04/RT/16 Lending Conditions and Loan Default: What Can We

04/RT/16

Lending Conditions and Loan Default:

What Can We Learn From UK Buy-to-Let Loans?

Robert Kelly and Conor O’Toole

Lending Conditions and Loan Default: What Can We Learn

From UK Buy-to-Let Loans?

Robert Kelly

and Conor O’Toole

b∗

Monetary Policy Division, Central Bank of Ireland

Financial Stability Division, Central Bank of Ireland

June 2016

Abstract

This research considers one approach as to how originating lending conditions on debt-

service ratios and loan-to-value ratios aﬀect future default risk in the “Buy-to-Let” mar-

ket. Using a sample of mortgage loans for the UK, we estimate a “double trigger” default

model, with originating equity and aﬀordability terms. We ﬁnd default increasing with

originating loan-to-value (OLTV) and falling in original rent coverage (ORC). A non-linear

cubic spline model is used to identify threshold eﬀects in the relationship between OLTV,

ORC and default, with loans of OLTV greater than 75 and ORC below 1.5 showing a large

increase in default risk. These results provide empirical evidence for the non-linear nature

of default in these origination terms and provides useful insights into for understanding

OLTV and ORC limits in a macro prudential context. In addition, we investigate how

multiple loan portfolios interact with these thresholds. While there is no impact on the

main ﬁndings of 75 and 1.5, there is strong evidence to support tighter restrictions on

loans for second and subsequent properties.

Keywords: Macroprudential, Credit Risk, Mortgages, UK.

JEL Classiﬁcation: E32, E51, F30, G21, G28

∗

E-mail: robert.kelly@centralbank.ie; conor.oto[email protected]. We thank seminar participants at the

Central Bank of Ireland internal seminar series for helpful comments and suggestions. Particular thanks go to

Mark Cassidy, Gabriel Fagan, Niamh Hallisey, Gerard O’Reilly and Maria Woods. The views presented in this

paper are those of the authors alone and do not represent the oﬃcial views of the Central Bank of Ireland or

the European System of Central Banks. Any remaining errors are our own.

Non Technical Summary

With an aim towards boosting systemic resilience in the ﬁnancial system, there has been a recent

refocusing of ﬁnancial regulation towards the use of macroprudential instruments. Regulators globally

are engaged in a process of introducing, and designing, measures to limit aggregate risk through a

toolbox of macroprudential regulations.

While there are a range of instruments available to policymakers such as capital buﬀers and risk

weight management, one area of considerable focus has been the introduction of limits on mortgage

lending such as loan-to-value and loan-to-income ratios. This is mainly in response to the elevated

level of mortgage delinquency in many economies following the crisis, the link between the mortgage

market and the wider ﬁnancial turmoil and the evidence linking looser mortgage credit conditions

through credit growth to increases in house prices.

In order to set the parameters of macroprudential policy appropriately, information is needed on

the role of originating lending conditions in determining subsequent loan default. In this paper, we

draw on a unique loan-level dataset for the UK which contains the loans of Irish bank’s subsidiaries

in that jurisdiction. This is one of the few loan-level datasets available for the UK which spans the

period pre and post the ﬁnancial crisis and also contains information on current and origination income

and loan-to-values. Our estimation strategy uses a standard mortgage default model augmented to

explore non-linearities in the relationship between original rent coverage (ORC: our proxy for the

debt-service-ratio) and original loan-to-values (OLTV) using non-linear cubic splines.

We ﬁnd default is increasing with LTV at origination and falling in original rent coverage. We also

ﬁnd threshold eﬀects suggesting there are indeed non-linearities in the relationship between originated

OLTV, ORC and subsequent default. We also extend our empirical framework to control for portfolio

values of OLTV and ORC for borrowers with multiple loans outstanding and ﬁnd default rates double

in the case of multi-loan properties, with signiﬁcantly greater sensitivity to OLTV and ORC increases.

1 Introduction

With an aim towards boosting systemic resilience in the ﬁnancial system, there has been a recent

refocusing of ﬁnancial regulation towards the use of macroprudential instruments. Regulators globally

are engaged in a process of introducing, and designing, measures to limit aggregate risk through a

toolbox of macroprudential regulations (Kashyap et al., 2011; IMF, 2013; Claessens and Kodres, 2014;

Claessens, 2014).

