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1 May 2013 CFA Institute Journal Review

A Stochastic U.S. House Price Model for Valuing Residential Mortgages and Other House Price–Dependent Assets (Digest Summary)

  1. Marc L. Ross, CFA

A stochastic house price model can value and measure the risk of mortgages and other house price–dependent assets. The author develops a model that is designed for financial institutions that hold mortgage portfolios.

What’s Inside?

The author develops a model that focuses on house prices and their distribution; he uses the model for mortgage valuation and risk measurement. The model takes a long view of future house prices to account for the long potential cash flows of mortgage assets, and the author is the first to provide this type of valuation tool.

How Is This Research Useful to Practitioners?

Mortgage value is derived from house prices; house prices are a function of rental and interest rates, which are proxies for inflation. The fundamental value and volatility of house prices affect the two embedded options in mortgages: the default option and the prepayment option. The author’s model generates a full-term structure of house price volatility. An understanding of the long-term structure of house price volatility provides insight into the proper valuation and risk measurement of house price–dependent assets.

The model tracks quarterly changes in house prices, accounting for serial correlation and mean reversion to fundamental value. Fundamental value is a function of the stochastic variables of rental rates discounted by the 10-year risk-free rate (using U.S. Treasury STRIPS). Rental growth and interest rates are positively correlated. Higher rates result from inflation because of economic growth.

House prices are serially correlated; they drift over the long term but revert to fundamental value. Longer-term distributions of house prices, rather than a mean, account for mortgages’ embedded options. The volatility of house prices increases over time, reflecting a term structure of volatility. Serial correlation in interest rates and rental rates results in the volatility of fundamental value increasing over time as well. But both actual prices and fundamental value experience mean reversion over the longer term.

Because of the volatility of house prices, embedded options in mortgages are a function of interest rate risk. House prices also have an impact on credit risk: House prices decreasing because of rates increasing damages the home’s collateral value in the event of a borrower’s unwillingness or inability to make mortgage payments.

Fixed-income portfolio managers who hold mortgage-backed securities and risk managers at financial institutions, as well as the managers of structured products and policymakers, will find the conclusions of this research useful.

How Did the Author Conduct This Research?

The author intersperses a review of the relevant literature with the development of his model to forecast long-term house price behavior. The components of the house price model are equations to evaluate quarterly house price changes and the house’s fundamental value (the present value of its discounted cash flows), the market rental rate, and the 10-year Treasury rate. The author proceeds to disaggregate these components to forecast the market rental rate.

For model inputs, he uses a constant-quality U.S. house price index (the Federal Housing Finance Agency Index) because of its long history and broad geographic coverage. To measure market rental rates, he uses the U.S. Consumer Price Index’s Rent of Primary Residence series. Finally, for zero-coupon Treasuries, he uses the historical estimates of Gurkaynak, Sack, and Wright (Federal Reserve Board working paper 2006) because pricing discrepancies exist between on-the-run and off-the-run issues. Additionally, precise 10-year maturity STRIPS are typically not available.

The author then estimates the parameter values of the model equations. He observes clear evidence of serial correlation and mean reversion to fundamental value in house prices. Additionally, he captures the rising historical volatility of house prices with the return horizon. Price volatility exceeds that of fundamental value but mean reverts in the long run.

House prices and interest rates determine mortgage cash flows and valuation. Interest rates affect house prices because they discount cash flows from housing, and rental rates are positively correlated with interest rates. Both are factors in calculating a house’s fundamental value.

Abstractor’s Viewpoint

The author defines and presents a unique stochastic model for U.S. house prices. He demonstrates the term structure of house price volatility, serial correlation, and mean reversion in the valuation of mortgages and other house price–dependent assets. It would be interesting to see this model applied to housing markets across countries. Mispricing and misunderstanding of housing risk before and during the financial crisis are not unique to the United States. House prices are an important barometer of risk for many economies and their financial markets.

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