serial date numbers or date strings.
`Period`	(Optional) Scalar or vector specifying number of quasi-coupons per year. Default = 2.
`Basis`	(Optional) Day-count basis of the bond. A vector of integers. 0 = actual/actual (default) 1 = 30/360 (SIA) 2 = actual/360 3 = actual/365 4 = 30/360 (PSA) 5 = 30/360 (ISDA) 6 = 30/360 (European) 7 = actual/365 (Japanese) 8 = actual/actual (ISMA) 9 = actual/360 (ISMA) 10 = actual/365 (ISMA) 11 = 30/360E (ISMA) 12 = actual/365 (ISDA)
`EndMonthRule`	(Optional) End-of-month rule. A vector. This rule applies only when `Maturity` is an end-of-month date for a month having 30 or fewer days. 0 = ignore rule, meaning that a bond's coupon payment date is always the same numerical day of the month. 1 = set rule on (default), meaning that a bond's coupon payment date is always the last actual day of the month.

Description

Yield = zeroyield(Price, Settle, Maturity, Period, Basis, EndMonthRule) calculates the bond-equivalent yield for a portfolio of general short and long term zero-coupon instruments given the price of the instruments. Yield is a column vector containing a yield for each zero-coupon instrument.

When the maturity date is fewer than 182 days away and the basis is actual/365, the function uses a simple-interest algorithm. If maturity is more than 182 days away, the function uses present value calculations.

When the basis is actual/360, the simple interest algorithm gives the money-market yield for short (1 to 6 months to maturity) Treasury bills.

The present value algorithm always gives the bond equivalent yield of the zero-coupon instrument. The algorithm is equivalent to calling bndyield with the zero-coupon information within one basis point.

Formulas

To compute the yield when there is zero or one quasi-coupon periods to redemption, zeroyield uses the formula

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

The elements of the equations are defined as follows.

Variable	Definition
DSC	Number of days from the settlement date to next quasi-coupon date as if the security paid periodic interest.
DSR	Number of days from the settlement date to redemption date (call date, put date, and so on).
E	Number of days in quasi-coupon period.
M	Number of quasi-coupon periods per year (standard for the particular security involved).
Nq	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.
P	Dollar price per $100 par value.
RV	Redemption value.
Yield	Annual yield (decimal) when held to redemption.

Examples

Example 1. Compute the yield of a short-term zero-coupon instrument.

Settle   = '24-Jun-1993';
Maturity = '1-Nov-1993';
Basis    = 0;
Price    = 95;

Yield = zeroyield(Price, Settle, Maturity, [], Basis)  

Yield =

    0.1490

Example 2. Recompute the yield of the same instrument using a different day-count basis.

Settle   = '24-Jun-1993';
Maturity = '1-Nov-1993';
Basis    = 1;
Price    = 95;

Yield = zeroyield(Price, Settle, Maturity, [], Basis) 

Yield =

    0.1492

Example 3. Compute the yield of a long-term zero-coupon instrument.

Settle   = '24-Jun-1993';
Maturity = '15-Jan-2024';
Basis    = 0;
Price    = 9;

Yield = zeroyield(Price, Settle, Maturity, [], Basis)

Yield =

    0.0804

References

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