While there are a range of instruments available to policymakers such as capital buﬀers and risk

weight management, one area of considerable focus has been the introduction of limits on mortgage

lending such as loan-to-value and loan-to-income ratios. This is mainly in response to the elevated

level of mortgage delinquency in many economies following the crisis (Gerardi et al., 2008; Elul et

al., 2010; Jiang et al., 2014; Lydon and McCarthy, 2013; Kelly and OMalley, 2016), the link between

the mortgage market and the wider ﬁnancial turmoil (Brunnermeier, 2009; Duca et al., 2010) and the

evidence linking looser mortgage credit conditions through credit growth to increases in house prices

(Gerlach and Peng, 2005; Duca et al., 2011). While there has been a large number of papers considering

the eﬃcacy of such measures, there has been less work undertaken on the speciﬁc calibration of the

level of LTI and LTV limits and less still on the important investment mortgage asset class. One

possible method to inform such measures is to focus on how macroprudential limits on debt-service-

ratios and loan-to-value ratios could be set to limit default in residential investment (“Buy-to-Let”

(BTL)) mortgages. We use a unique loan-level administration dataset for the UK which contains the

loans of Irish banks’ subsidiaries in that market. The dataset links originating mortgage credit terms

to the current loan performance and spans the period pre and post the ﬁnancial crisis.

Using these data, our contribution to the literature is threefold. First, our empirical strategy

speciﬁes a “double trigger” model which links mortgage default to originating values of loan-to-value

and rent coverage (our proxy for the debt-service-ratio

) controlling for a range of other loan and

borrower characteristics. The focus on originating conditions allows us to test how limits on these

variables could impact default. Second, we allowing a non-linear relationship between originating LTV

(OLTV) and originating rent coverage (ORC) and default to test whether there are particular turning

points which could provide useful information on understanding the relationship between originating

values of OLTV and ORC and future default. These turning points indicate where increases in risk

occur and could be informative to regulators as one input into the design phase of policy caps. Thirdly,

we investigate whether there are diﬀerences in the default rates between borrowers who have one loan

and borrowers who have a portfolio of loans across multiple properties. We then extend our empirical

Rent coverage is the proportion of the monthly installment covered by the current rent. Rental pricing

is captured at the property level in the dataset and is updated using local area rental yields driving from the

younger loans in the dataset. For further information, see Section 2.1.

framework to control for portfolio values of loan-to-value and rent coverage for borrowers with multiple

loan relationships.

Banks cannot control ex-post how borrowers are hit by equity or aﬀordability shocks. They can

simply be regulated to manage loan conditions ex-ante with the expectation that this provides adequate

buﬀers. Therefore, following Kelly et al. (2015), default is modeled as a function of OLTV and ORC

and not the more common current equity and income shock approach, although results are tested for

robustness to current characteristics. Our research is novel in that no existing studies have evaluated a

“double trigger” default model of residential investment mortgages with a view to exploring the possible

parameterisation of originating macroprudential regulations for both single and portfolio investors.

Our research is linked to three main literatures. First, our work is related to the emerging research

on the eﬀectiveness and calibration of macroprudential regulation in housing markets.

A majority

of these studies use aggregate data to assess the interaction between these measures and house-prices

through the credit-growth channel (Arregui et al., 2013; Nabar and Ahuja, 2011; Gerlach and Peng,

2005; Vandenbussche et al., 2015; Wong et al., 2014) and ﬁnd such limits are eﬀective in managing

credit growth with less certainty on the link to house prices.

Closer to our research are the studies in this ﬁeld using micro data. Claessens et al. (2013) use bank

balance sheet data across 48 countries and ﬁnd that limits on debt-to-income and loan-to-value ratios

are eﬀective in reducing leverage, asset and noncore to core liabilities of banks during boom times.

Igan and Kang (2011) use survey data for Korea and ﬁnd that loan-to-value and debt-to-income limits

are associated with a decline in house price appreciation and transaction activity. Fuster and Zafar

(2014) evaluate borrower willingness to pay based on diﬀerent loan-to-value ratios.

However, none of this research focuses on the potential impact of macroprudential instruments on

default or informing the levels of caps should be speciﬁed to best achieve acceptable bank and borrower

resilience. In fact, Jacome and Mitra (2015) note that to date the setting of cap levels has been done

on a completely arbitrary and ad-hoc basis. One study which does address this concern is Kelly et

al. (2015) who estimate whether there is justiﬁcation from a default perspective to provide ﬁrst time

homebuyers with diﬀerential regulatory treatment. However, they do not consider the calibration of

investment mortgages which is the focus of our research. Additionally, our paper is also linked to

the studies which assess the eﬃcacy of other macroprudential measures such as capital requirements

(Gauthier et al., 2012; Aiyar et al., 2014) or measures to manage liquidity shocks (Valderrama, 2015).

