Making the Risk of a Collateralized Mortgage-  
Obligation (CMO) transparent  
Interest rate risk of a CMO tranche can be significant because of the complex waterfall structure  
allocating the cashflow to each tranche of the deal. Can we measure the CMOs’ performance  
accurately given a complex structure? If so, can bond analytics assist us to select bonds for our  
portfolios? The use of (1) Waterfall Structure Graph, (2) Option adjusted spread (OAS) analytics,  
and (3) return attribution can provide a systematic in selecting a CMO bond. The waterfall graph  
depicts the risk of a tranche within a deal given the principal and interests allocations. OAS analytics  
give the measures of value and cheap/rich. (3) Return attribution interprets the analysis, providing us  
the feedback on our decision making process. This systemic approach can satisfy the regulatory  
requirements on understanding a complex structure of a CMO.  
To illustrate a CMO waterfall structure, let us consider the deal FNR 2 6/25/2042, in particular the  
composite tranche FNR 13-001 PG (3136ABB28).  
A CMO Structure Explained  
Table 1 provides a summary of the FNR 13-001H structure. For our analysis to follow, note that PG and  
PD are PAC bonds supported by ZU as explained in the Table.  
Table 1
 
|
FNR 13-001H Structure  
Waterfall Graphs  
Figure 1 and Figure 2 waterfall structure graphs below depict the principal redemption of each bond in  
FNR 13-001H under 100 PSA and 200 PSA respectively. The graphs show that the weighted average  
life of the supporting tranche ZU shortens significantly at a higher prepayment speed, while PG and  
PD are somewhat protected. The waterfall graphs can clearly depict the behavior the bonds within a  
composite and therefore provides the reasons behind the risk or stability of a bond cash flow.  
Figure 1 | Waterfall Structure of FNR 13-001H 100 PSA  
FNR 13-001 PG FNR 13-001 PI FNR 13-001 PD FNR 13-001 ZU  
FNR 13-001 FB FNR 13-001 SA FNR 13-001 IB  
1,400,000  
1,200,000  
1,000,000  
800,000  
600,000  
400,000  
200,000  
-
Figure 2 | Waterfall Structure of FNR 13-001H 200 PSA  
FNR 13-001 PG FNR 13-001 PI FNR 13-001 PD FNR 13-001 ZU  
FNR 13-001 FB FNR 13-001 SA FNR 13-001 IB  
2,500,000  
2,000,000  
1,500,000  
1,000,000  
500,000  
-
Option Adjusted Spread (OAS) Analysis of FNR 13-001 PG (3136ABB28)  
The risk and value of a bond as depicted by the Waterfall Structure graph can be quantified using the  
option adjusted (OAS) approach. OAS is the spread off the Treasury curve net of the value of any  
embedded option of a bond. The bond is described below as of 6/28/2013.  
The tranche FNR 13-001-PG has a coupon rate of 2%, maturity of 29.06 years and is priced at 99.76.  
The conditional prepayment rate (CPR) of CMO bond (FNR 13-001 PG 3136ABB28), are 17% and 11%  
for one year and life respectively. Therefore the prepayment profile should be more similar to that of  
Figure 2 which has a CPR of 12% life. And, Figure 1 shows the impact on the prepayment profile when  
there is an extension risk.  
The OAS analytics as of 6/28/2013 are summarized below.  
Table 2 | OAS analyticsas of 6/28/2013  
YTM (%) Spread (%) OAS (%) WAL (year) Eff. Dur Eff. Conv  
2.03  
0.91  
0.46  
5.26  
5.23  
2.23  
The amortization and prepayments lead to the weighted average life (WAL) to be much lower than  
its maturity. As a result, the effective duration is 5.23 year and the convexity is quite high. The OAS is  
46 basis points while the yield is 2.03%.  
By way of comparison, a FN agency bond of similar duration has a YTM of 1.94%and OAS of 32 basis  
points and therefore the tranche is cheaper than an agency bond by 14 basis points only.  
Return Attributions of FNR 13-001 PG (3136ABB28) 6/3/2013 – 6/28/2013  
How does the OAS analysis translate into realized performance? We here consider the performance  
of the bond for the month of May. Below depicts the Treasury spot yield curves at the beginning and  
end of the month.  
Figure 3 | The Treasury Spot Curves  
4.50  
4.00  
3.50  
3.00  
2.50  
2.00  
1.50  
1.00  
0.50  
0.00  
1m 3m 6m 1y 2y 3y 4y 5y 7y 10y 15y 20y 30y  
June 03, 2013  
June 28, 2013  
The return attribution results presented below shows that the bond loses over 2.1% over that month.  
Much of the loss is attributed to the yield curve parallel shift (1.55% loss). Note that the long rate has  
shifted 40 basis points but the 2 year rate has barely shifted. The result shows that for this bond, the  
yield curve has shifted roughly 30 basis points on average. (duration* shifts% = % change in value;  
5*0.3 = 1.5). During this period, the OAS as also widened resulting in 0.75% loss in value of the bond.  
The result shows that duration remain the most important factor and that the OAS may mean revert  
and may add value in subsequent months. Because the bond is a PAC protected by the supporting  
tranches, there is no prepayment effect.  
Conclusions  
While a CMO structure can be complicated, we can analyze any bond by applying: the waterfall graph  
(identifying the prepayment risk), the OAS analysis (measuring value and risk), return attribution  
(relating performance to measures- a reality check). This process can apply to a bond or a portfolio.  
Contact us if you have any questions, suggestions or comments. What would you like us  
to discuss in coming issues? We look forward to hear from you.  
support@thomasho.com Voice: 1-212-732-2878 Fax: 1-212-608-1233  
Http://www.thomasho.com 55 Liberty Street, 4B, New York, NY 10005-1003 USA  
Thomas Ho Company (THC) has decades of banking experience; a leading ALM solution for the banking community, sole  
provider of risk modeling (NPV model) to OCC for seven years.  
Thomas S.Y. Ho PhD, President of THC, senior consultant to federal regulatory agencies and senior consultant to enterprise  
risk management departments of largest financial institutions 1999-2005.; elected member of the US Financial Economists  
Roundtable; Board member of the Finance Mathematics Program, Courant Institute of Mathematics, New York University;  
Research Professor at Owen School of Business, Vanderbilt University; nomination committee IAFE financial engineer of the  
year. He was named one of the most prolific authors in finance based on a study by Cooley and Heck, (Journal of Finance, 2003).  
Author of the Ho-Lee model (the first arbitrage-free stochastic interest rate model) and key rate durations (the widely used  
interest rate risk measure for over $12 trillion assets.). Associate Editor of Journal of Derivatives and Journal of Investment  
Management; co-authored four books and has published in major journals including Journal of Finance, Journal of Derivatives,  
Journal of Fixed Income, and Journal of Portfolio Management. Books include The Oxford Guide to Financial Modeling,  
Strategic Fixed Income Investments, Securities Valuation. Received his Ph.D. in Mathematics in 1978 from the University of  
Pennsylvania, New York University's Stern School of Business as Professor of Finance from 1978 until 1990; full professor in  
1985.  
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