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The Optimal Mortgage Loan Portfolio in UK Regional Residential Real Estate

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Abstract

In this study, we propose a method based on large deviation theory (LDT), which minimises credit risk (expected loss). We demonstrate how mortgage loan portfolios can be optimised using geographical differences in the risk characteristics of mortgage loans in the UK. Our empirical results show that credit risk can be reduced by a third when the LDT method is used instead of the benchmark portfolios that we calculate with regional-gross-value-added weights and equal weights. More importantly, the difference in the expected loss between these portfolios increases further during bearish housing markets. To see that such numbers matter, in an extreme scenario, the UK mortgage lenders could lose more than 2% a year as the consequence of mortgage defaults, which is equivalent to an annual loss of approximately 20 billion pounds in the UK. Although this extreme state would not continue for a long time, it nevertheless represents a huge potential loss for mortgage lenders and investors.

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Notes

  1. Hypostat 2005, A Review of Europe’s Mortgage and Housing Markets, European Mortgage Federation, EMF Publication, November 2006. For example, Northern Rock offered up to a maximum combined 125% LTV mortgage and unsecured loan.

  2. See Bernanke (2008), Keys et al. (2009 and 2010), and An et al. (2009) for a more detailed discussion about the conduit mortgage lending and originate-to-distribute model.

  3. See Sornette (1998) and Pham (2007) for various applications of LDT to the portfolio optimisation problem and to other problems in insurance, option pricing, portfolio credit risk management.

  4. Other methods of modelling default dependence have been proposed, such as the factor approach (Jarrow and Yu 2001; Frey and Backhaus 2004; Bielecki and Rutkowski 2003), and the mixture model approach (Frey and McNeil 2003; Schmock and Seiler 2002), among many others.

  5. Defaults and losses given default are observed infrequently, e.g., quarterly or semi-annually, and thus the numbers of time series observations for these two data sets are small even for a few decades.

  6. The 11 regions are the North East, North West, Yorkshire and Humberside, the East Midlands, the West Midlands, East Anglia, Greater London, the South East, the South West, Wales, and Scotland.

  7. For example, Foster and van Order (1984) show that even when the LTV rises to as much as 110%, only 4.2% of borrowers are in default.

  8. The logit function is selected because it gives a probability within the range of [0,1] for any value of y, and has a closed form distribution.

  9. Individual banks and building societies have different concepts of default, and the definition of default is itself context-specific. In the relevant literature, including that of Kau et al. (1992) and Ambrose and Buttimer (2001), default incidence is defined as the lender’s act of taking possession (i.e. foreclosure) of the borrower’s property, whereas delinquency is defined as the non-payment of the mortgage payment due, i.e., mortgage borrowers being in arrears. According to industry practice (Ambrose et al. 1997), technical defaults, in which three payments have been completely missed and the next payment is due and paid, do not necessarily lead the lender to initiate foreclosure of the property. Basel II defines default as the condition in which: “the obligor is past due more than 90 days on any material credit obligation”. However, this differs from the notion of repossession, which is the physical possession of the property. Ford et al. (2001) have claimed that voluntary repossessions initiated by the mortgage obligor can be as large as 20% of defaults.

  10. The data source relating to mortgage arrears and possessions in the UK is the Council of Mortgage Lenders (CML), whose membership comprises banks, building societies, insurance companies and other specialist residential mortgage lenders, which together represented approximately 98% of UK mortgage assets in 2006. The statistics are based on a survey of the largest mortgage lenders. These large lenders cover approximately 86% of the mortgage lending industry.

  11. Using the interpolation method of a simple average may induce an auto-correlation problem. We also generated quarterly default rates using random variables by assuming that the variance of quarterly default rates is half of the variance of semi-annual default rates. As expected, these quarterly default rates are far less auto-correlated, but roughly speaking, these estimates do not differ significantly from those reported in our study.

  12. There was a change in the source of data collection in the third quarter of 2005. Prior to the third quarter of 2005, these figures were based on the Survey of Mortgage Lenders (SML). However, since that time, they have been collected by the Regular Mortgage Survey (RMS) of the Council of Mortgage Lenders (CML).

  13. As quarterly default rates are created via the interpolation of semi-annual default rates, they appear to be more persistent. Therefore, interpolation would make it difficult to find conitegration relationships between default rates and other variables.

  14. The correlations between divorce rates and unemployment rates, mortgage interest rates, loan-to-value ratios, and household incomes are 0.45, 0.33, 0.2, and −0.4, respectively.

