bndtotalreturn

Total return of fixed-coupon bond

Syntax

[BondEquiv,EffectiveRate] = bndtotalreturn(Price,CouponRate,Settle,Maturity,ReinvestRate)

[BondEquiv,EffectiveRate] = bndtotalreturn(___,Name,Value)

Description

[BondEquiv,EffectiveRate] = bndtotalreturn(Price,CouponRate,Settle,Maturity,ReinvestRate)calculates the total return for fixed-coupon bonds to maturity or to a specific investment horizon.

[BondEquiv,EffectiveRate] = bndtotalreturn(___,Name,Value) adds optional name-value pair arguments.

Examples

Compute the Total Return of a Fixed-Coupon Bond

Use bndtotalreturn to compute the total return for a fixed-coupon bond, given an investment horizon date.

Define fixed-coupon bond.

Price = 101;
CouponRate = 0.05;
Settle = '15-Nov-2011';
Maturity = '15-Nov-2031';
ReinvestRate = 0.04;

Calculate the total return to maturity.

[BondEquiv, EffectiveRate] = bndtotalreturn(Price, CouponRate, ...
Settle, Maturity, ReinvestRate)

BondEquiv = 
0.0460

EffectiveRate = 
0.0466

Specify an investment horizon.

HorizonDate = '15-Nov-2021';
[BondEquiv, EffectiveRate] = bndtotalreturn(Price, CouponRate, ...
Settle, Maturity, ReinvestRate, 'HorizonDate', HorizonDate)

BondEquiv = 
0.0521

EffectiveRate = 
0.0528

Perform scenario analysis on the reinvestment rate.

ReinvestRate = [0.03; 0.035; 0.04; 0.045; 0.05];
[BondEquiv, EffectiveRate] = bndtotalreturn(Price, CouponRate, ...
Settle, Maturity, ReinvestRate, 'HorizonDate', HorizonDate)

BondEquiv = 5×1

    0.0557
    0.0538
    0.0521
    0.0505
    0.0490

EffectiveRate = 5×1

    0.0565
    0.0546
    0.0528
    0.0511
    0.0496

Compute the Total Return of a Fixed-Coupon Bond Using datetime Inputs

Use bndtotalreturn with datetime inputs to compute the total return for a fixed-coupon bond, given an investment horizon date.

Price = 101;
CouponRate = 0.05;
Settle = datetime('15-Nov-2011','Locale','en_US');
Maturity = datetime('15-Nov-2031','Locale','en_US');
HorizonDate = datetime('15-Nov-2021','Locale','en_US');
ReinvestRate = 0.04;
[BondEquiv, EffectiveRate] = bndtotalreturn(Price, CouponRate, ...
Settle, Maturity, ReinvestRate, 'HorizonDate', HorizonDate)

BondEquiv = 
0.0521

EffectiveRate = 
0.0528

Input Arguments

Price — Clean price at settlement date

matrix

Clean price at the settlement date, specified as a scalar or a NINST-by-1 vector.

Data Types: double

CouponRate — Coupon rate

decimal

Coupon rate, specified as a scalar or a NINST-by-1 vector of decimal values.

Data Types: double

Settle — Settlement date of fixed-coupon bond

datetime array | string array | date character vector

Settlement date of the fixed-coupon bond, specified as scalar or a NINST-by-1 vector using a datetime array, string array, or date character vectors. If supplied as a NINST-by-1 vector of dates, settlement dates can be different, as long as they are before the Maturity date and HorizonDate.

To support existing code, bndtotalreturn also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

Maturity — Maturity date of fixed-coupon bond

datetime array | string array | date character vector

Maturity date of the fixed-coupon bond, specified as scalar or a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, bndtotalreturn also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

ReinvestRate — Reinvestment rate

decimal

Reinvestment rate (the rate earned by reinvesting the coupons), specified as scalar or a NINST-by-2 vector of decimal values.

Data Types: double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: [BondEquiv,EffectiveRate] = bndtotalreturn(Price,CouponRate,Settle,Maturity,ReinvestRate,'HorizonDate','15-Nov-2021')

HorizonDate — Investment horizon date

Maturity date (default) | datetime array | string array | date character vector

Investment horizon date, specified as the comma-separated pair consisting of 'HorizonDate' and a scalar or a NINST-by-1 vector using a datetime array, string array, or date character vectors.

If HorizonDate is unspecified, the total return is calculated to Maturity.

To support existing code, bndtotalreturn also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

HorizonPrice — Price at investment horizon date

calculated based on ReinvestRate (default) | numeric

Price at investment horizon date, specified as the comma-separated pair consisting of 'HorizonPrice' and a scalar or a NINST-by-1 vector.

If HorizonPrice is unspecified, the price at the HorizonDate is calculated based on the ReinvestRate. If the HorizonDate equals the Maturity date, the HorizonPrice is ignored and the total return to maturity is calculated based on the Face value.

Data Types: double

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 NINST-by-1 vector using the values: 0, 1, 2, 3, 4, 6, or 12.

Data Types: double

Basis — Day-count basis

0 (actual/actual) (default) | integers of the set [0...13] | vector of integers of the set [0...13]

Day-count basis, specified as the comma-separated pair consisting of 'Basis' and a scalar or a NINST-by-1 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.

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 NINST-by-1 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

datetime array | string array | date character vector

Bond Issue date, specified as the comma-separated pair consisting of 'IssueDate' and a scalar or a NINST-by-1 vector using a datetime array, string array, or date character vectors.

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

To support existing code, bndtotalreturn also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

FirstCouponDate — Irregular or normal first coupon date

datetime array | string array | date character vector

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

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

To support existing code, bndtotalreturn also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

LastCouponDate — Irregular or normal last coupon date

datetime array | string array | date character vector

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

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

To support existing code, bndtotalreturn also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

StartDate — Forward starting date of payments

datetime array | string array | date character vector

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

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

To support existing code, bndtotalreturn also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | 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 NINST-by-1 vector.

Data Types: double

CompoundingFrequency — Compounding frequency for yield calculation

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 NINST-by-1 vector.

• 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

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 NINST-by-1 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

The default behavior is for SIA bases (0-7) to use the actual/actual day count to compute discount factors, and for ICMA day counts (8 – 12) and BUS/252 to use the specified DiscountBasis.

Data Types: double

Output Arguments

BondEquiv — Total return in bond equivalent basis

numeric

Total return in bond equivalent basis, returned as a NUMBONDS-by-1 vector.

EffectiveRate — Total return in effective rate basis

numeric

Total return in effective rate basis, returned as a NUMBONDS-by-1 vector.

References

[1] Fabozzi, Frank J., Mann, Steven V. Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures and Valuation. John Wiley and Sons, New York, 2010.

Version History

Introduced in R2012b

R2022b: Serial date numbers not recommended

Although bndtotalreturn supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.