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The latest implied forward rate forecast from Kamakura Corporation shows projected 10 year U.S. Treasury yields mixed compared to last week while fixed rate mortgage yields are 0.15% to 0.08% lower. The implied forecast comes in the midst of the U.S. debt ceiling impasse which saw trading volume in credit default swaps on the United States of America jump to 56 contracts for $2.03 billion in the week ended September 27. The week also saw 1 month Treasury bill rates rise from the 0.01-0.03% level of recent weeks to 0.11% on Friday. 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 2.62% at Thursday's close (down 0.04% from last week) to 3.069% (down 0.01% from last week) in one year. The 10 year U.S. Treasury yield in ten years is forecast to reach 4.571%, 4 basis points higher than last week. The 15 year fixed rate mortgage rate is forecast to rise from the effective yield of 3.39% on Thursday (down 0.08% from last week) to 3.84% (down 0.10% from last week) in one year and 5.80% in 10 years, down 0.15% from last week. 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. Treasury-related exchange traded funds affected by the forward rates include:

Long-duration Treasury Exchange-Traded Funds: (NYSEARCA:TLH), (NYSEARCA:IEF), (NYSEARCA:DTYL), (NYSEARCA:DLBL), (NYSEARCA:ILTB), (NYSEARCA:TENZ), (NYSEARCA:ITE), (NYSEARCA:TLO), (NYSEARCA:EDV), (NASDAQ:VGIT), (NASDAQ:VGLT), (NYSEARCA:TMF), (NYSEARCA:TYD), (NYSEARCA:LBND), (NYSEARCA:UBT), (NYSEARCA:UST), (NYSEARCA:TMV), (NYSEARCA:TYO), (NYSEARCA:DSTJ), (NYSEARCA:DSXJ), (NYSEARCA:SBND), (NYSEARCA:PST), , (NYSEARCA:DTYS), (NYSEARCA:DLBS), (NYSEARCA:TBF), (NYSEARCA:TTT), (NYSEARCA:TYNS), (NYSEARCA:TYBS), (NYSEARCA:TBX)

Shorter-duration Treasury Exchange-Traded Funds: (NYSEARCA:SHY), (NYSEARCA:SHV), (NYSEARCA:IEI), (NYSEARCA:BIL), (NYSEARCA:TUZ), (NYSEARCA:FIVZ), (NYSEARCA:DTUL), (NASDAQ:VGSH), (NYSEARCA:DTUS), (NYSEARCA:DFVS), (NYSEARCA:DFVL), (NYSEARCA:SST), (NYSEARCA:ISTB), (NYSEARCA:TBZ).

Today's forecast for U.S. Treasury yields is based on the October 3, 2013 constant maturity Treasury yields that were reported by the Board of Governors of the Federal Reserve System in its H15 Statistical Release at 4:15 p.m. Eastern Daylight Time October 4, 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) are in line with the projections from last week, showing a slight drop in rates at 2016 as graphed below. The projected 1 month rate of 4.493% in August 2023 is up 5 basis points from last week. The 10 year U.S. Treasury yield is projected to rise steadily to reach 4.571% on August 31, 2023, 4 basis points higher than projected last week.

(click to enlarge)

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.

(click to enlarge)

The effective yield on 15 year fixed rate mortgages is projected to rise from 3.391% today to 5.796% in 10 years, down 15 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 0.938% to 1.243% in 10 years, down 19 basis points from last week.

Mortgage servicing rights metrics are available in the full text of the Kamakura Corporation interest rate analysis.

Background Information on Input Data and Smoothing

The Federal Reserve H15 statistical release is available here.

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). Additional information on the maximum smoothness forward rate approach can be found at this link.

The maximum smoothness approach to credit spread smoothing is available at this related link.

The academic paper outlining the Jarrow-van Deventer 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 Curve," 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 U.S. Treasury Yield Forecast

The 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:

(click to enlarge)
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:

(click to enlarge)

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

(click to enlarge)
The forecast yields for months 61 to 120 are given here:

(click to enlarge)

Today's 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 ®:

(click to enlarge)

Only fixed rate mortgage data is used in this analysis in order to avoid the more complex embedded options found in floating rate mortgages, with the risk that the mortgage valuation yield curve of fixed and floating rate mortgages is not identical.

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:

(click to enlarge)

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

(click to enlarge)

Source: U.S. Debt Ceiling Impasse Leaves Treasury Forecast Mixed, Mortgage Forecast Down

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