As a second major contribution, our work provides a bridge between the general research on

modelling default in investment mortgages (Grovenstein et al., 2005; Archer et al., 2002; Goldberg and

Capone, 2002) and the broader macroprudential stress testing literature (Acharya et al., 2014; Borio et

Further detailed summaries of the literature on macroprudential policy can be found in Galati and Moessner

(2013) or Galati and Moessner (2014).

al., 2014; Gaﬀney et al., 2014) of which modelling mortgage default is an important aspect of assessing

bank resilience to shocks (Buncic and Meleck, 2013). Regarding the traditional literature on commercial

or investment mortgage default, theoretical models suggest a “double trigger” consideration of negative

equity and income shocks which drive default (Goldberg and Capone, 2002). In these models, investors

exercise the default option when they experience a) an equity shock which reduces the value of the

asset to lower than the loan size or b) an income shock whereby the rental earnings do not cover

interest payments. Empirically, these channels are tested by linking current loan-to-value ratios and

debt-service ratios to default. However, while there are numerous studies that test these channels as

noted above, we can ﬁnd no existing research which links such investment mortgage default models to

macroprudential policy measures. Given the high level of delinquency in this loan class in many crisis

economies, it is important that macroprudential authorities appropriately assess and set the measures

in this market to manage systemic risks. It may even be more important to manage credit conditions

in this market as investors are potentially more sensitive to equity triggers of default (exercising the

option) due to not having home ownership links to the underlying property.

Our research is the ﬁrst

study to address this gap in the literature.

Third, our research is linked to the broader literature on modelling default and arrears in the UK

mortgage market. There are relatively few studies in this space due to a lack of adequate micro data.

One obvious exception is McCann (2014) who uses panel data on UK mortgages to estimate default

transitions. This research ﬁnds important roles for housing equity, unemployment and interest rates in

determining loan defaults and loan cures. Our research diﬀers from this study by both incorporating

a borrower-speciﬁc income channel and focusing on an originating macroprudential speciﬁcation.

A number of ﬁndings emerge. As expected, we ﬁnd a positive and signiﬁcant impact of OLTV on

default and a negative and signﬁcant eﬀect of ORC, controlling for a range of other loan and borrower

characteristics. To provide some insight into the magnitude of the eﬀects, a one standard deviation

increase in OLTV would increase the default rate by 28 per cent while a one standard deviation decrease

in ORC would increase default rates by 23 per cent.

To help provide useful information for understanding the link between originating credit conditions

and future loan performance, we test whether the eﬀect of OLTV and ORC is non-linear and whether

there exist turning points in these relationships that could inform the selection of cap levels i.e. does

the default risk spike at particular values of OLTV or ORC and could these be used to inﬂuence

policy measures? Using a non-linear cubic spline approach, we ﬁnd that for OLTV values below 75 per

There are a number of examples of regulatory authorities imposing speciﬁc macroprudential limits on

investment loans. Ireland introduced an LTV limit of 70 per cent on buy-to-let mortgages. Diﬀerent LTV

limits for non-owner occupiers have been used in Hong Kong, Israel, Malaysia, New Zealand, and Singapore,

with limits ranging from 70 per cent (New Zealand) to 20 per cent (for non-individuals in Singapore with one

or more outstanding loans). For more details please see Jacome and Mitra (2015).

cent, there is no considerable diﬀerence in default rates. However, above 75 per cent, there is a steep

increase in the predicted default rates. Regarding the eﬀects of ORC, default risk falls with higher

values but begins to taper out after approximately 1.5 (widening error bands after this level). These

results provide empirical evidence for the non-linear nature of default in these origination terms and

provides guidance for the setting of OLTV and ORC limits in a macro prudential context.

As the above assessment was estimated at the loan-level, it did not take into account any con-

siderations relating to whether investors have portfolios of loans across multiple properties. Having

multiple loans may provide diﬀerential risk to borrowers with single investment mortgages. To assess

this issue, we investigate whether there are diﬀerences in the default rates between borrowers who have

one loan relative to those who have a portfolio of loans and extend our empirical framework to control

for portfolio values of OLTV and ORC for borrowers with multiple loan relationships. In general, the

default proﬁles across OLTV and ORC distributions are broadly similar to the loan level estimates

above, with sharp increases in default risk for OLTV above 75 per cent and ORC below 1.2. However,

the spline of multi-loan borrowers is a statistically signiﬁcant level-shift higher than those for single-

loan borrowers from approximately 60 OLTV to close to 95 OLTV and between ORC values of 0.3 and

1.2. These results suggest there are potential gains in terms of default mitigation, by designing rules

which bind at more stringent OLTV and ORC levels on second and subsequent investment mortgages.

