convfactor

Bond conversion factors

Syntax

CF = convfactor(RefDate,Maturity,CouponRate)

CF = convfactor(___,Name,Value)

Description

CF = convfactor(RefDate,Maturity,CouponRate) computes a conversion factor for a bond futures contract.

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

Examples

Compute the Conversion Factors For a Bond Futures Contract

This example shows how to calculate CF, given the following RefDate, Maturity, and CouponRate.

RefDate  = [datetime(2002,12,1);
               datetime(2003,3,1);
               datetime(2003,6,1);
               datetime(2003,9,1);
               datetime(2003,12,1);
               datetime(2003,9,1);
               datetime(2002,12,1);
               datetime(2003,6,1)];
 
Maturity = [datetime(2012,11,15);
               datetime(2012,8,15);
               datetime(2012,2,15);
               datetime(2011,2,15);
               datetime(2011,8,15);
               datetime(2010,8,15);
               datetime(2009,8,15);
               datetime(2010,2,15)];
 
CouponRate = [0.04; 0.04375; 0.04875; 0.05; 0.05; 0.0575; 0.06; 0.065];
 
CF = convfactor(RefDate, Maturity, CouponRate)

CF = 8×1

    0.8539
    0.8858
    0.9259
    0.9418
    0.9403
    0.9862
    1.0000
    1.0266

Compute the Conversion Factor For a German Bond

This example shows how to calculate cf, given the following RefDate, Maturity, and CouponRate for a German bond.

cf = convfactor(datetime(2009,3,10),datetime(2018,1,4), .04,.06,3)

cf = 0.8659

Input Arguments

RefDate — Reference dates

datetime array | string array | date character vector

Reference dates for which conversion factor is computed (usually the first day of delivery months), specified as an N-by-1 vector using a datetime array, string array, or date character vectors

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

Maturity — Maturity date

datetime array | string array | date character vector

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

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

CouponRate — Annual coupon rates for underlying bond

vector in decimals

Annual coupon rates for underlying bond, specified as an numBonds-by-1 vector in decimals.

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: CF = convfactor(RefDate,Maturity,CouponRate,'Convention',2)

Convention — Conversion factor convention

1 US Treasury bond (30-year) and Treasury note (10-year) futures contract (default) | integer from 1 to 5

Conversion factor convention, specified as the comma-separated pair consisting of 'Convention' and a N-by-1 vector using the following values:

• 1 = US Treasury bond (30-year) and Treasury note (10-year) futures contract

• 2 = US 2-year and 5-year Treasury note futures contract

• 3 = German Bobl, Bund, Buxl, and Schatz

• 4 = UK gilts

• 5 = Japanese Government Bonds (JGBs)

Data Types: double

FirstCouponDate — Irregular first coupon date

datetime array | string array | date character vector

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

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

RefYield — Reference semiannual yield

0.06 (6%) (default) | vector in decimals

Reference semiannual yield, specified as the comma-separated pair consisting of 'RefYield' and an N-by-1 vector in decimals.

Data Types: double

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 N-by-1 vector using a datetime array, string array, or date character vectors.

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

Output Arguments

CF — Conversion factors against the 6% yield par-bond

vector

Conversion factors against the 6% yield par-bond, returned as an N-by-1 vector.

More About

Conversion Factors

Conversion factors of US Treasury bonds and other government bonds are based on a bond yielding 6%.

Optionally, you can specify other types of bonds and yields using inputs for RefYield and Convention. For US Treasury bonds, verify the output of convfactor by comparing the output against the quotations provided by the Chicago Board of Trade (https://www.cmegroup.com/company/cbot.html).

For German bonds, verify the output of convfactor by comparing the output against the quotations provided by Eurex (https://www.eurexchange.com).

For UK Gilts, verify the output of convfactor by comparing the output against the quotations provided by Euronext (https://www.euronext.com).

For Japanese Government Bonds, verify the output of convfactor by comparing the output against the quotations provided by the Tokyo Stock Exchange (https://www.jpx.co.jp/english/).

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 convfactor 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.