bndfutimprepo

Implied repo rates for bond future given price

Syntax

ImpRepo = bndfutimprep(Price,FutPrice,FutSettle,Delivery,ConvFactor,CouponRate,Maturity)

ImpRepo = bndfutimprep(___,Name,Value)

Description

ImpRepo = bndfutimprep(Price,FutPrice,FutSettle,Delivery,ConvFactor,CouponRate,Maturity) computes the implied repo rate for a bond future given the price of a bond, the bond properties, the price of the bond future, and the bond conversion factor. The default behavior is that the coupon reinvestment rate matches the repo rate. However, you can specify a separate reinvestment rate using optional inputs.

ImpRepo = bndfutimprep(___,Name,Value) specifies options using one or more optional name-value pair arguments in addition to the input arguments in the previous syntax.

Examples

Compute the Repo Rate For a Bond Future

This example shows how to compute the repo rate for a bond future using the following data.

bndfutimprepo(129,98,datetime(2000,9,21),datetime(2000,12,29),1.3136,.0875,datetime(2020,8,15))

ans = 
0.0584

Input Arguments

Price — Bond prices

vector

Bond prices, specified as an numBonds-by-1 vector in decimals.

Data Types: double

FutPrice — Future prices

vector

Future prices, specified as an numBonds-by-1 vector.

Data Types: double | cell

FutSettle — Future settlement dates

datetime array | string array | date character vector

Future settlement dates, specified as an numBonds-by-1 vector using a datetime array, string array, or date character vectors.

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

Delivery — Future delivery dates

datetime array | string array | date character vector

Future delivery dates, specified as an numBonds-by-1 vector using a datetime array, string array, or date character vectors.

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

ConvFactor — Bond conversion factors

vector

Bond conversion factors, specified as an numBonds-by-1 vector. For more information, see convfactor.

Data Types: double

CouponRate — Coupon rates

vector

Coupon rates, specified as an numBonds-by-1 vector of numeric decimals.

Data Types: double

Maturity — Maturity dates

datetime array | string array | date character vector

Maturity dates, specified as an numBonds-by-1 vector using a datetime array, string array, or date character vectors.

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

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: ImpRepo = bndfutimprepo(Price,FutPrice,FutSettle,Delivery,ConvFactor,CouponRate,Maturity,'Basis',5,'Face',1000,'Period',4)

Basis — Day count basis

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

Day count basis, specified as the comma-separated pair consisting of 'Basis' and a scalar integer from 0 to 13.

• 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 floorlet dates

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

End-of-month rule flag, specified as the comma-separated pair consisting of 'EndMonthRule' and a scalar with a nonnegative integer [0, 1].

• 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 of the bond

100 (default) | scalar numeric

Face value of the bond, specified as the comma-separated pair consisting of 'Face' and a scalar numeric. Face has no impact on key rate duration.

Data Types: double

FirstCouponDate — Irregular first coupon date

if you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs (default) | datetime scalar | string scalar | date character vector

Irregular first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a scalar datetime, string, or date character vector.

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

When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure.

IssueDate — Bond issue date

if you do not specify an IssueDate, the cash flow payment dates are determined from other inputs (default) | datetime scalar | string scalar | date character vector

Bond issue date, specified as the comma-separated pair consisting of 'IssueDate' and a scalar datetime, string, or date character vector.

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

LastCouponDate — Irregular last coupon date

datetime scalar | string scalar | date character vector

Irregular last coupon date, specified as the comma-separated pair consisting of 'LastCouponDate' and a scalar datetime, string, or date character vector.

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

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.

Period — Coupons per year

2 per year (default) | vector

Coupons per year, specified as the comma-separated pair consisting of 'Period' and a scalar integer. Values for Period are 0, 1, 2, 3, 4, 6, and 12.

Data Types: double

ReinvestBasis — Day count basis for reinvestment rate

identical to RepoBasis (default) | integer from 0 to 13

Day count basis for the reinvestment rate, specified as the comma-separated pair consisting of 'ReinvestBasis' and a scalar integer from 0 to 13.

• 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

ReinvestRate — Underlying bond annual coupon

scalar decimal numeric

Underlying bond annual coupon, specified as the comma-separated pair consisting of 'ReinvestRate' and a scalar decimal numeric.

Data Types: double

RepoBasis — Day count basis for repo rate

2 (actual/360) (default) | integer from 0 to 13

Day count basis for repo rate, specified as the comma-separated pair consisting of 'RepoBasis' and a scalar integer from 0 to 13.

• 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

StartDate — Forward starting date of payments

Settle date (default) | datetime scalar | string scalar | date character vector

Forward starting date of payments (the date from which a bond cash flow is considered), specified as the comma-separated pair consisting of 'StartDate' and a scalar datetime, string, or date character vector.

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

Output Arguments

ImpRepo — Implied repo rate

vector

Implied repo rate, or the repo rate that would produce the price input, returned as numBonds-by-1 vector.

More About

Implied Repo Rates

Implied repo rates are the rates that can be inferred from the pricing of certain financial instruments, particularly in the context of the repurchase agreement (repo) market.

A repo is a form of short-term borrowing, where one party sells a security to another party with the agreement to repurchase it at a later date for a higher price. The difference between the sale price and the repurchase price reflects the cost of borrowing, which is essentially the repo rate.

References

[1] Burghardt, G., T. Belton, M. Lane, and J. Papa. The Treasury Bond Basis. McGraw-Hill, 2005.

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

Version History

Introduced in R2009b

R2022b: Serial date numbers not recommended

Although bndfutimprepo 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.