The financial reporting of fair value based on managerial inputs versus market inputs: evidence from mortgage servicing rights

This research examines whether the fair value of mortgage servicing rights (MSRs) based on managerial inputs (Level 3) better reflects the cash flow and risk characteristics of the underlying assets than the fair value of MSRs based on market inputs (Level 2). Using mortgage servicing fees as a proxy for the underlying cash flows, we find that the valuation multiples for MSRs based on Level 3 inputs are more positively associated with the persistence of future servicing fees compared with the fair value of MSRs based on Level 2 inputs. We also document that only the valuation multiples based on Level 3 fair values are negatively associated with proxies for risk factors. Our results suggest that, although unobservable inputs are subject to managerial discretions, managers can generate higher quality fair value estimates than market inputs due to their information advantage, especially when the market for the underlying asset is inactive.     

A path-dependent approach to security valuation with application to interest rate contingent claims

The last two decades have witnessed a tremendous growth in the volume of assets and liabilities whose cash flows depend, in a variety of ways, on the path of interest rates. Some of these, including floating-rate notes and swap agreements, contractually base cash flows on current and past interest rates and contain caps, floors, and other, more complex features. Others, including mortgages, many corporate bonds, and time deposits, are fixed-rate instruments that contain embedded options, such as those to prepay, call, or withdrawal. The irregular exercise of these options causes cash flows to vary as time proceeds and interest rates rise or fall. This paper develops a state-contingent claims technique for valuing such securities. It is derived from the option-based model of Breeden and Litzenberger (1978) using the transition matrix approach of Banz and Miller (1978). Particular attention is paid to valuing so-called path-dependent securities whose contemporaneous cash flows depend on the historical path of interest rates as well as their current level. A detailed example is provided in which an adjustable-rate mortgage is valued under a variety of economic and security specific assumptions.     

A Closed Form Formula for Valuing Mortgages

We develop a closed form formula for the value of a fixed-rate residential mortgage that includes the provision that the borrower can prepay at any time with no penalty. The value of the mortgage equals the expectation, under the risk neutral probability measure, of the future cash flows. We model future cash flows by estimating an empirical model of prepayment behavior. A second change of measure leads to a closed form expression for the expectation. The closed form values explain most of the time series variation in MBS prices. The closed form formula significantly shortens the time to calculate mortgage values and durations and can be a useful tool for portfolio management and hedging.     

Option compensation,risky mortgage lending,and the financial crisis

We examine how option compensation affects banks' risky mortgage origination and sale decisions before the financial crisis in 2008. We find that, in the period immediately before the financial crisis, option compensation has little impact on the riskiness of mortgages originated and is negatively associated with mortgage lenders' propensity to sell risky mortgages. The results are consistent with banks' incentives to maximize revenues from origination and servicing fees while managing risk exposure by adjusting the sale of risky mortgages. For identification, we use bank-year fixed effects and matched loan applications to control for both supply- and demand-side factors of mortgage lending. We find similar results when using the variation in option compensation generated by the implementation of FAS 123R.     

Securitization and optimal foreclosure

Does securitization distort the foreclosure decisions of non-performing mortgages? In a model of mortgage-backed securitization with an endogenous foreclosure policy, we find that the securitizing bank adopts a tougher foreclosure policy than the first-best, despite resulting in higher loan losses. This is optimal because foreclosure mitigates the adverse selection problem in securitization by making the optimal security, a risky debt, less information-sensitive. We further show that policies that limit mortgage foreclosure would discourage the bank’s ex ante screening effort, reducing the quality of securitized mortgages. Our model yields novel testable predictions on the effect of mortgage securitization on foreclosure rates, loan performance, and mortgage servicing.     

Quantifying time value errors

Time valuation of cash flows is an essential part of personal financial planning and management. Many financial arrangements are priced according to a cash-flow valuation model. Expected cash flows associated with a stock or bond are discounted at an appropriate risk-adjusted rate in order to determine the fair value of the financial asset. Home mortgage loans are priced according to the discounted value of the future principal and interest cash flows. Yet, despite the importance of the discounted cash flow methodology in pricing assets, computational errors are often made when discount factors are not calculated precisely. This article attempts to quantify the magnitude of the error when the mathematical function for present value is ignored and interpolation is used instead to determine the discount factor.     

Developing Equity Release Markets: Risk Analysis for Reverse Mortgages and Home Reversions

Equity release products are sorely needed in an aging population with high levels of home ownership. There has been a growing literature analyzing risk components and capital adequacy of reverse mortgages in recent years. However, little research has been done on the risk analysis of other equity release products, such as home reversion contracts. This is partly due to the dominance of reverse mortgage products in equity release markets worldwide. In this article we compare cash flows and risk profiles from the provider's perspective for reverse mortgage and home reversion contracts. An at-home/in long-term care split termination model is employed to calculate termination rates, and a vector autoregressive (VAR) model is used to depict the joint dynamics of economic variables including interest rates, house prices, and rental yields. We derive stochastic discount factors from the no arbitrage condition and price the no negative equity guarantee in reverse mortgages and the lease for life agreement in the home reversion plan accordingly. We compare expected payoffs and assess riskiness of these two equity release products via commonly used risk measures: Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR).     

