bndyield (Financial Toolbox)

Yield to maturity for a fixed income security (SIA compliant)

Syntax

Yield = bndyield(Price, CouponRate, Settle, Maturity, Period, Basis, 
EndMonthRule, IssueDate, FirstCouponDate, LastCouponDate, 
StartDate, Face)

Arguments

Required and optional inputs can be number of bonds (NUMBONDS) by 1 or 1-by-NUMBONDS conforming vectors or scalar arguments. Optional inputs can also be passed as empty matrices ([]) or omitted at the end of the argument list. The value NaN in any optional input invokes the default value for that entry. Dates can be serial date numbers or date strings.

Price
Clean price of the bond (current price without accrued interest).

CouponRate
Decimal number indicating the annual percentage rate used to determine the coupons payable on a bond.

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) Coupons per year of the bond. A vector of integers. Allowed values are 0, 1, 2, 3, 4, 6, and 12. Default = 2.

Basis
(Optional) Day-count basis of the bond. A vector of integers. 0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365.

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.

IssueDate
(Optional) Date when a bond was issued.

FirstCouponDate
(Optional) Date when a bond makes its first coupon payment. When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure.

LastCouponDate
(Optional) Last coupon date of a bond prior to the maturity date. In the absence of a specified FirstCouponDate, a specified LastCouponDate determines the coupon structure of the bond. The coupon structure of a bond is truncated at the LastCouponDate regardless of where it falls and will be followed only by the bond's maturity cash flow date.

StartDate
(Future implementation; optional) Date when a bond actually starts (the date from which a bond's cash flows can be considered). To make an instrument forward-starting, specify this date as a future date. If StartDate is not explicitly specified, the effective start date is the settlement date.

Face
(Optional) Face or par value. Default = 100.

`Price`	Clean price of the bond (current price without accrued interest).
`CouponRate`	Decimal number indicating the annual percentage rate used to determine the coupons payable on a bond.
`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) Coupons per year of the bond. A vector of integers. Allowed values are 0, 1, 2, 3, 4, 6, and 12. Default = 2.
`Basis`	(Optional) Day-count basis of the bond. A vector of integers. 0 = actual/actual (default), 1 = 30/360, 2 = actual/360, 3 = actual/365.
`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.
`IssueDate`	(Optional) Date when a bond was issued.
`FirstCouponDate`	(Optional) Date when a bond makes its first coupon payment. When `FirstCouponDate` and `LastCouponDate` are both specified, `FirstCouponDate` takes precedence in determining the coupon payment structure.
`LastCouponDate`	(Optional) Last coupon date of a bond prior to the maturity date. In the absence of a specified `FirstCouponDate`, a specified `LastCouponDate` determines the coupon structure of the bond. The coupon structure of a bond is truncated at the `LastCouponDate` regardless of where it falls and will be followed only by the bond's maturity cash flow date.
`StartDate`	(Future implementation; optional) Date when a bond actually starts (the date from which a bond's cash flows can be considered). To make an instrument forward-starting, specify this date as a future date. If `StartDate` is not explicitly specified, the effective start date is the settlement date.
`Face`	(Optional) Face or par value. Default = 100.

Description

Yield = bndyield(Price, CouponRate, Settle, Maturity, Period, Basis, EndMonthRule, IssueDate, FirstCouponDate, LastCouponDate, StartDate, Face) given NUMBONDS bonds with SIA date parameters and clean prices (excludes accrued interest), returns the bond equivalent yields to maturity.

Yield is a NUMBONDS-by-1 vector of the bond equivalent yields to maturity with semi-annual compounding.

Price and Yield are related by the formula

Price + Accrued_Interest = sum(Cash_Flow*(1+Yield/2)^(-Time))

where the sum is over the bonds' cash flows and corresponding times in units of semi-annual coupon periods.

Examples

Compute the yield of a treasury bond at three different price values.

Price = [95; 100; 105]; 
CouponRate = 0.05; 
Settle = '20-Jan-1997'; 
Maturity = '15-Jun-2002'; 
Period = 2; 
Basis = 0; 

Yield = bndyield(Price, CouponRate, Settle,... 
Maturity, Period, Basis)

Yield =

    0.0610
    0.0500
    0.0396

See Also

bndprice, cfamounts

bndprice bolling