In addition, this will also act to lean against the amplifying eﬀect of the credit cycle by restricting

the extent to which housing equity gains can be used as further collateral. Counter-cyclical aspects of

macroprudential policies are important to ensure ﬁnancial cycles are not reinforced.

From a macroprudential policy setting perspective, a number of implications arise from our re-

search. Using this methodology, we have been able to identify turning points in the relationship between

OLTV, ORC and default which could be one useful input when regulators are considering potential

cap parameterisation. This assumes the policymakers’ objective function is purely building balance

sheet resilience without consideration to wider economic developments. As our model is reduced form,

it cannot provide an assessment of the feedback loops between capping credit conditions and the real

economy that can be assessed in a structural or dynamic stochastic general equilibrium setting. In this

respect, our methodology could be seen as one part of the toolkit for parameterising macroprudential

limits in investment mortgages and used in conjuction with DSGE or other macroeconomic approaches

(Buncic and Meleck, 2013; Clancy and Merola, 2014). Nonetheless, our non-linear default model with

loan conditions included at origination can provide insight for policymakers attempting to manage

future default risk through macroprudential limits.

The rest of this paper is structured as follows: Section 2 presents the data, empirical model and

summary statistics. Section 3 outlines the main empirical ﬁndings and Section 4 concludes.

2 Data and Empirical Model

2.1 Data

This research uses loan-level data from the UK subsidiaries of Irish headquartered banks: Allied Irish

Banks (AIB, including EBS Building Society), Bank of Ireland (BoI), and Permanent TSB (PTSB).

These data were collected by the Central Bank of Ireland as part of the Financial Measures Programme

(FMP) which assessed the capitalisation and liquidity requirements of the Irish banks as part of the

IMF-EC-ECB oﬃcial ﬁnancing support. The Irish sample of these data has been used extensively in

research on the performance and credit market functionality in Ireland (Kelly and OMalley, 2016; Kelly

et al., 2015; Lydon and McCarthy, 2013). It was also used to assess the recapitalisation requirements

of the banking sector following the recent Irish ﬁnancial crisis. Additional information on this dataset

is presented in Kennedy and McIndoe Calder (2011). While these data are some of the only loan-level

information available for the UK, it is instructive to assess their potential representativeness to the

wider UK market. McCann (2014) notes Irish-headquartered banks represent approximately 2 per

cent of the total UK mortgage market.

These loan-level data (LLD) contain a range of information ﬁelds that are ﬁlled by the borrower at

mortgage application stage and subsequently used by the bank as part of the credit assessment. This

includes the following items valued at origination: drawn balance, initial installment, borrower income,

the valuation of the underlying collateral, the mortgage term, interest rate type and payment type

(e.g. amortising or interest-only). For BTL mortgages, information is also available on the original

rent, some borrower-speciﬁc information such as borrower age and further data on the dwelling the

loan is used to acquire (the postcode and region of location and whether the property is an apartment

or house). There is also information on a range of current loan information which is reported by the

ﬁnancial institution including: the current non-performing status of each loan, the current loan-to-

value, current installment, and the current interest rate type and level.

In our analysis, we take a cross-section of loans that were held on the banks’ books in December

2014. Given the variables above, our sample contains a mix of characteristics that are measured either

at the time of loan origination or as of December 2014. Given the focus of our research, the sample

is limited to only mortgage for residential investment purposes or “Buy-To-Let” loans. In total the

sample contains 106,775 observations. The sample includes loans that were originated between the

years 1987 and 2014 so we observe loans allocated across the credit boom and ﬁnancial crisis period.

A listing of the variable deﬁnitions is presented in table 1. To measure loan performance, we use a

binary indicator of default as deﬁned by standard Basel II deﬁnitions (> 90 days in arrears). Interest

rate type controls are either ﬁxed or adjustable rate (variable and tracker loans) while payment status

Table 1: Main Variable Deﬁnitions

Variable Description

Dependent Variable

Default Status > 90 days in arrears

Borrower Controls, X

Borrower Age Borrower age at origination (in months)

Region Groups (London, East Midlands etc.)

Loan Controls, Z

Bank Dummies for each banking group

Loan Age Number of months since loan origination.

Term Loan term at origination (in months)

Interest Rate Type Interest rate type at origination. i.e. Fixed, Variable

Payment Type Dummy for interest only

DBO Log drawn balance at origination

Macro Prudential

OLTV Loan to value at origination.

