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Donald R. Van Deventer, Ph.D.

Don founded Kamakura Corporation in April 1990 and currently serves as its chairman and chief executive officer where he focuses on enterprise wide risk management and modern credit risk technology. His primary financial consulting and research interests involve the practical application of leading edge financial theory to solve critical financial risk management problems. Don was elected to the 50 member RISK Magazine Hall of Fame in 2002 for his work at Kamakura.

# Kamakura Mortgage Valuation Yield Curve, Mortgage Servicing Rights Valuation, and U.S. Treasury Forecast

02/21/2014 12:46 PM

The latest implied forward rate forecast from Kamakura Corporation shows projected 10 year U.S. Treasury yields up 0.02% to 0.07% from last week while fixed rate mortgage yields are 0.02% to 0.14% higher.  Mortgage yields, determined by the Monday through Wednesday weekly survey of the Federal Home Loan Mortgage Corporation, lag Treasury movements simply because of the 3-day yield calculation used in the Primary Mortgage Market Survey ®.  We also present three potential scenarios consistent with the implied forecast that represent alternative paths for interest rates.

Here are the highlights of this week’s implied forecast:

• The 10 year U.S. Treasury yield is projected to rise from 2.76% at Thursday’s close (up 0.03% from last week) to 3.176% (up 0.03% from last week) in one year.
• The 10 year U.S. Treasury yield in ten years is forecast to reach 4.458%, 6 basis points higher than last week.
• The 15 year fixed rate mortgage rate is forecast to rise from the effective yield of 3.45% on Thursday (up 0.020% from last week) to 3.946% (up 0.038% from last week) in one year and 5.95% in 10 years, up 0.140% from last week.

The implied forecast takes the Treasury yield curve as a given and does not attempt to reverse the impact on the curve of quantitative easing by the Federal Reserve.  See Jarrow and Li (2012) and Chadha, Turner and Zampolli (2013) for estimates of the impact of quantitative easing on Treasury yield levels.

We explain the background for these calculations in the rest of this note, along with some mortgage servicing rights metrics. The forecast allows investors in exchange traded U.S. Treasury funds (TLT) (TBT), total return bond funds (BOND), bond index funds (BND), municipal bonds (NUV) and exchange traded mortgage funds (REM) to assess likely total returns over the next 120 months.

Today’s forecast for U.S. Treasury yields is based on the February 20, 2014 constant maturity Treasury yields that were reported by the Department of the Treasury at 3 p.m. Eastern Standard Time February 20, 2014. The forecast for primary mortgage market yields and the resulting mortgage servicing rights valuations are derived in part from the Federal Home Loan Mortgage Corporation Primary Mortgage Market Survey ® made available on the same day.

The U.S. Treasury “forecast” is the implied future coupon bearing U.S. Treasury yields derived using the maximum smoothness forward rate smoothing approach developed by Adams and van Deventer (Journal of Fixed Income, 1994) and corrected in van Deventer and Imai, Financial Risk Analytics (1996). The primary mortgage yield forecast applies the maximum smoothness approach to primary mortgage market credit spreads, which embed the risk neutral probabilities of mortgage default and prepayment risk.  References explaining this approach are given below.

Both forecasts, plus the mortgage servicing rights parameters, are available via Kamakura Risk Information Services: Treasury Yield Service, Mortgage Yield Service, and MSR Valuation Service.  For information, please contact Kamakura Corporation at info@kamakuraco.com.  Similar forecasts for the marginal cost of bank funding and the Libor-swap curve are also available on request.

U.S. Treasury Yield Forecast

This week’s projections for the 1 month Treasury bill rate (investment basis) twist around the full length of projected curve from last week. The projected 1 month rate of 4.306% in January 2024 is up 9 basis points from last week.  The 10 year U.S. Treasury yield is projected to rise steadily to reach 4.458% on January 31, 2024, 6 basis points higher than projected last week.

3 Scenarios around the Forward Rate Curve

In the rest of this section, we highlight three of the infinite number of scenarios that could come about.  We ensure that these scenarios are consistent with an efficient, “no arbitrage” market for U.S. Treasury as described by Heath, Jarrow and Morton (1992).  We start with the current U.S. Treasury curve. We assume that a 9 factor model drives U.S. Treasury rates at maturities ranging from 3 months to 30 years.  This is 6 more factors than the Federal Reserve uses in its 2014 Comprehensive Capital Analysis and Review stress tests and 3 more factors than required by the December 2010 version of the Basel II market risk framework of the Bank for International Settlements. We use more factors for maximum consistency with U.S. yield curve history. The parameters of the model are estimated by Kamakura Corporation using quarterly data from 1962 to the present, with an optimization of parameters on the 2001-2013 low rate period.  The model parameters are available by subscription from Kamakura Risk Information Services.  The consensus “implied forecast” is shown later in this report.  We now turn to three specific scenarios selected by Kamakura’s analytics team for their special features.

