bndyield

Yield to maturity for fixed-income security

In R2017b, the specification of optional input arguments has changed. While the previous ordered inputs syntax is still supported, it may no longer be supported in a future release. Use the optional name-value pair inputs: Period, Basis, EndMonthRule, IssueDate,FirstCouponDate, LastCouponDate, StartDate,Face, CompoundingFrequency, DiscountBasis, and LastCouponInterest.

Syntax

Yield = bndyield(Price,CouponRate,Settle,Maturity)

Yield = bndyield(___,Name,Value)

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(___,Name,Value) adds optional name-value arguments.

Examples

Compute Yield to Maturity for a Treasury Bond

This example shows how to 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 = 3×1

    0.0610
    0.0500
    0.0396

Compute Yield to Maturity for a Treasury Bond Using datetime Inputs

This example shows how to use datetime inputs to compute the yield of a Treasury bond at three different price values.

Price = [95; 100; 105];
CouponRate = 0.05;
Settle = datetime('20-Jan-1997','Locale','en_US');
Maturity = datetime('15-Jun-2002','Locale','en_US');
Period = 2;
Basis = 0;
Yield = bndyield(Price, CouponRate, Settle,...
Maturity, Period, Basis)

Yield = 3×1

    0.0610
    0.0500
    0.0396

Compute the Yield of a Treasury Bond Using the Same Basis for Discounting and Generating the Cash Flows

Compute the yield of a Treasury bond.

Price = [95; 100; 105];
CouponRate = 0.0345;
Settle = '15-May-2016';
Maturity = '02-Feb-2026';
Period = 2;
Basis = 1;
format long

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

Yield = 3×1

   0.040764403932618
   0.034482347625316
   0.028554719853118

Using the same data, compute the yield of a Treasury bond using the same basis for discounting and generating the cash flows.

DiscountBasis = 1;

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

Yield = 3×1

   0.040780176658036
   0.034495592361619
   0.028565614029497

Input Arguments

Price — Clean price of the bond

numeric

Clean price of the bond (current price without accrued interest), specified as a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector.

Data Types: double

CouponRate — Annual percentage rate used to determine coupons payable on a bond

decimal

Annual percentage rate used to determine the coupons payable on a bond, specified as decimal using a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector.

Data Types: double

Settle — Settlement date of bond

serial date number | date character vector | datetime

Settlement date of the bond, specified as a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays. The Settle date must be before the Maturity date.

Data Types: double | char | datetime

Maturity — Maturity date of bond

serial date number | date character vector | datetime

Maturity date of the bond, specified as a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays.

Data Types: double | char | datetime

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: Yield = bndyield(Price,CouponRate,Settle,Maturity,'Period',4,'Basis',9)

'Period' — Number of coupon payments per year

2 (default) | numeric with values 0, 1, 2, 3, 4, 6 or 12

Number of coupon payments per year, specified as the comma-separated pair consisting of 'Period' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using the values: 0, 1, 2, 3, 4, 6, or 12.

Data Types: double

'Basis' — Day-count basis of instrument

0 (default) | numeric values: 0,1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13

Day-count of the instrument, specified as the comma-separated pair consisting of 'Basis' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using a supported value:

• 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 (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

For more information, see Basis.

Data Types: double

'EndMonthRule' — End-of-month rule flag

1 (in effect) (default) | nonnegative integer 0 or 1

End-of-month rule flag, specified as the comma-separated pair consisting of 'EndMonthRule' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS 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.

Data Types: logical

'IssueDate' — Bond issue date

serial date number | date character vector | datetime

Bond Issue date, specified as the comma-separated pair consisting of 'IssueDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays.

If you do not specify an IssueDate, the cash flow payment dates are determined from other inputs.

Data Types: double | char | datetime

'FirstCouponDate' — Irregular or normal first coupon date

serial date number | date character vector | datetime

Irregular or normal first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays.

If you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs.

Data Types: double | char | datetime

'LastCouponDate' — Irregular or normal last coupon date

serial date number | date character vector | datetime

Irregular or normal last coupon date, specified as the comma-separated pair consisting of 'LastCouponDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays.

If you do not specify a LastCouponDate, the cash flow payment dates are determined from other inputs.

Data Types: double | char | datetime

'StartDate' — Forward starting date of payments

serial date number | date character vector | datetime

Forward starting date of payments, specified as the comma-separated pair consisting of 'StartDate' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector using serial date numbers, date character vectors, or datetime arrays.

If you do not specify a StartDate, the effective start date is the Settle date.

Data Types: double | char | datetime

'Face' — Face value of bond

100 (default) | numeric

Face value of the bond, specified as the comma-separated pair consisting of 'Face' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector.

Data Types: double

'CompoundingFrequency' — Compounding frequency for yield calculation

SIA uses 2, ICMA uses 1 (default) | integer with value of 1, 2, 3, 4, 6, or 12

Compounding frequency for yield calculation, specified as the comma-separated pair consisting of 'CompoundingFrequency' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector. Values are:

• 1 — Annual compounding

• 2 — Semiannual compounding

• 3 — Compounding three times per year

• 4 — Quarterly compounding

• 6 — Bimonthly compounding

• 12 — Monthly compounding

Note

By default, SIA bases (0-7) and BUS/252 use a semiannual compounding convention and ICMA bases (8-12) use an annual compounding convention.

Data Types: double

'DiscountBasis' — Basis used to compute the discount factors for computing the yield

SIA uses 0 (default) | integers of the set [0...13] | vector of integers of the set [0...13]

Basis used to compute the discount factors for computing the yield, specified as the comma-separated pair consisting of 'DiscountBasis' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector. Values are:

• 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 (ICMA)

• 9 = actual/360 (ICMA)

• 10 = actual/365 (ICMA)

• 11 = 30/360E (ICMA)

• 12 = actual/365 (ISDA)

• 13 = BUS/252

For more information, see Basis.

Note

If a SIA day-count basis is defined in the Basis input argument and there is no value assigned for DiscountBasis, the default behavior is for SIA bases to use the actual/actual day count to compute discount factors.

If an ICMA day-count basis or BUS/252 is defined in the Basis input argument and there is no value assigned for DiscountBasis, the specified bases from the Basis input argument are used.

Data Types: double

'LastCouponInterest' — Compounding convention for computing yield of a bond in last coupon period

compound (default) | values are simple or compound

Compounding convention for computing the yield of a bond in the last coupon period, specified as the comma-separated pair consisting of 'LastCouponInterest' and a scalar or a NUMBONDS-by-1 or 1-by-NUMBONDS vector. This is based on only the last coupon and the face value to be repaid. Acceptable values are:

• simple

• compound

Data Types: char | cell

Output Arguments

Yield — Yield to maturity with semiannual compounding

numeric

Yield to maturity with semiannual compounding, returned as a NUMBONDS-by-1 vector.

More About

Price and Yield Conventions

The Price and Yield are related to different formulae for SIA and ICMA conventions.

For SIA conventions, Price and Yield are related by the formula:

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

where the sum is over the bond's cash flows and corresponding times in units of semiannual coupon periods.

For ICMA conventions, the Price and Yield are related by the formula:

 Price + Accrued Interest = sum(Cash_Flow*(1+Yield)^(-Time))

Algorithms

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

$$PV=\frac{CF}{{(1+\frac{z}{f})}^{TF}},$$

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

References

[1] Krgin, D. Handbook of Global Fixed Income Calculations. Wiley, 2002.

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

[3] Stigum, M., Robinson, F. Money Market and Bond Calculation. McGraw-Hill, 1996.