stepcpnyield

Yield to maturity of bond with stepped coupons

Syntax

Yield = stepcpnyield(Price,Settle,Maturity,ConvDates,CouponRates)

Yield = stepcpnyield(___,Period,Basis,EndMonthRule,Face)

Description

Yield = stepcpnyield(Price,Settle,Maturity,ConvDates,CouponRates) computes the yield to maturity of bonds with stepped coupons given the price. The function supports any number of conversion dates.

Yield = stepcpnyield(___,Period,Basis,EndMonthRule,Face) adds additional optional arguments.

Examples

Compute Yield to Maturity for Bonds with Stepped Coupons

Find the yield to maturity of three stepped-coupon bonds of known price, given three conversion scenarios:

• Bond A has two conversions, the first one falling on the settle date and immediately expiring.

• Bond B has three conversions, with conversion dates exactly on the coupon dates.

• Bond C has three conversions, with one or more conversion dates not on coupon dates. This case illustrates that only cash flows for full periods after conversion dates are affected, as illustrated below.

The following table illustrates the interest-rate characteristics of this bond portfolio.

Define the specifications for the bonds.

format long
Price = [117.3824; 113.4339; 113.4339];
Settle = datenum('02-Aug-1992');

ConvDates = [datenum('02-Aug-1992'), datenum('15-Jun-2003'), nan;
datenum('15-Jun-1997'), datenum('15-Jun-2001'), datenum('15-Jun-2005'); 
datenum('14-Jun-1997'), datenum('14-Jun-2001'), datenum('14-Jun-2005')];
        
Maturity = datenum('15-Jun-2010');

CouponRates = [0.075 0.08875 0.0925 nan;
               0.075 0.08875 0.0925 0.1;
               0.075 0.08875 0.0925 0.1];
Basis = 1;
Period = 2;
EndMonthRule = 1;
Face = 100;

Use stepcpnyield to compute the yield to maturity for the bonds with stepped coupons.

Yield = stepcpnyield(Price, Settle, Maturity, ConvDates, CouponRates, Period, Basis, EndMonthRule, Face)

Yield = 3×1

   0.072214402049150
   0.072214267800360
   0.072864799557221

Input Arguments

Price — Price of bond

numeric

Price of bond, specified as a scalar or NUMBONDS-by-1 vector of numeric values.

Data Types: double

Settle — Settlement date

serial date number | date character vector

Settlement date, specified either as a scalar or NUMBONDS-by-1 vector using serial date numbers or date character vectors.

Settle must be earlier than Maturity.

Data Types: double | char

Maturity — Maturity date

serial date number | date character vector

Maturity date, specified as a scalar or an NUMBONDS-by-1 vector using serial date numbers or date character vectors that represent the maturity date for each bond.

Data Types: double | char

ConvDates — Conversion dates

serial date number | date character vector

Conversion dates, specified as a NSTP-by-max(NCONV) matrix using serial date numbers or date character vectors that contain conversion dates after Settle. The size of the matrix is equal to the number of instruments by the maximum number of conversions. Fill unspecified entries with NaN.

Data Types: double | char

CouponRates — Bond coupon rate

positive decimal value

Bond coupon rate, specified as an NSTP-by-max(NCONV+1) matrix containing coupon rates for each bond in the portfolio in decimal form. The matrix size is equal to the number of instruments by maximum number of conversions + 1. First column of this matrix contains rates applicable between Settle and the first conversion date (date in the first column of ConvDates). Fill unspecified entries with NaN

ConvDates has the same number of rows as CouponRates to reflect the same number of bonds. However, ConvDates has one less column than CouponRates. This situation is illustrated by

Settle---------ConvDate1-----------ConvDate2------------Maturity

         Rate1               Rate2                 Rate3

Data Types: double

Period — Coupons per year

2 per year (default) | vector

(Optional) Coupons per year, specified as an NUMBONDS-by-1 vector. Values for Period are 1, 2, 3, 4, 6, and 12.

Data Types: double

Basis — Day-count basis

0 (actual/actual) (default) | integer from 0 to 13

(Optional) Day-count basis of each instrument, specified as an NUMBONDS-by-1 vector.

• 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 for generating dates when Maturity is end-of-month date for month having 30 or fewer days

1 (in effect) (default) | nonnegative integer [0,1]

(Optional) End-of-month rule flag for generating dates when Maturity is an end-of-month date for a month having 30 or fewer days, specified for each bond as a nonnegative integer [0, 1] using a NUMBONDS-by-1 vector.

• 0 = Ignore rule, meaning that a payment date is always the same numerical day of the month.

• 1 = Set rule on, meaning that a payment date is always the last actual day of the month.

Data Types: logical

Face — Face value

100 (default) | vector of nonnegative values

(Optional) Face value, specified for each bond as an NUMBONDS-by-1 vector of nonnegative face values.

Data Types: double

Output Arguments

Yield — Yield to maturity

vector

Yield to maturity, returned as a NUMBONDS-by-1 vector in decimal form.

Note

For bonds with fixed coupons, use bndyield. You receive the error incorrect number of inputs if you use a fixed-coupon bond with stepcpnyield.

More About

Stepped Coupon

A stepped coupon is a type of bond or fixed-income security that features a coupon rate that increases (or "steps up") at predetermined intervals over the life of the bond.

The stepped coupon structure is designed to provide investors with higher interest payments as time progresses, making it attractive in environments where interest rates are expected to rise.

Version History

Introduced before R2006a