mbsyield - Mortgage-backed security yield given price

Syntax

[MYield, BEMBSYield] = mbsyield(Price, Settle, Maturity, IssueDate, 
GrossRate, CouponRate, Delay,  PrepaySpeed, PrepayMatrix)

Arguments

`Price`	Clean price for every $100 face value.
`Settle`	Settlement date. A serial date number or date string. `Settle` must be earlier than `Maturity`.
`Maturity`	Maturity date. A serial date number or date string.
`IssueDate`	Issue date. A serial date number or date string.
`GrossRate`	Gross coupon rate (including fees), in decimal.
`CouponRate`	(Optional) Net coupon rate, in decimal. Default = `GrossRate`.
`Delay`	(Optional) Delay (in days) between payment from homeowner and receipt by bondholder. Default = 0 (no delay between payment and receipt.
`PrepaySpeed`	(Optional) Relation of the conditional payment rate (CPR) to the benchmark model. Default = 0 (no prepayment). Set `PrepaySpeed` to `[]` if you input a customized prepayment matrix.
`PrepayMatrix`	(Optional) Customized prepayment matrix. A matrix of size `max(TermRemaining)`-by-`NMBS`. Missing values are padded with `NaN`s. Each column corresponds to a mortgage-backed security, and each row corresponds to each month after settlement.

All inputs (except PrepayMatrix) are number of mortgage-backed securities (NMBS) by 1 vectors.

Description

[MYield, BEMBSYield] = mbsyield(Price, Settle, Maturity, IssueDate, GrossRate, CouponRate, Delay, PrepaySpeed, PrepayMatrix) computes a mortgage-backed security yield to maturity and the bond equivalent yield, given time information, price at settlement, and optionally, a prepayment model.

MYield is the yield to maturity of the mortgage-backed security (the mortgage yield). This yield is compounded monthly (12 times a year).

BEMBSYield is the corresponding bond equivalent yield of the mortgage-backed security. This yield is compounded semiannually (two times a year).

Examples

Example 1. Given a mortgage-backed security with the following characteristics, compute the mortgage yield and the bond equivalent yield of the security.

Price = 102;
Settle = '15-Apr-2002';
Maturity = '1 Jan 2030';
IssueDate = '1-Jan-2000';
GrossRate = 0.08125;
CouponRate = 0.075;
Delay = 14;
Speed = 100;

[MYield, BEMBSYield] = mbsyield(Price, Settle, Maturity, ... 
IssueDate, GrossRate, CouponRate, Delay,  Speed)

MYield =

    0.0715

BEMBSYield =

    0.0725

Example 2. Given a portfolio of mortgage-backed securities, compute the mortgage yields and the bond equivalent yields.

Price = 102;
Settle = datenum(['13-Feb-2000';'17-Apr-2002';'17-May-2002';... 
'13-Jan-2000']);
Maturity  = datenum('1-Jan-2030');
IssueDate = datenum('1-Jan-2000');
GrossRate = 0.08125;
CouponRate = [0.075; 0.07875; 0.0775; 0.08125];
Delay = 14;
Speed = 100;

[MYield, BEMBSYield] = mbsyield(Price, Settle, Maturity,... 
IssueDate, GrossRate, CouponRate, Delay,  Speed)

MYield =

    0.0717
    0.0751
    0.0739
    0.0779

BEMBSYield =

    0.0728
    0.0763
    0.0750
    0.0791

References

[1] PSA Uniform Practices, SF-49

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