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This paper presents a default model for mortgages on single-family houses implying a higher probability of negative equity and thus default in real estate markets with high price volatility. Mortgage lenders compensate for the increased default probability in volatile markets by demanding higher downpayments or increased creditworthiness of loan applicants, thus making mortgage loans more difficult to obtain. An empirical analysis finds greatly varying price volatility in single-family real estate markets in a sample of 42 cities. Consistent with the implications of the model, the empirical analysis finds that the fraction of low-downpayment loans declines in volatile markets.

The comparison of price developments in regional real estate markets reveals their marked differences from each other. Some markets, such as New England and California, experienced dramatic price fluctuations over the past few years. Other markets, mainly those located in the Midwest, exhibited a comparatively smooth price development. Assuming that past price volatility in a market is an indicator of future price volatility, this paper analyzes how these differences in price development affect business practices of financial institutions accepting credit risk of home mortgage loans. It is found that financial institutions operate more cautiously in markets with a history of volatile prices, and access to loans is curtailed. A result of the model presented in this paper is that under conditions of high price volatility profit maximizing mortgage lenders are more likely to reject applications for low-downpayment loans. In anticipation of this increased rejection probability, loan applicants make efforts to increase the size of their downpayments. For both reasons, average downpayment sizes increase in volatile markets. As lack of sufficient funds for the downpayment is often the biggest obstacle in gaining access to mortgage loans, a number of loan applicants who can obtain loans in stable real estate markets are credit constrained in volatile markets. Even though the model is written with primary mortgage market lenders in mind, its results apply to other profit maximizing financial institutions bearing mortgage default risk as well. In particular, the model results are relevant for the private mortgage insurance industry, which assumes credit risk of low- downpayment loans, and the government sponsored enterprises GSEs. Fannie Mae and Freddie Mac, which purchase and accept the credit risk of a large fraction of the loans originating in the primary market. The paper presents empirical evidence supporting the model predictions. It is found that the volatility of real estate price varies greatly in a sample of 42 cities, making it plausible that mortgage lenders adjust their lending standards in response. Among loans sold on the secondary mortgage market, the fraction of loans with low downpayments declines in cities with highly volatile markets, as implied by the model. The model rests on the assumption that perceived default probabilities of mortgage loans are the primary factor determining availability of loans. Negative equity, which occurs when the house price falls below the present value of the mortgage, is assumed to be a necessary precondition for default. In markets with high house price volatility, the probability of negative equity increases, and causes mortgage lenders to adopt more restrictive lending practices. The assumptions made here are that mortgage lenders observe local real estate markets, forecast house prices based on past behavior of local house prices, interpret past price volatility in local markets as a predictor of future price volatility, and that lenders adjust their lending practices in response. I argue that the burden of reduced mortgage lending in volatile markets is not distributed evenly; applicants for low-downpayment mortgage loans are much more restricted than applicants for high-downpayment loans. The reason for this asymmetry is that price volatility increases the probability of negative equity in low-downpayment loans significantly. For highdownpayment loans the probability of negative equity is low, even if price volatility is comparatively high. Mortgage lenders often compensate for higher price volatility by increasing downpayment requirements, to reduce the probability of negative equity. The necessity to make downpayments is a major impediment restricting access to mortgage loans. Many households are constrained by this requirement; they must either delay purchasing a house or they have to buy a smaller house than originally planned.2 To obtain a measure of volatility of real estate prices, I use time series data of median sale prices for existing single family houses from 42 cities. I find strong variability in the volatility of real estate prices. The standard deviation of annual growth rates of real median house prices ranges from 2.5% in Minneapolis to 16.4% in Hartford. In the next step, I use an extensive data set of individual observations of mortgage loans made in the cities for which I have information on price volatility. I regress the downpayment ratios of the mortgage loans on the measure of volatility and a set of control variables. I find an increase of the volatility measure from its mean of 5.8% by one standard deviation to 8.2% is associated with a decrease of the probability that a loan has a low downpayment ratio by 0.5 to 0.9 percentage points, depending on the specification evaluated at the means of all independent variables.. Of all loans in the sample 21.8% are low-downpayment loans with downpayments of 20% of the purchase price or less. In related literature Buist and Yang w4x present a simulation model} without closed form solutions}analyzing the effects of price volatility and expected price growth on lender revenue. Most implications of their model are similar to the data implications of the model presented here. In the empirical study of mortgage lending in Miami, Ling and Wachter w19x find the acceptance probability of loan applications declines in neighborhoods with expected price decreases. In a study of mortgage lending in Boston, Munnell et al. w20x find a measure of price volatility is negatively correlated with the acceptance probability of applications for mortgage loans. As a measure of price volatility, Munnell et al. use the ratio of rent-to-housevalues on the census tract level presuming that neighborhoods with higher volatility have a higher rent-to-value ratio. The contribution of this study is the analysis of the effects of price volatility on the acceptance probability of loan applications and on access to low-downpayment loans using a simple and intuitive model. Some of the implications of the model are corroborated by empirical evidence gained from a large cross sectional data set on mortgage origination in conjunction with real estate volatility measures derived from time series data.

One insight of the model presented here is that house price volatility matters, even after controlling for expected house price depreciation. Mortgage insurers and lenders are reluctant to make and insure loans in areas they perceive as risky. Particularly affected by volatility are lowdownpayment loans, because the same increase in volatility increases the probability of negative equity more for a low-downpayment loan than for a loan with a large downpayment. By assuming that the loan termination probability is exogenous, and that default occurs in the event of negative equity at the time of termination, the model takes an analytical shortcut which makes it very tractable. It is simple compared to a conventional option based default model, yet its implications are transparent and intuitive. Some empirical observations, such as the use of credit scoring by lenders, are easier to reconcile with the current model than with a conventional option based model. The central empirical result presented in the paper is that loans sold to GSEs contain a smaller fraction of high LTV loans in MSAs with high price volatility than in MSAs with low price volatility. This is compatible with the model, which predicts that fewer high LTV loans are made in MSAs with high price volatility. The results provide support to the hypothesis that some borrowers, who are able to borrow in a low volatility market, are credit constrained in a volatile market. However, given the limitations of the data, alternative explanations cannot be ruled out with certainty. It is interesting to compare the results in this study with Ambrose et al. w1x who find that in cities with volatile markets primary lenders sell a bigger fraction of their loans to the GSEs. A possible interpretation reconciling the results in both papers is that primary lenders try to pass on the increased risk in volatile markets by selling a larger fraction of their loans to the GSEs; however, mortgage insurers are hesitant to insure high LTV loans in volatile markets.