Value Creation through Securitization: Evidence from the CMBS Market

Despite recent volatility and constraints in secondary market funding, analysts have ascribed substantial value creation to the securitization of commercial mortgages. Such value creation likely emanates from liquidity enhancements, regulatory arbitrage, price discrimination and risk diversification by pooling and tranching, gains from specialization in origination, servicing, and holding of mortgages, and the like. Indeed, such value creation would be consistent with past accelerated growth in the mortgage- and asset-based securities markets and the sizable profits earned by secondary market intermediaries. In this paper, we estimate the pricing effects of commercial mortgage securitization. We do so by applying loan level data from 1992–2003 to compare the pricing of conduit and portfolio loans held in CMBS structures. In contrast to portfolio loans, which are held for investment by originating institutions, conduit loans are originated for the sole purpose of sale and securitization in the secondary market. If securitization creates value, it should be evidenced in the relative pricing of conduit loans sold into CMBS pools and in a lower cost of capital to loan originators. We estimate a reduced-form model, in which the interest rate spread between commercial mortgages and comparable-maturity treasury securities varies with loan characteristics, capital market conditions, and conduit loan status. Estimation results indicate that securitization of conduit loans leads to an 11 basis points reduction in commercial mortgage interest rates. We assess robustness of results via hazard model tests for omitted variables and originator-specific effects. We further estimate a simultaneous equations model that accounts for the potential endogeneity of mortgage loan terms to the mortgage-treasury rate spread. Results of that analysis suggest a larger 20 basis points reduction in loan pricing among conduit loans sold into CMBS structures.     

Derivative mortgage securities: An overview

Derivative mortgage securities have proliferated since planned amortization and floating rate CMO classes were introduced in late 1986. Other recently created derivative securities include reverse floaters and deep-discount bonds of CMOs, CMO residuals, and stripped and senior/subordinated passthroughs. These securities, which are derived from fixed-rate mortgages, were created to meet investor demands for maturity certainly, interest rate and prepayment hedging, and enhanced credit. The rapid growth of derivative securities reflects expansion of the investor base for fixed-rate mortgages. It also suggests that these mortgages will continue to be a viable housing finance instrument in a volatile interest rate environment. For the future, the increased creation of derivative securities will make the secondary mortgage market more efficient, facilitating the funding of fixed-rate mortgage originations.The substance of this paper was originally written in late 1987 and many of the specific data reflect that time period.     

The closing rate on residential mortgage commitments: An econometric analysis

Mortgage lenders routinely guarantee rates and points for periods of 60 days or more and hedge the inherent interest rate risk by selling the proportion of mortgages expected to close in forward markets. This article presents a model of the decision to close on the mortgage and demonstrates that the estimates of the model increase the precision of closing rate forecasts. The analysis indicates that changes in mortgage rates are important determinants of the closing rate for fixed-rate mortgages (FRM) and adjustable-rate mortgages (ARM). Other important factors include whether the mortgage is for a new purchase, for owner occupancy, and for a single-family house, and what the overall level of mortgage rates and the loan-to-value ratio are and whether the rate guarantee was granted at the application date or later.     

House‐Price Expectations,Alternative Mortgage Products,and Default

The goal of this paper is to better understand the forces that spurred use of alternative mortgages during the housing boom. A theoretical model shows that, when future house‐price expectations become more favorable, reducing default concerns, mortgage choices shift toward alternative products, which are characterized by backloading of payments. The empirical work confirms this prediction by showing that an increase in past house‐price appreciation, which captures more favorable expectations for the future, raises the market share of alternative mortgages. In addition, the paper tests the fundamental presumption that backloaded mortgages are more likely to default, finding support for this view.     

The Economic Effects of Legal Restrictions on High-Cost Mortgages

We analyze the effects of state predatory mortgage lending laws, which have been a model for recent changes in the United States federal legislation enacted to regulate the mortgage contract terms common in higher-risk mortgage market segments. Using the Rothschild-Stiglitz approach to model credit markets under asymmetric information, legal restrictions are shown to reduce the use and attractiveness of mortgage credit. Consistent with model predictions, empirical results indicate that originations of regulated high-cost mortgages were significantly less than predicted in states with more restrictive laws. The differences between predicted and actual originations of high-cost mortgages in states with less restrictive laws were not significant. These differences were also not significant for non-high-cost originations across all states. Thus, credit regulation was differentially associated with reduction in originations of high-cost mortgages, and non-high-cost lending did not consistently expand in areas where high-cost mortgages were restricted.     

