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.

Input Arguments

`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 `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 For more information, see basis. 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. Default: If you do not specify an `IssueDate`, the cash flow payment dates are determined from other inputs.
`FirstCouponDate`	Date when a bond makes its first coupon payment; used when bond has an irregular first coupon period. When `FirstCouponDate` and `LastCouponDate` are both specified, `FirstCouponDate` takes precedence in determining the coupon payment structure. Default: If you do not specify a `FirstCouponDate`, the cash flow payment dates are determined from other inputs.
`LastCouponDate`	Last coupon date of a bond before the maturity date; used when bond has an irregular last coupon period. 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 is followed only by the bond's maturity cash flow date. Default: If you do not specify a `LastCouponDate`, the cash flow payment dates are determined from other inputs.
`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. Default: 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.

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.

Default: SIA bases use the actual/actual day count to compute discount factors.

LastCouponInterest

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.

Default: compound

Output Arguments

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

Algorithms

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.

For ISMA conventions, the frequency of annual coupon payments determines bond price and yield.

References

Krgin, Dragomir, Handbook of Global Fixed Income Calculations, John Wiley & Sons, 2002.

Mayle, Jan, "Standard Securities Calculations Methods: Fixed Income Securities Formulas for Analytic Measures", SIA, Vol 2, Jan 1994.

Stigum, Marcia, and Franklin Robinson, Money Market and Bond Calculations, McGraw-Hill, 1996.

How To

Yield Functions

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