The latest implied forward rate forecast from Kamakura Corporation shows projected 10 year U.S. Treasury yields down 0.11% to 0.18% from last week while fixed rate mortgage yields are 0.01% to 0.04% 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. We introduce those scenarios with a graph of 52 years of U.S. Treasury yield history and a video of daily yield curve movements.

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

- The 10 year U.S. Treasury yield is projected to rise from 2.65% at Thursday's close (down 0.11% from last week) to 3.040% (down 0.14% from last week) in one year.
- The 10 year U.S. Treasury yield in ten years is forecast to reach 4.281%, 18 basis points lower than last week.
- The 15 year fixed rate mortgage rate is forecast to rise from the effective yield of 3.49% on Thursday (up 0.040% from last week) to 3.976% (up 0.030% from last week) in one year and 5.99% in 10 years, up 0.039% 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:BND), 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 February 27, 2014 constant maturity Treasury yields that were reported by the Department of the Treasury at 3 p.m. Eastern Standard Time February 27, 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) produce a significantly flatter curve compared to last week (below). The projected 1 month rate of 4.112% in January 2024 is down 19 basis points from last week. The 10 year U.S. Treasury yield is projected to rise steadily to reach 4.281% on January 31, 2024, 18 basis points lower 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 start with some history, graphing the 1 year, 10 year and 30 year Treasury yields from January 1962 until February 27, 2014:

The purpose of the history lesson is to remind readers that the way U.S. Treasury yields are today is not "normal" and it is not likely to stay this way for long. For a daily review of yield curve movements since 1962, we recommend a narrated video from Kamakura Corporation.

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 are still more than 200 basis points higher than they are today.

**Scenario B: Extended Pain and Suffering**

In the second scenario, the U.S. Treasury curve powers up consistently, year after year, with steady jumps in May 2014 (light blue) and May 2015 (in green). Rates jump again in May 2016 (in yellow) and May 2017 (in red). By this time most of the U.S. Treasury curve is near 7.00%.

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

In scenario 3, the U.S. Treasury curve drops slightly in May 2014 (in light blue). Rates twist in May 2015 (in green) with short rates up and long rates down. By May 2016 (in yellow), yields are up with a serious hump in the curve at the 7 year maturity. The full curve twists again in May 2017 (in red), with short term rates over 4.00%. The good news, however, is that long rates stay below where they are today.

**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 3.492% today to 5.990% in 10 years, up 4 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 1.024% to 1.733% in 10 years, up 21 basis points from last week.

**Implied Valuation of Mortgage Servicing Rights**

The complete text of the weekly Kamakura Corporation interest rate analysis contains a detailed description of the implications of the yield analysis for the valuation of mortgage servicing rights. We refer interested readers to that version of the interest rate release.

**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:

**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.