mbsdurp

Duration of mortgage pool given price

Syntax

[YearDuration,ModDuration] = mbsdurp(Price,Settle,Maturity,IssueDate,GrossRate)

[YearDuration,ModDuration] = mbsdurp(___,CouponRate,Delay,PrepaySpeed,PrepayMatrix)

Description

[YearDuration,ModDuration] = mbsdurp(Price,Settle,Maturity,IssueDate,GrossRate) computes the mortgage-backed security Macaulay (YearDuration) in years and modified (ModDuration) durations in years, given time information, price at settlement, and optionally, a prepayment model.

[YearDuration,ModDuration] = mbsdurp(___,CouponRate,Delay,PrepaySpeed,PrepayMatrix) specifies options using one or more optional arguments in addition to the input arguments in the previous syntax.

Examples

Find the Duration of a Mortgage Pool

This example shows how to find the duration of mortgage pool given a mortgage-backed security with the following characteristics.

Price = 101;
Settle = datenum('15-Apr-2002');
Maturity = datenum('1 Jan 2030');
IssueDate = datenum('1-Jan-2000');
GrossRate = 0.08125;
CouponRate = 0.075;;
Delay = 14;
Speed = 100;

[YearDuration, ModDuration] = mbsdurp(Price, Settle, Maturity,... 
IssueDate, GrossRate, CouponRate, Delay, Speed)

YearDuration = 
6.4380

ModDuration = 
6.2080

Input Arguments

Price — Clean price for every $100 face of issue

vector

Clean price for every $100 face of issue, specified as an NMBS-by-1 vector.

Data Types: double

Settle — Settlement dates

vector

Settlement dates, specified as an NMBS-by-1 vector of serial date numbers or a cell array of character vectors. Settle must be earlier than Maturity.

Data Types: double | cell

Maturity — Maturity dates

vector

Maturity dates, specified as an NMBS-by-1 vector of serial date numbers or a cell array of character vectors.

Data Types: double | cell

IssueDate — Issue dates

vector

Maturity dates, specified as an NMBS-by-1 vector of serial date numbers or a cell array of character vectors.

Data Types: double | cell

GrossRate — Gross coupon rate (including fees)

vector

Gross coupon rate (including fees), specified as an NMBS-by-1 vector of numeric decimals.

Data Types: double

CouponRate — Net coupon rate

GrossRate (default) | vector

(Optional) Net coupon rate, specified as an NMBS-by-1 vector of numeric decimals.

Data Types: double

Delay — Delay in days

0 (no delay) (default) | vector

(Optional) Delay in days, specified as an NMBS-by-1 vector.

Data Types: double

PrepaySpeed — Speed relative to PSA standard

0 (no prepayment) (default) | vector

(Optional) Speed relative to PSA standard, specified as an NMBS-by-1 vector. The PSA standard is 100.

Note

Set the PrepaySpeed to [] if you input a customized PrepayMatrix.

Data Types: double

PrepayMatrix — Customized prepayment vector

matrix

(Optional) Customized prepayment vector, specified as a NaN-padded matrix of size max(TermRemaining)-by-NMBS. Each column corresponds to each mortgage-backed security, and each row corresponds to each month after settlement.

Note

Use PrepayMatrix only when PrepaySpeed is unspecified.

Data Types: double

Output Arguments

YearDuration — Macaulay duration in years

scalar numeric

Macaulay duration in years, returned as a scalar numeric.

ModDuration — Modified duration in years

scalar numeric

Modified duration in years, returned as a scalar numeric.

More About

Duration of Mortgage Pool

The duration of a mortgage pool is a measure of the sensitivity of the price of mortgage-backed securities (MBS) to changes in interest rates.

Duration quantifies the weighted average time it takes for the cash flows from the mortgage pool to be received, providing insight into the interest-rate risk associated with the pool.

References

[1] PSA Uniform Practices, SF-49

Version History

Introduced before R2006a