財務筆記: Fixed Income Valuation - MBSs and ABSs (part 28) @ 經濟,財務,統計學,數理科學與政治評論

寫在前面:這裡會簡單介紹債券市場中Mortgage-backed sector與Asset-backed sector,與其相關的交易與市場特性!!最後我們在Fixed-Income這個部分會用簡單的MBS與ABS的評價做結尾!再過來就先談Derivatives valuation,Portfolio Management,然後再回頭談Alternative Asset Valuation與介紹,以及常用的Econometrics, Economic & Finance !!

Hello there:

一. 首先,這裡要簡單介紹MBSs!!Mortgage-Backed Securities是美國的一項創舉,同時也是美國人在債券市場中,企圖為了一般長期資金的法人,比如保險公司,退休基金與銀行等等金融機構,提供一個能夠追求自身Asset-liability Risk Management,而去市場買賣由MBS再包裝的Collateral Mortgage Obligation(CMO);而CMO扮演的角色就是Cash flow redistribution and prepayment and credit risk redistributed,使得其中的Tranches具有不同的contraction risk與extension risk(一般統稱為prepayment risk),以符合不同投資人的風險管理與資金持有長短的需求!!而CDO則為重要的信用風險管理工具!!我們當然知道美國經過金融海嘯之後,還是有不少好銀行,比如Wells Fargo等等金融機構,甚至是Warren Buffet旗下的金融機構,對於優質房貸戶,通常都不會再將其貸款賣給SPV去包裝成MBS等金融商品,而是長期持有這些客戶,並與其進行其他的金融交易,來賺取手續費用與其它除房貸之外的利息與非利息收益!!但有MBS畢竟是好的!!!

名詞解釋還是需要您自行查閱:Residential Mortgage Loans,servicing fee,mortgage passthrough securities, WAC, WAM, prepayment risk(contraction risk and extension risk),refinancing or prepayment burnout

I. Measuring the prepayment rate

a. Single Monthly Mortality Rate (SMM)

= Prepayment in month t/(Beginning balance for month t - Scheduled principal payment for month t)

i.e., prepayment in month t

= SMM * (Beginning balance for month t - Scheduled principal payment for month t)

b. Conditional Prepayment Rate (CPR)

= 1 - (1 - SMM)**12

i.e., SMM = 1 - (1 - CPR)**(1/12)

c. PSA Prepayment benchmark

t <= 30 -> CPR = 6% * (t/30)

t > 30 -> CPR = 6%

=> T PSA = T/100 * CPR

SMM = (1 - T PSA)**(1/12)

II. Collateralized Mortgage Obligations (CMO)

下列名詞解釋也是需要您自行了解的:Sequential-Pay Tranches,Accrual Tranches or a Z bond (no interest paid but used for the principal balance of earlier tranche),Floating-Rate Tranches(floating rate Tranche and Inverse floating rate Tranche), Structured Interest-Only Trahches (the notional amount created from the excess interest),Nonagency Residential MBS

a. Planned Amortization Class Tranches (PAC Tranches) with support Tranches

1. The PAC Tranche is created from two PSA prepayment rates, one is a lower PSA prepayment and the other is an upper PSA prepayment. The higher PSA one has higher prepayment amount in the early years compared with the lower PSA one!! We use the lower prepayment of these two paths as the path chosen.PAC Tranches相對上面因為prepayment risk已經被Support Tranche所吸收因此其年限與相對上的現金流都穩定很多,這也是為何很多金融機構喜歡持有它的原因(reinvestment risk與interest rate risk相對上都被降低了!!)

2. Support Tranches保證PAC Tranches不必面對contraction risk與extension risk所產生的prepayment risk!!只是當Support Tranches的本金完全提前償還完時,PAC Tranches就退化成Sequential-Pay Tranches!!而此時我們稱此一情況為 a broken or busted PAC!!

3.PAC window必須依賴實際的償付情況,因此會出現理論window與最後Effective collars是不同的,而此一不同取決於Acrual Prepayments!!

4.Accrual Tranche將資金用於償付順序高的Tranche本金,自身是不支付任何利息的,直到到期為止!!因此需要長天期者能夠購買Accrual Tranche!

b. An Actual CMO structure

Actual CMO其中包含好幾個PAC (or PAC I) bonds,PAC II(a. It is a support tranche with a schedule; b.Scheduled Tranches which has no specified prepayment collar compared with PAC I),好幾個Target Amortization class(TAC) Tranches,以及好幾個Support Tranches(可以為floating-rate與inverse floating rate的形式)!值得注意的是一般我們說的Accrual tranche(Z-bond)指的是在其他Tranches被清償前,完全沒有被分配到現金流入的Tranche,原來該領到的都被拿去清償前面Tranches的本金;而Support Tranche則指的是專幫PAC Tranches或Scheduled Tranches避免掉prepayment risk(contraction與extension risks)的Tranche,因此她也有可能被提前清償掉,而造成PAC Tranche變成busted or broken而失去了自身contraction與extension risk的保護!!!