ORC Rental value to installment at origination

Additional Controls, C

ADBO Total Drawn Balance of Equity Release

Property Type Indicator for Apartment

is a binary indicator for whether or not the loan is amortising or interest only. Drawn loan balance at

origination is measured in natural logs.

To provide insight into the calibration of macroprudential measures in the mortgage market, we

require information on variables that are commonly subjected to such limits. In the case of BTL

mortgages, two commonly used limits are on the loan-to-value ratio and the rent coverage ratio which

imposes minimum downpayment or aﬀordability conditions on borrowers.

From the perspective of a

macroprudential supervisor, limits on these credit conditions are set at loan origination with a view to

providing default buﬀers in future. The standard literature on investment mortgage default suggests

a role for both loan-to-value and income (rental) channels in driving future delinquency. In our data,

we focus on both originating loan-to-value (OLTV) and originating rent-coverage (ORC) (rent as a

fraction of the loan installment both at loan origination)

as deﬁned in table 1 and discuss how they

aﬀect future mortgage default.

Summary statistics for the main variables are included in table 2. The average default rate across

the sample is 2 per cent of loans. For comparison, the average default rate in our data is higher than

that reported in the mortgage backed pools of UK BTL loans (Moodys, 2015). Our sample therefore

has somewhat poorer loans than those allocated by other institutions in the UK. However, from a

research perspective, our sample is still one of the largest loan-level datasets available for the UK

The Bank of England Financial Policy Committee notes the use of interest coverage ratios as the standard

debt-to-income measure for buy-to-let loans. See http://www.bankofengland.co.uk/ﬁnancialstability/

With this deﬁnition, a value of 1 indicates that the rent exactly covered the required loan installment

and, given the high delinquencies, these loans are potentially important to analyse in the context of

potential ﬁnancial stability risks and the appropriateness of macroprudential oversight.

Table 2: Loan Level Summary Statistics

Mean St. Dev

Default(%) 2.35 15.18

DBO (pounds) 114,707.20 73,606.93

Loan Term (months) 253.85 58.54

Loan Age 91.49 23.48

IntType

Fixed(%) 2.48 NA

Variable(%) 97.52 NA

Pay Type, IO(%) 87.61 32.95

Borrower Age (years) 43.86 9.78

Origin Rental Yield (%) 5.61 5.45

OLTV (%) 72.87 13.30

ODSR 1.19 0.43

Location

East Midlands(%) 0.01 NA

East Anglia(%) 6.91 NA

London(%) 9.52 NA

North East(%) 17.39 NA

North West(%) 3.96 NA

Scotland(%) 14.15 NA

South East(%) 3.58 NA

South west(%) 14.41 NA

Wales(%) 9.93 NA

West Midlands(%) 5.06 NA

York-Humber(%) 6.80 NA

Observations 106,326

The average drawn loan size in our data was 114,539 with a standard deviation of 73,620. The

average term length at origination was circa 254 months (just over 21 years). The majority of origi-

nating mortgage interest rates were adjustable (ARMs), nearly 98 per cent

with the remainder ﬁxed

rate (FRM). Over 87 per cent of the mortgages were interest only, non-amortising loans. In terms of

the regional breakdown of lending, the highest lending shares were 17 per cent of loans to the North

East, 14 per cent for the South West and Scotland and just under 10 per cent for Wales and London.

The average rental yield in the data is approximately 6 per cent

For the macroprudential variables, the average OLTV for loans in the dataset was 73 per cent i.e.

borrowers posted a 27 per cent deposit. However, there is considerable variation across the distribution

of loan-to-value ratios as presented in ﬁgure 6. While a considerable clustering of the distribution is

evident between 75 and 90, there is a large portion of loans that were allocated at above 100 per cent

LTV. Average rent coverage ratio (ORC) was 1.2, i.e. rent was approximately 20 per cent greater than

loan installment at origination. However, there is considerable variation in ORCs as noted in ﬁgure

This includes both variable rates as well as tracker mortgages which vary with a ﬁxed spread over a

reference rate.

Yield is deﬁned as originating rent divided by collateral valuation.

Figure 1: Default, OLTV and ORC of UK BTL Loans by Origination Year

1.A: Default Rate 1.B: OLTV and ORC

6. Many loans were allocated with a rent coverage lower than 1 (rent does not cover the installment

fully). The distribution of this variable also has a long right tail with some loans granted with very

high rent coverage ratios.

