The latest implied forward rate forecast from Kamakura Corporation shows projected 10 year U.S. Treasury yields down 0.01% to 0.03% from last week while fixed rate mortgage yields are 0.01% to 0.03% 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.

- The 10 year U.S. Treasury yield is projected to rise from 2.89% at Thursday's close (up 0.01% from last week) to 3.344% (unchanged from last week) in one year.
- The 10 year U.S. Treasury yield in ten years is forecast to reach 4.769%, 7 basis points lower than last week.
- The 15 year fixed rate mortgage rate is forecast to rise from the effective yield of 3.41% on Thursday (unchanged from last week) to 3.889% (up 0.006% from last week) in one year and 5.74% in 10 years, down 0.011% 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 December 12, 2013 constant maturity Treasury yields that were reported by the Department of the Treasury at 3 p.m. Eastern Standard Time December 12, 2013. 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) have even more variation on the short end than last week, resulting in the twisting curves illustrated below. The projected 1 month rate of 4.626% in November 2023 is down 4 basis points from last week. The 10 year U.S. Treasury yield is projected to rise steadily to reach 4.769% on November 30, 2023, 7 basis points lower than projected last week.

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 3.411% today to 5.739% in 10 years, down 1 basis point 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 0.724% to 1.006% in 10 years, up 5 basis points from last week.

For detailed information on the implications of the implied forecast for the valuation of mortgage servicing rights, see the complete text of the Kamakura Corporation weekly interest rate analysis.

**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.