Performance of MBS: ARMs vs FRM  
The yield curve steepened significantly in the month of May (see Figure 1) and that affected the  
performance of adjustable rate mortgages (ARMs) and fixed rate mortgages (FRMs) differently. Not  
only FRM is exposed to higher duration risk (parallel shift of the yield curve) but also different non-  
parallel yield curve risks (steepening and curvature of the yield curve) relative to the ARMs. As the  
yield curve may poise to start a rate rising and steepening regime, understanding the driving forces  
that affect the ARMs and FRMs total return is more important now for investment, portfolio revision  
and loans originations.  
For illustration, let us consider the total returns of a 30 year fixed rate FN 3.5 5/2042, 3138EETL3 and  
an ARM FN 2.86, 10/2035, 31413NV69. The bond analytics are presented in Table 1. Both MBSs are  
trading at significant premiums with similar long maturities. The FRM has a higher option adjusted  
spread (OAS) of 66 basis points, while the ARM has 29 basis points. As expected, FRM has a higher  
duration of 4.12 year while the ARM has a duration of only 0.89 years. That is, the FRM is exposed to  
higher interest rate risk when the yield curve makes a parallel upward shift. But we will show that the  
FRM is exposed to other risks as well.  
Table 1 | Risk Exposure of the MBS  
coupon hybrid  
market  
eff  
maturity  
index margin  
YTM OAS  
rate  
type  
price  
duration  
FN FRM 3.5  
FN ARM 2.86  
28.83  
24.5  
106.7  
107.5  
2.3 0.7 4.12  
1.7 0.3 0.89  
1 YEAR  
5/1  
174  
LIBOR  
To determine that risk drivers of the MBS, we consider the attribution of the total returns of the MBS  
in Figure 2 and Figure 3 respectively. These return attribution results breakdown the observed total  
returns into their components, and thus identifying all the factors that affect the bond returns. Further,  
these results highlight the main contributors of the profit or loss of the MBS.  
The results show that the FRM lost over 2.7% in the month of May, with the yield curve risks  
contributing 1.8%. The remainder of the loss for the most part is attributed to the widening of the  
option adjusted spread, resulting in 0.65%. By way of contrast, let us consider the return attribution  
of the ARM over the same period.  
The results on the ARM are quite different. The ARMs has a profit of 0.06%. While the parallel shift  
of the yield curve and the widening of the OAS led to loss of over 0.28%, the yield curve movement  
gains 0.176% and the prepayment speed was slower than expected leading to another 0.2% gain.  
Most Important Contributors to Total Returns  
As expected, the parallel shift of the yield curve was the most significant factor that led to the  
losses of the bonds. But for the ARMs, the steepening of the yield curve led to a gain,  
mitigating the losses from much of the rise of the yield curve.  
In May 2013, when interest rates rose, the OAS widened, leading to losses in both cases, but it  
affected the FRM more significantly. The OAS shift can also be an important factor.  
Conclusions  
ARMs can benefit from a steepening of the yield curve, an attribute that is often over looked.  
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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