bnddury (Financial Toolbox)

Bond duration given yield (SIA compliant)

Syntax

[ModDuration, YearDuration, PerDuration] = bnddury(Yield, 
CouponRate, Settle, Maturity, Period, Basis, EndMonthRule, 
IssueDate, FirstCouponDate, LastCouponDate, StartDate, Face)

Arguments

Yield
Yield to maturity on a semi-annual basis.

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.

`Yield`	Yield to maturity on a semi-annual basis.
`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.

All specified arguments must be number of bonds (NUMBONDS) by 1 or 1-by-NUMBONDS conforming vectors or scalar arguments. Use an empty matrix ([]) as a placeholder for an optional argument. Fill unspecified entries in input vectors with NaN. Dates can be serial date numbers or date strings.

Description

[ModDuration, YearDuration, PerDuration] = bnddury(Yield, CouponRate, Settle, Maturity, Period, Basis, EndMonthRule, IssueDate, FirstCouponDate, LastCouponDate, StartDate, Face) computes the Macaulay and modified duration of NUMBONDS fixed income securities given yield to maturity for each bond. This function determines the duration for a bond whether or not the first or last coupon periods in the coupon structure are short or long (i.e., whether or not the coupon structure is synchronized to maturity). This function also determines the Macaulay and modified duration for a zero coupon bond.

ModDuration is the modified duration in years; YearDuration is the Macaulay duration in years; PerDuration is the periodic Macaulay duration reported on a semi-annual bond basis (in accordance with SIA convention). Outputs are NUMBONDS-by-1 vectors.

Examples

Find the duration of a bond at three different yield values.

Yield = [0.04; 0.055; 0.06];  
CouponRate = 0.055; 
Settle = '02-Aug-1999'; 
Maturity = '15-Jun-2004'; 
Period = 2; 
Basis = 0; 

[ModDuration,YearDuration,PerDuration]=bnddury(Yield,... 
CouponRate, Settle, Maturity, Period, Basis)

ModDuration =

    4.2444
    4.1924
    4.1751

YearDuration =

    4.3292
    4.3077
    4.3004

PerDuration =

    8.6585
    8.6154
    8.6007

See Also

bndconvp, bndconvy, bnddurp

bnddurp bndprice