floatdiscmargin

Discount margin for floating-rate bond

Syntax

Margin = floatdiscmargin(Price,SpreadSettle,Maturity,RateInfo,LatestFloatingRate)

Margin = floatdiscmargin(___,Name,Value)

Description

Margin = floatdiscmargin(Price,SpreadSettle,Maturity,RateInfo,LatestFloatingRate) calculates the discount margin or zero discount margin for a floating-rate bond.

The input RateInfo determines whether the discount margin or the zero discount margin is calculated. Principal schedules are supported using Principal.

Margin = floatdiscmargin(___,Name,Value) adds optional name-value pair arguments.

Examples

Compute the Zero Discount Margin Using a Yield Curve

Use floatdiscmargin to compute the discount margin and zero discount margin for a floating-rate note.

Define data for the floating-rate note.

Price = 99.99;
Spread = 50;
Settle = '20-Jan-2011';
Maturity = '15-Jan-2012';
LatestFloatingRate = 0.05;
StubRate = 0.049;
SpotRate = 0.05;
Reset = 4;
Basis = 2;

Compute the discount margin.

dMargin = floatdiscmargin(Price, Spread, Settle, Maturity, ...
[StubRate, SpotRate], LatestFloatingRate,'Reset', Reset, 'Basis', Basis, ...
'AdjustCashFlowsBasis', true)

dMargin = 48.4810

Usually you want to set AdjustCashFlowsBasis to true, so cash flows are calculated with adjustments on accrual amounts.

Create an annualized zero-rate term structure to calculate the zero discount margin.

Rates = [0.0500;
         0.0505;
         0.0510;
         0.0520];
StartDates = ['20-Jan-2011';
              '15-Apr-2011';
              '15-Jul-2011';
              '15-Oct-2011'];
EndDates =   ['15-Apr-2011';
              '15-Jul-2011';
              '15-Oct-2011';
              '15-Jan-2012'];
ValuationDate = '20-Jan-2011';
RateSpec = intenvset('Compounding', Reset, 'Rates', Rates,...
'StartDates', StartDates, 'EndDates', EndDates,...
'ValuationDate', ValuationDate, 'Basis', Basis);

Calculate the zero discount margin using the previous yield curve.

dMargin = floatdiscmargin(Price, Spread, Settle, Maturity, ...
RateSpec, LatestFloatingRate,'Reset', Reset, 'Basis', Basis, ...
'AdjustCashFlowsBasis', true)

dMargin = 46.0688

Compute the Zero Discount Margin Using a Yield Curve With datetime Inputs

Use floatdiscmargin to compute the discount margin and zero discount margin for a floating-rate note using datetime inputs.

Price = 99.99;
Spread = 50;
Settle = '20-Jan-2011';
Maturity = '15-Jan-2012';
LatestFloatingRate = 0.05;
StubRate = 0.049;
SpotRate = 0.05;
Reset = 4;
Basis = 2;

Settle = datetime(Settle,'Locale','en_US');
Maturity = datetime(Maturity,'Locale','en_US');
dMargin = floatdiscmargin(Price, Spread, Settle, Maturity, ...
[StubRate, SpotRate], LatestFloatingRate,'Reset', Reset, 'Basis', Basis, ...
'AdjustCashFlowsBasis', true)

dMargin = 48.4810

Input Arguments

Price — Bond prices where discount margin is to be computed

matrix

Bond prices where discount margin is to be computed, specified as a NINST-by-1 matrix.

Note

The spread is calculated against the clean price (the function internally does not add the accrued interest to the price specified by the Price input). If the spread is required against the dirty price, the price of a bond that includes the accrued interest, you must supply the dirty price for the Price input.

Data Types: double

Spread — Number of basis points over the reference rate

numeric

Number of basis points over the reference rate, specified as a NINST-by-1 matrix.

Data Types: double

Settle — Settlement date of the floating-rate bonds

serial date number | date character vector | datetime

Settlement date of the floating-rate bonds, specified as serial date number, date character vector, or datetime array. If supplied as a NINST-by-1 vector of dates, all settlement dates must be the same (only a single settlement date is supported)

Data Types: double | char | datetime

Maturity — Maturity date of the floating-rate bond

serial date number | date character vector | datetime

Maturity date of the floating-rate bond, specified as serial date number, date character vector, or datetime array.