Scenario A: A Rise to May 2015 and Then a Rate Decline

The Federal Reserve’s Comprehensive Capital Analysis and Review (“CCAR”) process focuses on three specific scenarios provided by the Federal Reserve.  In this section of our weekly commentary, we start with the forward curve for the current date, which we explain below in our implied forecast.  In this section of the report we use Monte Carlo simulation in the Heath Jarrow and Morton framework using Kamakura Risk Manager.  We project 13 quarters, consistent with the CCAR program, but we generate a large number of scenarios randomly.  We select 3 that we hope will be of interest to readers. In the first scenario, the initial U.S. Treasury yield curve is shown in dark blue.  By May 20, 2014, the curve shifts up considerably to the light blue curve shown below.  Then yields move up strongly in May 2015 (in green) followed by a slight decline in May 2016 (in yellow).  The May 2016 Treasury curve is higher than May 2015 levels on the short end of the curve.  By May 2017, the U.S. Treasury curve is lower generally, but short rates continue to rise as the Fed seeks to slow the economy and bring long rates lower still.

Scenario B: Extended Pain and Suffering

In the second scenario, the U.S. Treasury curve powers up consistently, with the exception of a dip in long term rates in May 2014 (light blue) and May 2015 (in green). Rates jump sharply in May 2016 (in yellow) and then rise again in May 2017 (in red). By this time most of the U.S. Treasury curve is near 6.00%.

Scenario C: Long Rates Controlled by a Spike in Short Term Rates

In scenario 3, the U.S. Treasury curve twists in beginning in May 2014 (in light blue), with the short end rising and long rates dipping slightly.  Rates shift up across the board in May 2015 (in green) but short rates continue to lead the rise.  By May 2016 (in yellow), the twist is more dramatic as the short end of the curve hits the 5.00% area and long rates drop more than 0.50%.  The full curve shifts up again in May 2017 (in red), with short term rates over 6.00%.  The good news, however, is that long rates stay near 4.00%.

All of these scenarios are plausible in that (a) they begin with the current U.S. Treasury curve and they are (b) simulated forward in a no arbitrage fashion (c) using historical U.S. Treasury volatilities.  That being said, there are an infinite number of possible forward curve shapes and paths, and these three have been selected more for their drama than anything else.  If one were to select only one scenario to focus on, it would be the forward rate “implied forecast” explained in more detail below.

Mortgage Valuation Yield Curve and Mortgage Yield Forecast

The zero coupon yield curve appropriate for valuing mortgages in the primary mortgage market is derived from new issue effective yields reported by the Federal Home Loan Mortgage Corporation in its Primary Mortgage Market Survey ®. The maximum smoothness credit spread is produced so that this spread, in combination with the U.S. Treasury curve derived above, correctly values new 15 year and 30 year fixed rate mortgages at their initial principal value less the value of points. The next graph compares the implied 15 year fixed rate mortgage yield with the implied 15 year U.S. Treasury fixed rate amortizing yield over the next ten years.

The effective yield on 15 year fixed rate mortgages is projected to rise from 3.451% today to 5.951% in 10 years, up 14 basis points compared to last week. The 15 year fixed rate mortgage spread over 15 year amortizing Treasury yields is forecasted to widen from its current level of 0.878% to 1.519% in 10 years, up 8 basis points from last week.

Implied Valuation of Mortgage Servicing Rights

Using the insights of Kamakura Managing Director of Research Prof. Robert Jarrow noted below, we have derived the risk-neutral values of mortgage cash flows which are based on market implied default risk and prepayment risk.  We use these zero coupon bond prices to value mortgage-related cash flows relevant to mortgage servicing rights.  These zero coupon bond prices, when multiplied by current primary mortgage market terms, value new mortgages at their principal value less the value of points:

Today’s implied mortgage valuation yield curve results in the following risk-neutral valuation split between interest-only and principal-only cash flows:

We apply the same mortgage valuation yield curve zero coupon bond prices to various levels of net servicing fees to get their risk-neutral present value in today’s market:

If we use the market convention that the net cost to service is a constant dollar amount, the risk-neutral present value of the net cost to service can be derived using the same zero coupon bond prices from the mortgage valuation yield curve.

Kamakura Corporation works with clients on a consulting basis to do this valuation on a risk-neutral inflation adjusted basis as well as the constant nominal dollar cost basis.