III. Stripped MBS

主要包含兩種Strips: Principal-only Strips與Interest-Only Strips!PO Strips的價值會隨著mortgage rate上升而下降,因為MBS將因為mortgage rate上升而越來越不會提前償還本金甚至是利息!!同理,IO的價值會隨著mortgage rate上升而上升!!

IV. Commercial Mortgage-Backed Securities (CMBS)

CMBS背後只有其擔保品擔保當其擔保品被拍賣償付債權不足時,投資人不能像issuer求償!!另外其call protection (at the loan level or at the structure level)的部分主要在因為避免被提前清償所面臨到的prepayment risk,其他部分就請自行參閱相關書籍!!the Baloon Maturity Provision也請自行參閱書籍了!!

二. 再來討論Asset-Backed Securities!!

I. 在ABS的建構當中,我們必須先了解到the process of securitization,而其中的參與者有seller,issuer/trust(這裡多為SPV),servicer(一般分成hybrid transaction與true securitization)!而承襲MBS,我們在建構ABS時,除了必須考量到傳統上agency bond的prepayment risk,還必須多考量到credit risk,因此ABS的架構除了有prepayment tranche外,還必須多考量到credit tranche!!而一般採用的Senior-Subordinate structure就是考量到credit risk redistribution的產物,一般也將其視為internal credit enhancement的必然!!

II. ABS一般包含兩類:Amortization asset與Non-amortization asset所組成的ABS;除了prepayment之外,前者必須考量到interest與principal的償付,而後者則必須考量到loan does not have scheduled payment amount!Non-amortization ABS則必須注意到通常其具有lockout period,在這段期間收到的principal payment不會被分配給bondholders,而是將資金再投入其他的new loans或assets當中!!

III. Credit Enhancements有兩種:Internal與External!!External credit enhancement包含Corporate guarantees,Letter of credit與Bond insurance,前兩者都會影響到ABS與原發行者的關係,因為有issuer擔保,很難將此視為是true sale,而有weak link approach的關係,因此會影響到ABS的信用評等!!而Internal credit enhancement包含cash reserve funds, excess spread funds, overcollateralization與A senior/subordinate structure(因其有shift interest mechanism於其中),這個部分的名詞請參閱專書!!

IV. 另外有一些ABS請自行參閱專書:Home Equity Loans, Manufactured house-backed securities,Student loan-backed securities,Small Business Administration Loan-backed securities.....

V. 在Auto-loan ABS中,我們有一個名稱叫做ABS(from absolute prepayment rate)利用其計算SMM,SMM = ABS/[1-ABS*(M-1)],因此我們知道相對關係ABS = SMM/[1+SMM*(M-1)] .....Auto-loan ABS一般不太注意refinancing的問題!!

在Credit Card receivable-backed securities中,我們需要注意下列名詞:Passthrough structure, Controlled-amortization structure與Bullet-payment structure.....

VI. Collateralized Debt Obligations (CDOs)

構成CDO的成員有 U.S. domestic high-yield Corporate bonds, structured financial products(MBS與ABS),emerging market bonds,bank loans,special situation loans and distressed debt, CDS與其他credit derivatives!! 一般CDO中,其Senior tranche為floating-rate debt or loan,而mezzanine tranche為fixed-rate debt or loan,最下面一層通常是Equity tranche是發行者用來吸收credit risk與prepayment risk的,因此一般都由發行者持有!!(當然我們後來知道在2007-2008年美國金融風暴中,equity tranche通常也被販賣到市場上面,特別是歐美的大型金融機構都是如此做的,e.g.DB,UB..Ci....等等!!這是非常奇怪的事情!!還有人跟保險公司針對這部分再買類似的CDS....)

1.Cash Flow CDO是真正持有相對應的債券或債務所形成的CDO,一般持有人賺取持有商品背後的interest與principal payment以淘汰senior與mezzanine tranche,另外還需要了解的有:Ramp up phase, Reinvestment phase與Pay down phase等等!!

2.Market Value CDO則是經理人積極處分其中已經價高的金融商品,然後買入其他便宜的相關金融商品!!

3.Synthetic CDO則是透過衍生性金融商品去承擔相同的credit risk而並未持有Cash Flow CDO,一般持有的就是Credit Default Swaps(CDS),一般說來都有兩個主要section:Junior與Senior兩個部分,而Junior Tranches通常為CDS的seller,而Senior tranches則為CDS的buyer....

4.Arbitrage CDO則是在collateral與funding costs之間透過arbitrage追求較高的Spread!!

5.Balance-Sheet CDO則是金融機構透過此一商品將其所持有的投資組合中的信用風險轉嫁給持有BS-CDO者!