Data Types: double | char | datetime

RateInfo — Interest-rate information

numeric

interest-rate information, specified as NINST-by-2 vector where the:

• First column is the stub rate between the settlement date and the first coupon rate.

• Second column is the reference rate for the term of the floating coupons (for example, the 3-month LIBOR from settlement date for a bond with a Reset of 4).

Note

If the RateInfo argument is an annualized zero-rate term structure created by intenvset, the zero discount margin is calculated.

Data Types: double

LatestFloatingRate — Rate for next floating payment set at last reset date

numeric

Rate for the next floating payment set at the last reset date, specified as NINST-by-1 vector.

Data Types: double

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: Margin = floatdiscmargin(Price,Spread,Settle,Maturity,RateInfo,LatestFloatingRate,'Reset',2,'Basis',5)

'Reset' — Frequency of payments per year

1 (default) | numeric

Frequency of payments per year, specified as NINST-by-1 vector.

Data Types: double

'Basis' — Day-count basis used for time factor calculations

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

Day-count basis used for time factor calculations, specified as 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

'Principal' — Notional principal amounts

100 (default) | numeric

Notional principal amounts, specified as a NINST-by-1 vector or a NINST-by-1 cell array where each element is a NUMDATES-by-2 cell array where the first column is dates and the second column is the associated principal amount. The date indicates the last day that the principal value is valid.

Data Types: double | cell

'EndMonthRule' — End-of-month rule flag

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

End-of-month rule flag, specified as 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

'AdjustCashFlowsBasis' — Adjust cash flows according to accrual amount

0 (not in effect) (default) | nonnegative integer 0 or 1

Adjusts cash flows according to the accrual amount, specified as a NINST-by-1 vector of logicals.

Note

Usually you want to set AdjustCashFlowsBasis to 1, so cash flows are calculated with adjustments on accrual amounts. The default is set to 0 to be consistent with floatbyzero.

Data Types: logical

'Holidays' — Dates for holidays

holidays.m used (default)

Dates for holidays, specified as NHOLIDAYS-by-1 vector of MATLAB^® dates using serial date numbers, date character vectors, or datetime arrays. Holidays are used in computing business days.

Data Types: double | char | datetime

'BusinessDayConvention' — Business day conventions

'actual' (default) | character vector with values'actual', 'follow', 'modifiedfollow', 'previous'or 'modifiedprevious'

Business day conventions, specified as a NINST-by-1 cell array of character vectors of business day conventions to be used in computing payment dates. The selection for business day convention determines how nonbusiness days are treated. Nonbusiness days are defined as weekends plus any other date that businesses are not open (for example, statutory holidays). Values are:

• 'actual' — Nonbusiness days are effectively ignored. Cash flows that fall on non-business days are assumed to be distributed on the actual date.

• 'follow' — Cash flows that fall on a nonbusiness day are assumed to be distributed on the following business day.

• 'modifiedfollow' — Cash flows that fall on a non-business day are assumed to be distributed on the following business day. However if the following business day is in a different month, the previous business day is adopted instead.

• 'previous' — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day.

• 'modifiedprevious' — Cash flows that fall on a nonbusiness day are assumed to be distributed on the previous business day. However if the previous business day is in a different month, the following business day is adopted instead.

Data Types: char | cell

Output Arguments

Margin — Discount margin

numeric

Discount margin, returned as a NINST-by-1 vector of the discount margin if RateInfo is specified as a NINST-by-2 vector of stub and spot rates.

If RateInfo is specified as an annualized zero rate term structure created by intenvset, Margin is returned as a NINST-by-NCURVES matrix of the zero discount margin.

References

[1] Fabozzi, Frank J., Mann, Steven V. Floating-Rate Securities. John Wiley and Sons, New York, 2000.

[2] 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.

[3] O'Kane, Dominic, Sen, Saurav. “Credit Spreads Explained.” Lehman Brothers Fixed Income Quantitative Research, March 2004.