Our dataset contains loans originated across the credit boom and ﬁnancial crisis period up to

December 2014. It is instructive to consider whether we observe varying credit conditions and loan

allocation terms over this period and whether, for the period in which credit conditions were looser,

do these loans have a worse delinquency performance. Figure 1.A presents the average default rate as

well as median OLTV and ORC by the year of loan origination. The default rate is highest for loans

originated in the pre ﬁnancial crisis period (2006-2007). There is a steady increase in the default rate

on loans allocated between 2001 and 2008 with a fall oﬀ more recently. Figure 1.B presents the median

values of OLTV (left side) and ORC (right side) for loans allocated over the period 1999 to 2014.

There was a steady increase in the median OLTV over the period 2002 to 2008 as well as a loosening

of median rent coverage. Directly preceeding the crisis period (2006/2007), over 50 per cent of loans

were allocated on properties whose rent did not cover the monthly installment. These ﬁndings are in

line with research documenting the general loosening of credit conditions which predated the global

ﬁnancial crisis (Duca et al., 2010, 2011). More recently, as credit conditions have tightened, OLTVs

have fallen while ORCs have increased as banks now apply more prudent assessment criteria. While

we formally provide an econometric strategy in the next section to explore these linkages, this would

suggest a potential role for macroprudential limits on credit conditions during the boom period which

may have provided additional loan default buﬀers.

2.2 Empirical Model and Identiﬁcation Strategy

The aim of this research is to test the relationship between originating credit limits on OLTV, ORC

and loan default with an aim to inform the calibration of macroprudential policy. Their exists a

large literature which tests the determinants of default in relation to the standard “double trigger”

hypothesis of equity and aﬀordability concerns. This literature posits that, for investors, as the loan

moves into negative equity or as cash ﬂows become insuﬃcient to service loan terms, the propensity

to default increases (Grovenstein et al., 2005; Archer et al., 2002; Goldberg and Capone, 2002). In an

empirical model, this would suggest a positive (negative) relationship between contemporaneous LTV

(RC) and default.

However, using this approach is insuﬃcient for our purposes. Macroprudential supervisors set

regulatory limits at origination. They do not have control over ex-post house price or aﬀordability

shocks that may compromise the borrowers ability or desire to repay. They must therefore calibrate

the limits on LTV or RC at origination to provide suﬃcient buﬀers against such shocks. This leads to

the challenge of what speciﬁc level to set for the measures.

To address these issues, our identiﬁcation strategy is as follows. First, we propose a cross-sectional

default model which links current loan performance to OLTV and ORC, the factors regulators might

want to limit. Second, we test whether the relationship between OLTV (ORC) and default is non-

linear and whether there exist turning points in these relationships which might suggest values or

ranges for calibration of the macroprudential policy. A visual of the average default rate at diﬀerent

values of the distribution of OLTV and ORC (ﬁgure 3) would suggest their are some non-linearities

in the relationship. In particular, there is a signiﬁcant increase in the default risk for OLTV ratios

above 75 and a leveling in the default lowering for ORC above 1.4. Finally, we undertake robustness

checks to test whether our ﬁndings on the originating terms hold controlling for current house price

and aﬀordability shocks. By including originating characteristics, we rule out any potential reverse

causality between these terms and default.

2.2.1 Baseline Model

Our empirical approach uses a standard model of default which is common in the existing literature

(Jiang et al., 2013, 2014; Haughwout et al., 2008). Let the realisation of the latent propensity to default

for residential investment loans be characterised as:







1 NP

∗

≥ 0;

0 NP

∗

< 0.

where NP

∗

represents the censored underlying latent variable and N P

the observed indicator for

Figure 2: Default Rate by OLTV, ORC Cuts

default. Our baseline model uses a cross sectional logistic speciﬁcation and estimates the probability

that a BTL mortgage defaults as a function of the macroprudential controls at origination, borrower

characteristics, loan characteristics and dwelling controls as indicated in table 1:

P r(NP

= 1) = F (OLT V

, ORC

, X

, Z

, C

) (1)

where OLT V

is the originating loan-to-value ratio and ORC

is the originating rent coverage. Our

a-priori expectations for the signs on these variables are:

• H1: β

OLT V

> 0

• H2: β

OR C

< 0

H1 states that default is increasing in originating loan-to-value ratios while H2 states that default

is decreasing in originating rent coverage. Regarding other controls, X

contains a vector of borrower-

speciﬁc or dwelling controls including borrower age and a full set of regional dummies in all regressions.

is a vector of loan terms at origination including the log of drawn balance, loan vintage, term length,

binary indicators for interest rate type, interest only payment and bank of origination.

The vector C contains other controls that may aﬀect the performance of the original BTL loan.