Originators,wholesalers, and conduits: The marginal value of the contract rate on 30-year conventional mortgages

The model we present solves for the value of an incremental change in the mortgage contract given an expectation about the time the mortgage will be outstanding and a required return for this time span. The marginal value participants in the primary mortgage market place on the contract rate of a 30-year conventional mortgage determines the array of bids for new mortgage production. Mortgagors can issue mortgages at various discounts. High discounts are associated with low contract rates, and low discounts are associated with high contract rates. This article examines the way wholesale dealers and conduits value the various contract rates associated with current production of 30-year conventional mortgages.     

Credit History and the Performance of Prime and Nonprime Mortgages

Although nonprime lending has experienced steady or even explosive growth over the last decade very little is known about the performance characteristics of these mortgages. Using data from national secondary market institutions, this paper estimates a competing risks proportional hazard model, which includes unobserved heterogeneity. The analysis examines the performance of 30-year fixed rate owner occupied home purchase mortgages from February 1995 to the end of 1999 and compares nonprime and prime loan default and prepayment behavior. Nonprime loans are identified by mortgage interest rates that are substantially higher than the prevailing prime rate. Results indicate that nonprime mortgages differ significantly from prime mortgages: they have different risk characteristics at origination; they default at elevated levels; and they respond differently to the incentives to prepay and default. For instance, nonprime mortgages are less responsive to how much the option to call the mortgage or refinance is in the money and this effect is magnified for mortgages with low credit scores. Tests also reveal that default rates are less responsive to homeowner equity when credit scores are included in the specification.     

Putting the squeeze on a market for lemons: Government-sponsored mortgage securitization

Lenders either sell or obtain insurance for many of the mortgages they originate to reduce credit risk and enhance liquidity. An overwhelming majority of the mortgages sold are purchased by government-sponsored enterprises. The prevailing view is that government-sponsorship of mortgage securitization causes mortgage rates to be lower than they would otherwise be. Using a model that incorporates asymmetric information and adverse selection, we provide an example in which government-sponsored mortgage securitization raises the mortgage rate.The analysis and conclusions set forth are our own and do not indicate concurrence by members of the Federal Reserve Research stafls, by the Board of Governors, or by the Federal Reserve Banks. We wish to thank Mark Fisher for his Mathematica expertise. All errors are ours exclusively.     

Pricing fixed rate mortgages: Some empirical evidence

We develop a simple model based on the hypothesis that yields in the secondary mortgage market provide a basis for pricing new loans in the primary mortgage market. The model is then expanded to include potential interest rate variations due to lender characteristics and whether the loans meet securitization requirements. The empirical results, using a two-year sample of single-family mortgage rates, conform to the predictions of the model. In particular, we find that the interest rates on FRMs in the primary market move in a one-to-one relationship with secondary market yields. We also find significantly lower interest rates on these mortgages that can be sold in the secondary market versus those that cannot, thus indicating the value of the ability to securitize mortgages.     

Effects of Bankruptcy Exemptions and Foreclosure Laws on Mortgage Default and Foreclosure Rates

This study analyzes the effects of state bankruptcy asset exemptions and foreclosure laws on mortgage default and foreclosure rates across different segments of the mortgage market. We found that the effects of these legal provisions are larger for subprime than for prime mortgages and larger for adjustable rate mortgages than for fixed rate mortgages. These results demonstrate that the effect of variation in bankruptcy exemptions and foreclosure laws is most pronounced in the most risky segments of the mortgage market, which are those that have been most affected by the continuing housing slump in the United States.     

Credit Scoring and Mortgage Securitization: Implications for Mortgage Rates and Credit Availability

This article develops a model of the interactions between borrowers, originators, and a securitizer in primary and secondary mortgage markets. In the secondary market, the securitizer adds liquidity and plays a strategic game with mortgage originators. The securitizer sets the price at which it will purchase mortgages and the credit-score standard that qualifies a mortgage for purchase. We investigate two potential links between securitization and mortgage rates. First, we analyze whether a portion of the liquidity premium gets passed on to borrowers in the form of a lower mortgage rate. Somewhat surprisingly, we find very plausible conditions under which securitization fails to lower the mortgage rate. Second, and consistent with recent empirical results, we derive an inverse correlation between the volume of securitization and mortgage rates. However, the causation is reversed from the standard rendering. In our model, a decline in the mortgage rate causes increased securitization rather than the other way around.     

A Model of Mortgage Default

In this paper, we solve a dynamic model of households' mortgage decisions incorporating labor income, house price, inflation, and interest rate risk. Using a zero‐profit condition for mortgage lenders, we solve for equilibrium mortgage rates given borrower characteristics and optimal decisions. The model quantifies the effects of adjustable versus fixed mortgage rates, loan‐to‐value ratios, and mortgage affordability measures on mortgage premia and default. Mortgage selection by heterogeneous borrowers helps explain the higher default rates on adjustable‐rate mortgages during the recent U.S. housing downturn, and the variation in mortgage premia with the level of interest rates.