  15. For the robustness of the estimated regional default rates, we compare the estimated default rates and the proportion of mortgage possessions for 6 qrt, from the first quarter of 2005 to the second quarter of 2006. The figures of mortgage possession orders made in the county courts are available on the website of the Department of Constitutional Affairs (DCA): www.dca.gov.uk/statistics. Despite the differences between the definition of mortgage defaults and the court actions of mortgage possessions, in most regions we find similarities between the two.

  16. We also attempted to determine which variable causes more profound differences in regional default rates, and found that the marginal impacts of household income and the unemployment rate on the default rate are higher than those of LTV—in particular for relatively poor regions such as the North East, North West, Yorkshire-Humberside, and Wales in comparison with Greater London, the South East, and East Anglia, and during the earlier sample period from the bearish housing market. These results indicate that mortgage defaults increase more rapidly when households’ ability to afford mortgage payments deteriorates either directly or indirectly.

  17. Following Bond et al. (2007), under the assumption that sales follow the Poisson distribution, we use the negative exponential density function to model the time period from default to sale for the 11 regions using 20,351 cases where all three dates (the start of mortgage arrears, the court decision and the completion of the sale) are available among the 44,319. We find that the difference between regions is not significant, but it takes more than 8 qrt for the repossessed housed to be sold, which is considerably longer than the cases of the UK commercial property market, which Bond et al. (2007) estimated at approximately 9 months (around 280 days), or other residential houses sold in the UK housing market. The details can be obtained from the authors upon request.

  18. The 3 month Treasury-Bill rate is obtained from Bank of England (www.bankofengland.co.uk). We also used LIBOR in our analysis, but the results are not different from those reported in this paper. The results with the LIBOR rate can be obtained from the authors upon request.

  19. Principal component analysis on excess returns suggests that four factors can explain 99% of the volatility in the regional mortgage loan portfolios.

  20. In an earlier version of the paper, we reported the results of the minimum variance portfolio for the purpose of comparison. However, as pointed out by the referee, applying the minimum variance portfolio theory is misleading because investors care about the entire wealth portfolio rather than any component of the portfolio in separation (see Chapter 21, Geltner et al. (2007)). Moreover, the assumptions required by the minimum variance portfolio theory do not hold for mortgage loan portfolios.

  21. Since the sum of the restricted weights should be one, the largest (smallest) weight in Table 6 and Fig. 1 appears to be larger (smaller) than the limits of the RGV weights.

  22. We also tested the unconstrained LDT portfolio in the out-of-sample analysis but found that the LDT portfolio is dominated by a few regions; i.e., the South East in the early sample period and the South West after 2005.

  23. Note that LDT is an exact calculation, not an asymptotic one, so it should hold for all sample sizes. However, we calculate optimal weights using a small number of quarterly observations in the out-of-sample analysis. This will introduce estimation errors in our variables, which should be reduced as we use longer back histories in our estimation. The extent to which this will matter for the outcomes has not, to our knowledge, been studied before and is a topic for future research. We thank the referee for bringing this point.

  24. According to the Regulated Mortgage Survey, 17% of mortgage loans in the UK had LTV ratios of 95% or more in the last quarter of 2005. These high LTV mortgages were not available in the late 1980s and the early 1990s.

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Acknowledgments

This study is based on research funded by the ESRC RES-000-22-1606. We are grateful for their support. We also would like to thank Ba Chu and ChunAn Lin who helped us to finish this paper, as well as the review panel of the ESRC and Min Hwang for their helpful comments. In addition, we would like to thank participants at the 2009 AsRES-AREUEA Joint International Conference.

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Authors and Affiliations

  1. Department of Real Estate and Construction, Oxford Brookes University, Gipsy Lane, Oxford, OX3 0BP, UK

    Youngha Cho

  2. School of Economics, Sungkyunkwan University, 53 Myeongnyun-Dong 3-Ga, Jongno-Gu, Seoul, 110-745, Korea

    Soosung Hwang

  3. Faculty of Economics and Politics, Austin Robinson Building, Sidgwick Avenue, Cambridge, CB3 9DD, UK

    Steve Satchell

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  1. Youngha Cho
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Correspondence to Soosung Hwang.

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Cho, Y., Hwang, S. & Satchell, S. The Optimal Mortgage Loan Portfolio in UK Regional Residential Real Estate. J Real Estate Finan Econ 45, 645–677 (2012). https://doi.org/10.1007/s11146-010-9269-9

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