We include additional debt that may have been taken out on the property since the ﬁrst loan. In

many cases, these equity releases may be used to invest in additional properties or used as household

consumption ﬁnancing. The additional leverage potentially provides more limited capacity of borrowers

to manage shocks and is therefore expected to positively aﬀect default. We also include a binary

indicator for apartment property type. If apartments experience diﬀerent house price shocks than

other dwellings, the default rate may be higher for these properties.

2.2.2 Calibration Using a Non-Linear Approach

As noted above, to inform the speciﬁc calibration of macroprudential limits, we wish to test for

threshold eﬀects of the impact of diﬀerent LTV and RC levels at origination on default risk. One

methodology might be to split the distributions of OLTV and RS into groups of categories and test

whether the slope is constant across a variable. For example, we could group OLTV into arbitrary

buckets [0-5,5-10 etc.] and include these into the regression framework. However, this assumes that

the eﬀect within each group is constant and that jumps in the relationship happen at the boundaries

of the bands.

An alternative approach is to use a spline function which addresses these issues by ﬁtting a piecewise

regression which takes a functional form between points, known as knots, of the continuous variable.

Following a number of applications in the medical literature (Desquilbet and Mariotti (2010), Marrie

et al. (2009)), we allow for non-linear relationship between the knots using a restricted cubic spline

(RCS). When using a RCS, one obtains a continuous smooth function that is linear before the ﬁrst

knot, a piecewise cubic polynomial between adjacent knots, and linear again after the last knot. In

general, the logit RCS model, with restricted spline function f (S), with k knots is given by:

P r(NP

= 1) = F (OLT V

, ORC

, X

, Z

, C

, f(S))

with f (S) = β

+ β

+ ... + β

k−1

where X

and C

are deﬁned as in Equation 1. S is the variable upon which the spline function is

estimated, in our case OLTV and ORC. We locate knots at the 5, 27.5, 50, 72.5 and 95 percentiles of

the distributions of OLTV and ORC. This is in line with previous research (Kelly et al., 2015; Harrell,

2001).

3 Empirical Results

3.1 Baseline Results

The results of our baseline logit speciﬁcations are presented in table 3. Marginal eﬀects are presented

with standard errors robust to heteroskedasticity. Column 1 presents the basic speciﬁcation without

controls for OLTV and ORC. Columns (2) and (3) introduce these variables in a stepwise fashion while

column (4) includes the full speciﬁcation.

The main variables of interest are OLTV and ORC. In Column (2), OLTV is introduced with the

baseline control variables. The marginal eﬀect is positive and signiﬁcant as expected. In column (3),

ORC is included and the eﬀect is negative and signiﬁcant also as expected. Column (4) introduces

both factors simultaneously and the ﬁndings hold: default is increasing with LTV at origination and

falling in original rent coverage. To get a sense of the magnitude of the eﬀects, a one standard deviation

increase in OLTV would increase the default rate by 28 per cent while a one standard deviation decrease

in rent coverage would increase default rates by 23 per cent.

Regarding the control variables, we ﬁnd a positive and signiﬁcant eﬀect of the original drawn

balance on default: a one per cent increase in drawn balance increases the default probability by

0.009. The sign on this variable is as expected and indicates that, controlling for other factors, larger

loans are more risky. The marginal eﬀect of additional drawn balance is also positive and signiﬁcant

indicating that additional loans on the same collateral as the original facility heighten the default risk.

The magnitude of the eﬀect is slightly smaller than that for drawn balance but indicates that a 1 per

cent increase in the log of additional balance increases the default risk by 0.002. To recall the average

default in the sample is only 2 per cent so these eﬀects are economically meaning full.

Loan age or vintage controls for the number of months since origination of the loan. This captures

the timing of origination and has a statistically signiﬁcant and negative eﬀect on default in the full

speciﬁcation.

We ﬁnd loan terms have a negative eﬀect on the probability of default controlling for

other factors. If terms are increased, ceteris paribus, this should reduce the installment and improve

aﬀordability. We ﬁnd no statistical diﬀerence in default risk between loans on ﬁxed interest rates or

variable rates. Borrowers who have interest only contracts at origination are more likely to default.

Default is also decreasing in borrower age and is higher for apartments than other dwelling types.

While the baseline ﬁndings point to positive (negative) eﬀects for OLTV (ORC), we are interested to

test whether there are thresholds in these relationships which may provide insight for policy calibration.

