1

Spatial Variation and Pricing in the UK Residential Mortgage

Market

15th June 2012

Allison Orr, Gwilym Pryce

(University of Glasgow)

What is risk-based pricing in the mortgage market?

• In theory, the interest rate charged on a mortgage loan should reflect:– Risk-free cost of capital– Level of inflation expected over the duration of the loan– Costs associated with loan– Level of risk attached to borrower becoming

bankrupt/defaulting on loan.

• Risk-based pricing is where “risk premium” set by banks captures the risks attached to borrower defaulting (if market efficient) and potential losses.

What determines or influences default risk?

Two important determinants (Jackson & Kaserman, 1980):

1. Equity theory of default – Borrowers are rational and compare price of

house with financial costs associated with continuing or discontinuing the contractual payment of loan.• If value of house > value of loan, keep paying

• If value of loan > value of house, default.

– E.g. Hendershoot and van Order (1987); Case and Shiller (1996)

– Associated with loan-to-value ratio (LTV)

2. Ability to pay theory• Mortgage holders will not default as long as

income flows allows them to make their periodic payments.

• Associated with loan-to-income ratio (LTI) measures

Lambrecht et al (1997) – only micro-level study empirically compare equity and ability-to-pay theories in UK.– Contradicts US findings– Ability to pay factors more important– But weaknesses in modelling

3. Double trigger theory of default

1. Borrowers do not default just because their house price falls.

2. Usually needs to be combined with a “trigger event” that affects their ability to pay eg become unemployed; household split, illness [Bhattacharjee et al, 2009]

3. Some instances where defaults arise when only one trigger [Bajari et al, 2008]

Other factors influencing default

• Range of other factors influence probability of default but significance varies across studies.– Characteristics of loan – term to maturity; type of loan;

equity deposit; presence of refinancing.

– Personal characteristics of borrower – age; first time buyer; gender; credit score and history; occupation; changes in income and employment status

– Location specific factors – • liquidity of housing asset;, rising/falling house prices• likelihood of becoming unemployed and finding new

employment.

Do UK mortgage lenders use risk-based pricing?

• The evidence is mixed, often confusing and contradictory.

• If they did, you would expect to see spatial variation.

• But, risk-pricing dilemma

Why risk-pricing dilemma?

• Risk pricing, in theory, should:– Allow lenders to charge different mortgage rates to

cover costs associated with lending risks and possible costs

– More transparent housing finance system:• Encourage lower risk borrowers• Discourage higher risk (ill-suited) borrowers

• Other side:– Treats borrowers unequally with higher rates possibly

leading to higher default – Potential for discriminatory practices– May partly explain spatial pattern of house price

appreciation (and potential for housing inequality) [Levin & Pryce, 2011]

Simple illustration of average mortgage rates

Spatial map of interest rates on new mortgages

Source: RMS 2004, 1.3m observations.

So ……

1. Do lenders in the UK price risk? If MLM does we would expect the characteristics of the borrower, loan and property which the loan is secured against to explain much of the variation in interest rates.

2. Is there spatial variation in mortgage rates? If there is we would expect location to explain some of the variation in interest rates.

Modelling framework

Hierarchical data

Ignoring the clustering can give biased standard errors, which can result in random variation being mistaken for real

effects.

• Simple micro-level model:

• Simple macro-level model (captures area effects):

• Gives simple two-level hierarchical model (fixed effects):

• where Iij the interest rate premium for the ith level 1

unit within the jth level 2 unit.

ijkijkjjij eBI 0

jkjkj A 01000

ijkijkjjkjkij eBAI 0100

22var eihI 2cov jiij iII 2var eije

20var uj

• Allowing for random variation and effect of level-1 covariate changes across interest rates on a level-2 variable

• Combine into a two-level hierarchical model with fixed and random effects, and cross interactions:

njjnnnj a 0

Data

• Longitudinal Survey of Mortgage Lenders.• Rich source of information on sample of

mortgage applications. Contains information on:– Loan details and interest rate– Some borrower personal characteristics– Details on property which loan is secured against

• Available to public for 1991 to 2001• BUT, only available with regional codes.• Over 180,000 mortgage applications (not

discounted or deferred rates)

Results

Fixed Effects Model 4 Model 5 Fixed Effects Model 4 Model 5

Intercept 8.304 * 8.244 * Dum_IntOnly 0.788 * 0.784 *RegionUnempl 0.284 * 0.288 * Dum_TIL1 0.790 ** 0.786 **HPGrowth 0.006 0.006 Dum_TIG1 1.546 * 1.544 *Dum_93 -5.167 * -5.168 * Norooms -0.087 * -0.087 *Dum_94 -6.849 * -6.846 * Dum_Dwell5 -0.107 ** -0.107 **Dum_95 -8.8 * -8.795 * LIBOR3mth * Dum_TIL1 -0.401 * -0.4 *Dum_96 -9.13 * -9.134 * LIBOR3mth * Dum_TIG1 -0.369 * -0.369 *Dum_97 -8.386 * -8.363 * LIBOR * Dum_Endow -0.419 * -0.418 *Dum_98 -7.352 * -7.342 * LIBOR * Dum_IntOnly -0.185 * -0.185 *Dum_99 -9.074 * -9.072 * Dum_93 * LNIncome 0.344 ** 0.343 **Dum_00 -8.804 * -8.786 * Dum_94 * LNIncome 0.363 * 0.363 *Dum_01 -6.638 * -6.629 * Dum_95 * LNIncome 0.532 * 0.532 *Age<25yrs -0.108 ** -0.108 * Dum_96 * LNIncome 0.582 * 0.583 *Age50-65yrs 0.235 ** 0.235 ** Dum_97 * LNIncome 0.619 * 0.617 *Age>65yers 0.141 ** 0.141 ** Dum_98 * LNIncome 0.534 * 0.534 *Income -0.555 * -0.554 * Dum_99 * LNIncome 0.625 * 0.627 *Term>25yrs 0.083 ** 0.083 ** Dum_00 * LNIncome 0.584 * 0.584 *Dum_Endow 2.047 * 2.044 * Dum_01 * LNIncome 0.515 * 0.516 *

Results cont.

Estimates of Covariance Parameters Model 4 Model 5

Residual 1.334 * 1.331 *Intercept [subject =Variance REGION_ID] 0.194 **Intercept+LNIncome [submject=REGIONAL_id] UN (1,1) 0.355

UN (2,1) -0.007UN (2,2) 0.0001

Model Fit Statistics

-2 Restricted Log Likelihood 24,799 24,799Akaike's Information Criterion (AIC) 24,803 24,807Hurvich and Tsai's Criterion (AICC) 24,803 24,807Bozdogan's Criterion (CAIC) 24,819 24,839Schwarz's Bayesian Criterion (BIC) 24,817 24,835

Conclusions and implications

• There appears to be some risk pricing with borrower, loan and property traits explaining most of the variation (85.63% in Model 4)

• Regional intercepts significant, explaining 14.37% of variation in mortgage interest premium. – Potential for housing wealth inequality

– Support for Mortgage Interest Benefit single rate

• But still some unaccounted variation and insignificant/questionable effect of house price appreciation.– Regional?

– What about since 2001?