Kamakura Corporation projections for U.S. Treasuries and fixed rate mortgages this week show that the implied forward rates for 15 year fixed rate mortgages rise from a current effective yield of 3.467% to 5.75% in 10 years, down 0.06% from last week. The market implied risk-adjusted present value of each 0.05% in net mortgage servicing rights is $353.44, down $0.01 from last week, for a $100,000 15 year mortgage (after deducting points). For each 0.05% in net mortgage servicing rights for a 30 year $100,000 mortgage, the market-implied risk-adjusted value $278.47 is up $1.75 from last week. The $1.75 increase is a gain of 0.63% this week.

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

- The 15 year fixed rate mortgage rate is forecast to rise from the effective yield of 3.467% on Thursday (down 0.01% from last week) to 3.953% (down 0.03% from last week) in one year and 5.75% in 10 years, down 0.06% from last week.
- The mark to market value of a newly originated mortgage is divided as follows for a 15 year mortgage: 23.75% interest only, 74.65% principal only, and 0.60% points.
- For a 30 year mortgage, the market value is divided this way: 52.43% interest only, 46.87% principal only, and 0.70% points.
- The risk-neutral present value of each 0.05% of net servicing fee on a 15 year $100,000 mortgage (after deducting points) is $353.44.
- The same figure for a 30 year mortgage is $278.47.
- The risk-neutral present value of each constant $1 monthly servicing cost is $140.20 for a 15 year mortgage and $200.91 for a 30 year mortgage.

Other mortgage servicing metrics are given in detail below.

The forecast allows investors to assess likely total returns and related risk over the next 120 months for these important classes of common stock:

Financial institutions who are heavy originators or owners of mortgages and mortgage-backed securities

- Wells Fargo & Co. (NYSE:WFC) and Eastdil Secured
- JPMorgan Chase & Company (NYSE:JPM)
- Bank of America Merrill Lynch (NYSE:BAC)
- KeyBank (NYSE:KEY)
- PNC Real Estate (NYSE:PNC)
- CBRE Capital Markets (NYSE:CBG)
- Prudential Mortgage Capital Company (NYSE:PRU)

Financial services companies with large portfolios of mortgage servicing rights

- Wells Fargo & Co.
- Bank of America
- JPMorgan Chase & Company
- Citigroup (NYSE:C)
- US Bank (NYSE:USB)
- Ocwen (NYSE:OCN)
- Nationstar Mortgage Holdings (NYSE:NSM)
- ResCap (privately held)
- PHH Corporation (NYSE:PHH)
- PNC Financial Services Group

Mortgage Real Estate Investment Trusts (mREITs)

**Data Used in the Analysis**

Today's forecast for U.S. Treasury yields is based on the May 1, 2014 constant maturity Treasury yields that were reported by the Department of the Treasury on the same day. 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 April 30, 2014.

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.

**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.

**Mortgage Analysis for This Week**

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 a recent 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 for the primary mortgage market, relative to U.S. Treasuries:

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

**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:

We apply the same mortgage valuation yield curve zero coupon bond prices to various aspects of mortgage servicing cash flows to arrive at the risk-neutral present value of these cash flows:

- The risk-neutral valuation split between interest-only and principal-only cash flows.
- The levels of net servicing fees.
- The net cost to service, assuming costs are a constant dollar amount.
- The 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 below for "float periods" ranging from 1/4 of a month to a full month.
- The value of float on the payment of interest and principal for various lengths of the "float period."
- 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. The final 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.

The results of the analysis are shown in the following series of tables:

**Background Information on Input Data and Smoothing**

The Federal Reserve H15 statistical release is the source of most of the U.S. Treasury 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.

**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 (other than from Seeking Alpha). 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 this article.