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15th June 2012
Allison Orr, Gwilym Pryce
(University of Glasgow)
Spatial Variation and Pricing in the
UK Residential Mortgage
Market
1
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:
I ij   0 j    kj Bkij  eij
• Simple macro-level model (captures area effects):
 0 j   00    k1 A kj   0 j
• Gives simple two-level hierarchical model (fixed
effects):
I ij   00    k1 A kj   0 j    kj Bkij  eij
• where Iij the interest rate premium for the ith level 1
unit within the jth level 2 unit.
2
2
2
2 cov I I i


var
e


ij

ij
e
var I     
i j
ih

var  0 j    u2
e


 
•
Allowing for random variation and effect of level-1
covariate changes across interest rates on a level-2
variable
 nj   n 0   n a j   nj
•
Combine into a two-level hierarchical model with fixed
and random effects, and cross interactions:
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
Intercept
RegionUnempl
HPGrowth
Dum_93
Dum_94
Dum_95
Dum_96
Dum_97
Dum_98
Dum_99
Dum_00
Dum_01
Age<25yrs
Age50-65yrs
Age>65yers
Income
Term>25yrs
Dum_Endow
Model 4
8.304
0.284
0.006
-5.167
-6.849
-8.8
-9.13
-8.386
-7.352
-9.074
-8.804
-6.638
-0.108
0.235
0.141
-0.555
0.083
2.047
*
*
*
*
*
*
*
*
*
*
*
**
**
**
*
**
*
Model 5
8.244
0.288
0.006
-5.168
-6.846
-8.795
-9.134
-8.363
-7.342
-9.072
-8.786
-6.629
-0.108
0.235
0.141
-0.554
0.083
2.044
*
*
*
*
*
*
*
*
*
*
*
*
**
**
*
**
*
Fixed Effects
Dum_IntOnly
Dum_TIL1
Dum_TIG1
Norooms
Dum_Dwell5
LIBOR3mth * Dum_TIL1
LIBOR3mth * Dum_TIG1
LIBOR * Dum_Endow
LIBOR * Dum_IntOnly
Dum_93 * LNIncome
Dum_94 * LNIncome
Dum_95 * LNIncome
Dum_96 * LNIncome
Dum_97 * LNIncome
Dum_98 * LNIncome
Dum_99 * LNIncome
Dum_00 * LNIncome
Dum_01 * LNIncome
Model 4
0.788
0.790
1.546
-0.087
-0.107
-0.401
-0.369
-0.419
-0.185
0.344
0.363
0.532
0.582
0.619
0.534
0.625
0.584
0.515
*
**
*
*
**
*
*
*
*
**
*
*
*
*
*
*
*
*
Model 5
0.784
0.786
1.544
-0.087
-0.107
-0.4
-0.369
-0.418
-0.185
0.343
0.363
0.532
0.583
0.617
0.534
0.627
0.584
0.516
*
**
*
*
**
*
*
*
*
**
*
*
*
*
*
*
*
*
Results cont.
Estimates of Covariance Parameters
Model 4
Residual
1.334
Intercept [subject =Variance REGION_ID]
0.194
Intercept+LNIncome
[submject=REGIONAL_id]
UN (1,1)
UN (2,1)
UN (2,2)
Model Fit Statistics
-2 Restricted Log Likelihood
24,799
Akaike's Information Criterion (AIC)
24,803
Hurvich and Tsai's Criterion (AICC)
24,803
Bozdogan's Criterion (CAIC)
24,819
Schwarz's Bayesian Criterion (BIC)
24,817
*
**
Model 5
1.331
0.355
-0.007
0.0001
24,799
24,807
24,807
24,839
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?