Next, we value float per $100 of taxes and insurance on the underlying home. We assume that float is invested at the matched maturity U.S. Treasury forward rate for the matching float period below. The risk-neutral present value of the interest earned is calculated using the mortgage valuation yield curve, since an event of default or prepayment on the underlying mortgage ends this source of value. Value for a constant$100 amount is given here for “float periods” ranging from 1/4 of a month to a full month:

Again, the same analysis can be done on an inflation adjusted basis with insurance and taxes tied to the value of the home.

The value of float on the payment of interest and principal for various lengths of the “float period” is given in this table:

Another important component of mortgage servicing rights valuation is the net impact of cash flows to the servicer from the events of default and prepayment.  We can analyze this by asking this question: what would be the value of the mortgage if there were no events of default or prepayment? The answer is obtained by applying U.S Treasury zero coupon bond rates to the scheduled mortgage cash flows.  This table shows the net reduction in certain monthly cash flow that would be necessary for the value of the mortgage to adjust downward from this “no default/no prepayment value” to its current market value, discounted by the U.S. Treasury zero coupon bond prices. This adjusted basis converts the random probability of losses from prepayment and default to a known, certain cost of prepayment and default in the form of this “implied net constant monthly cash flow reduction.” The division of this negative cash flow impact between the servicer and other parties depends on the term of the servicing contract:

Background Information on Input Data and Smoothing

The Federal Reserve H15 statistical release is available here:

http://www.federalreserve.gov/Releases/H15/Update/

The Kamakura approach to interest rate forecasting, and the maximum smoothness forward rate approach to yield curve smoothing is detailed in Chapter 5 of van Deventer, Imai and Mesler (2013).

van Deventer, Donald R., Kenji Imai and Mark Mesler, 2013, Advanced Financial Risk Management, 2nd edition, John Wiley & Sons, Inc., Singapore.

The smoothing process for the maximum smoothness credit spread, derived from coupon-bearing bond prices, is given in Chapter 17 of van Deventer, Imai and Mesler (2013).

The problems with conventional approaches to mortgage servicing rights valuation and Kamakura’s approach to mortgage valuation yield curve derivation are also outlined here, along with the reasons for smoothing forward credit spreads instead of the absolute level of forward rates for the marginal bank funding cost curve.

The academic paper outlining the Kamakura approach to mortgage yield curve derivation was published in The Journal of Fixed Income:

Jarrow, Robert A. and Donald R. van Deventer, “A Simple, Transparent and Accurate Mortgage Valuation Yield,” The Journal of Fixed Income, Winter 2013, Vol. 22, No. 3, pages 37-44.

The mortgage valuation yield curve insights depend heavily on this important paper:

Jarrow, Robert A., “Risky Coupon Bonds as a Portfolio of Zero-Coupon Bonds,” Finance Research Letters, 1, no. 2 (June, 2004) pp. 100–105.

Today’s Kamakura U.S. Treasury Yield Forecast

The Kamakura 10 year monthly forecast of U.S. Treasury yields is based on this data from the Federal Reserve H15 statistical release:

The graph below shows in 3 dimensions the movement of the U.S. Treasury yield curve 120 months into the future at each month end:

These yield curve movements are consistent with the continuous forward rates and zero coupon yields implied by the U.S. Treasury coupon bearing yields above:

In numerical terms, forecasts for the first 60 months of U.S. Treasury yield curves are as follows:

The forecasted yields for months 61 to 120 are given here:

Today’s Kamakura Forecast for Effective Primary Mortgage Market Yields

Today’s forecast for the mortgage valuation yield curve is based on the following data from the Federal Home Loan Mortgage Corporation Primary Mortgage Market Survey ®:

Only fixed rate mortgage data is used in this analysis for reasons explained in the Kamakura mortgage valuation blog.
Applying the maximum smoothness forward rate smoothing approach to the forward credit spreads between the mortgage valuation yield curve and the U.S. Treasury curve results in the following zero coupon bond yields:

The forward rates for the mortgage valuation yield curve and U.S. Treasury curve are shown here:

The numerical values for 360 months of zero coupon bond prices and yields for the mortgage valuation yield curve are available by subscription to the KRIS Mortgage Yield Service via info@kamakuraco.com. For comments, questions, or more information about the yield curve smoothing and simulation capabilities in Kamakura Risk Manager, please contact us at info@kamakuraco.com.  Kamakura interest rate data are available in electronic form in both general and Kamakura Risk Manager database format.

Taqui Raza, Donald R. van Deventer and Martin Zorn
Kamakura Corporation
Honolulu, February 21, 2014

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Revised and updated with lessons from the 2007-2010 financial crisis, Advanced Financial Risk Management outlines a framework for fully integrated risk management and is an essential resource for anyone working in the financial field.