Projected one month bill rates for 2016-2018 rose by more than 0.20% this week after comments by Fed Chairman Janet Yellen on Wednesday. The forecast also shows projected 10 year U.S. Treasury yields up 0.04% to 0.13% from last week while fixed rate mortgage yields are about 0.04% lower. 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.

These scenarios are consistent with a multi-factor rate model benchmarked in 52 years of U.S. history, discussed below

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

- The 10 year U.S. Treasury yield is projected to rise from 2.79% at Thursday’s close (up 0.13% from last week) to 3.185% (up 0.13% from last week) in one year.
- The 10 year U.S. Treasury yield in ten years is forecast to reach 4.30%, 0.04% higher than last week.
- The 15 year fixed rate mortgage rate is forecast to rise from the effective yield of 3.407% on Thursday to 3.922% (down 0.03% from last week) in one year and 5.953% in 10 years, down 0.04% 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), bond funds (BOND)(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 March 13, 2014 constant maturity Treasury yields that were reported by the Department of the Treasury at 3 p.m. Eastern Standard Time March 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.

**U.S. Treasury Yield Forecast**

This week’s projections for the 1 month Treasury bill rate (investment basis) bend sharply upward by almost 0.30% in the years 2015 to 2021. The projected 1 month rate of 4.04% in February 2024 is up 0.05% from last week. The 10 year U.S. Treasury yield is projected to rise steadily to reach 4.30% on February 29, 2024, 0.04% higher than 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. The basis for this model is the study released by Kamakura Corporation on March 5, 2014 that proves at least 9 factors are needed to accurately model quarterly rate changes. The study makes use of more than 52 years of daily data from the U.S. Department of the Treasury and the Board of Governors of the Federal Reserve. The 9 factors used are 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 (see page 12, paragraph b) 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 June 2016 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 June 20, 2014, the curve shifts up considerably to the light blue curve shown below. Then yields shift dramatically upward in June 2015 (in green) followed by a sharp drop in June 2016 (in yellow). The June 2016 Treasury curve is lower than June 2015 levels across the full curve. By June 2017, the U.S. Treasury curve drops on the short end by a large amount, returning rates almost to current levels.

**Scenario B: Extended Pain and Suffering**

In the second scenario, the U.S. Treasury curve powers up consistently, with the largest rise coming in June 2015 (in green). Short rates swing upward in June 2016 (in yellow). Short rates in June 2017 (in red) end up just below the 10% level.

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

In scenario 3, the U.S. Treasury curve shifts up in June 2014 (in light blue), especially on the long end. Yields remain almost unchanged in June 2015 (in green). By June 2016 (in yellow), short rates twist upward, which flattens the long end of the yield curve and lowers longer term rates. The decline in long rates continues in June 2017 (in red), while the short end of the curve is slightly higher.

**A Reminder to Readers about These Three Scenarios**

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 3.407% today to 5.953% in 10 years, down 0.03% 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 0.794% to 1.69% in 10 years, down 0.07% 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:

**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:

**Background Information on Input Data and Smoothing**

The Federal Reserve H15 statistical release is the source of most of the data used in this analysis. 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). 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 by Prof. Robert A. Jarrow and Donald R. van Deventer outlining the Kamakura approach to mortgage yield curve derivation was published in *The Journal of Fixed Income*.

The mortgage valuation yield curve insights depend heavily on Prof. Robert A. Jarrow’s paper “ Risky Coupon Bonds as a Portfolio of Zero-Coupon Bonds,” published in *Finance Research Letters* in 2004.

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 data base format.

Donald R. van Deventer and Martin Zorn

Kamakura Corporation

Honolulu, March 21, 2014