To do this, we use the model given by column (4) but allow both OLTV and ORC to enter with a

cubic spline. We then estimate the predicted probabilities of default from the model for values of

OLTV and ORC holding all other variables at their mean values. The results are presented in ﬁgure

3. For OLTV, it appears that for values below 75, there is no considerable diﬀerence in default rates.

However, from 75 OLTV onwards, there is a very steep increase in the predicted default rates. This

suggests if supervisors are focused on building resilience against future default then calibrating the

OLTV limit to circa 75 will protect against the steep rise in default risk that is associated with greater

levels of OLTV.

This is based on the sample mean default rate of 0.02, the marginal eﬀect estimate for OLTV (ORC) of

0.0005 (-0.0128) and a standard deviation of 13.29 (0.426).

As a robustness check we also run the model with origin year ﬁxed eﬀects replacing loan age and the results

are unchanged.

Table 3: Marginal Eﬀects of Logit Model

Baseline LTV DSR Full

ln(Loan Balance) 0.0129

∗∗∗

0.0113

∗∗∗

0.0100

∗∗∗

0.0094

∗∗∗

(0.001) (0.001) (0.001) (0.001)

ln(Additonal Balance) 0.0019

∗∗∗

0.0025

∗∗∗

0.0024

∗∗∗

0.0029

∗∗∗

(0.000) (0.000) (0.000) (0.000)

Loan Age −0.0000 −0.0000 −0.0001

∗∗

−0.0001

∗∗

(0.000) (0.000) (0.000) (0.000)

IntType, Variable −0.0005 0.0012 0.0016 0.0024

(0.004) (0.004) (0.004) (0.004)

Loan Term −0.0000

∗

−0.0000

∗∗

−0.0000

∗

−0.0000

∗∗

(0.000) (0.000) (0.000) (0.000)

Pay Type, IO 0.0161

∗∗∗

0.0140

∗∗∗

0.0200

∗∗∗

0.0169

∗∗∗

(0.002) (0.002) (0.003) (0.003)

Borrower Age −0.0002

∗∗

−0.0001

∗

−0.0002

∗∗

−0.0001

∗

(0.000) (0.000) (0.000) (0.000)

PropType, Apt 0.0093

∗∗∗

0.0088

∗∗∗

0.0087

∗∗∗

0.0084

∗∗∗

(0.001) (0.001) (0.001) (0.001)

Region Controls

East Anglia −0.0050

∗

−0.0051

∗

−0.0048

∗

−0.0050

∗

(0.002) (0.002) (0.002) (0.002)

London −0.0100

∗∗∗

−0.0069

∗∗

−0.0099

∗∗∗

−0.0074

∗∗

(0.002) (0.002) (0.002) (0.002)

North East −0.0239

∗∗∗

−0.0207

∗∗∗

−0.0233

∗∗∗

−0.0210

∗∗∗

(0.002) (0.002) (0.002) (0.002)

North West −0.0015 −0.0033 −0.0013 −0.0030

(0.003) (0.003) (0.003) (0.003)

Scotland 0.0036

∗

0.0010 0.0040

∗

0.0017

(0.002) (0.002) (0.002) (0.002)

South East −0.0074

∗

−0.0091

∗∗

−0.0068

∗

−0.0087

∗∗

(0.003) (0.003) (0.003) (0.003)

South west −0.0210

∗∗∗

−0.0219

∗∗∗

−0.0204

∗∗∗

−0.0214

∗∗∗

(0.002) (0.002) (0.002) (0.002)

Wales −0.0147

∗∗∗

−0.0123

∗∗∗

−0.0140

∗∗∗

−0.0121

∗∗∗

(0.002) (0.002) (0.002) (0.002)

West Midlands −0.0040 −0.0052

∗

−0.0044 −0.0056

∗

(0.003) (0.003) (0.003) (0.003)

York-Humber −0.0084

∗∗∗

−0.0116

∗∗∗

−0.0089

∗∗∗

−0.0119

∗∗∗

(0.002) (0.002) (0.002) (0.002)

Macro Prudential

OLTV 0.0006

∗∗∗

0.0005

∗∗∗

(0.000) (0.000)

ORC −0.0163

∗∗∗

−0.0128

∗∗∗

(0.002) (0.002)

Standard errors in parentheses

∗

p < 0.05,

∗∗

p < 0.01,

∗∗∗

p < 0.001

Figure 3: RSC Fit of Mortgage Default

3.A: OLTV 3.B: ORC

Similarly, the predicted probabilities of default are much higher for lower levels of ORC. The eﬀects

appear to taper out after approximately 1.5 ORC with widening error bands after this level. This result

suggests that if policymakers set the limit of original rent to 1.5 times the original installment amount,

this will provide buