The latest implied forward rate forecast from Kamakura Corporation shows projected 10 year U.S. Treasury yields up 0.09% to 0.13% from last week, while fixed rate mortgage yields are 0.07% to 0.11% 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 2.74% at Thursday's close (up 0.09% from last week) to 3.164% (up 0.12% from last week) in one year.
- The 10 year U.S. Treasury yield in ten years is forecast to reach 4.382%, 10 basis points higher than last week.
- The 15 year fixed rate mortgage rate is forecast to rise from the effective yield of 3.41% on Thursday (down 0.085% from last week) to 3.899% (down 0.077% from last week) in one year and 5.88% in 10 years, down 0.111% 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 (NYSEARCA:TLT) (NYSEARCA:TBT), total return bond funds (NYSEARCA:BOND), municipal bonds (NYSE:NUV) and exchange traded mortgage funds (NYSEARCA:REM) to assess likely total returns over the next 120 months.

Today's forecast for U.S. Treasury yields is based on the March 6, 2014 constant maturity Treasury yields that were reported by the Department of the Treasury at 3 p.m. Eastern Standard Time March 6, 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) produce a steeper curve than projected last week, leading to higher rate forecasts on the intermediate and long ends. The projected 1 month rate of 4.211% in January 2024 is up 10 basis points from last week. The 10 year U.S. Treasury yield is projected to rise steadily to reach 4.382% on January 31, 2024, 10 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. The basis for this model is the study released by Kamakura Corporation on March 6, 2013 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 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 June 20, 2014, the curve shifts up considerably to the light blue curve shown below. Then yields move up strongly in June 2015 (in green) followed by a slight decline in long-term yields in June 2016 (in yellow). The June 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 remain high as the Fed seeks to slow the economy and bring long rates lower still.

**Scenario B: Extended Pain and Suffering with a Rise to 8.00%**

In the second scenario, the U.S. Treasury curve powers up consistently, with the exception of a dip in very short-term rates in June 2014 (light blue). Rates move up slightly by June 2015 (in green). Rates jump sharply in June 2016 (in yellow) and then rise again in June 2017 (in red). By this time, most of the U.S. Treasury curve is near 8.00%.

**Scenario C: The Japan Scenario**

In scenario 3, the U.S. Treasury curve shifts upward in June 2014 (in light blue). Rates shift sharply lower across the board in June 2015 (in green) with long rates well below today's levels. By June 2016 (in yellow), rates make one last move upward before falling back again the next year. The full curve shifts down in June 2017 (in red), with long rates below today's levels one more time. This is a variation on the low-rate Japan scenario.

**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 5.879% in 10 years, down 11 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 0.850% to 1.525% in 10 years, down 21 basis points from last week.

**Implied Valuation of Mortgage Servicing Rights**

The full text of the weekly Kamakura Corporation interest rate analysis contains implications for the valuation of mortgage servicing rights.

**Background Information on Input Data and Smoothing**

The Federal Reserve H15 statistical release is available here.

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:

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure:** Kamakura Corporation has business relationships with a number of organizations mentioned in the article.