bndyield - Yield to maturity for fixed income security

Syntax

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

Description

Yield = bndyield(Price, CouponRate, Settle, Maturity), given NUMBONDS bonds with SIA date parameters and clean prices (excludes accrued interest), returns the bond equivalent yields to maturity.

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

Yield = bndyield(Price, CouponRate, Settle, Maturity, 'ParameterName', 'ParameterValue ...) accepts optional inputs as one or more comma-separated parameter/value pairs. 'ParameterName' is the name of the parameter inside single quotes. ParameterValue is the value corresponding to 'ParameterName'. Specify parameter/value pairs in any order. Names are case-insensitive.

Inputs

`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.

Ordered Input or Parameter–Value Pairs

Enter the following inputs using an ordered syntax or as parameter/value pairs. You cannot mix ordered syntax with parameter/value pairs.

`Period`	Coupons per year of the bond. A vector of integers. Values are 0, 1, 2, 3, 4, 6, and 12. Default: 2
`Basis`	Day-count basis of the instrument. A vector of integers. 0 = actual/actual 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) 13 = BUS/252 Default: 0
`EndMonthRule`	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 coupon payment date is always the same numerical day of the month. 1 = set rule on, meaning that a bond coupon payment date is always the last actual day of the month. Default: 1
`IssueDate`	Issue date for a bond.
`FirstCouponDate`	Irregular or normal first coupon date.
`LastCouponDate`	Irregular or normal last coupon date.
`StartDate`	Date when a bond actually starts (the date from which a bond cash flow is considered). To make an instrument forward-starting, specify this date as a future date. If you do not specify `StartDate`, the effective start date is the `Settle` date.
`Face`	Face or par value. Default: 100

Parameter–Value Pairs

Enter the following inputs only as parameter/value pairs.

`CompoundingFrequency`	Compounding frequency for yield calculation. By default, SIA bases (0-7) and BUS/252 use a semiannual compounding convention and ISMA bases (8-12) use an annual compounding convention.
`DiscountBasis`	Basis used to compute the discount factors for computing the yield. The default behavior is for SIA bases to use the actual/actual day count to compute discount factors. If you use ISMA day counts and BUS/252, the specified bases are used.
`LastCouponPeriodInterest`	Compounding convention for computing the yield of a bond in the last coupon period. This computation is based on only the last coupon and the face value to be repaid. Acceptable values are `'simple'` or `'compound'`.

Outputs

Yield

NUMBONDS-by-1 vector of the yield to maturity with semiannual compounding.

Definitions

All nonscalar or empty matrix input arguments must be either NUMBONDS-by-1 or 1-by-NUMBONDS conforming vectors. Fill in unspecified entries input vectors with NaNs. Dates can be serial date numbers or date strings.

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)

This returns:

Yield =

    0.0610
    0.0500
    0.0396

Algorithm

For SIA conventions, the following formula defines bond price and yield:

where:

PV =	Present value of a cash flow.
CF =	The cash flow amount.
z =	The risk-adjusted annualized rate or yield corresponding to a given cash flow. The yield is quoted on a semiannual basis.
f =	The frequency of quotes for the yield.
TF =	Time factor for a given cash flow. Time is measured in semiannual periods from the settlement date to the cash flow date. In computing time factors, use SIA actual/actual day count conventions for all time factor calculations.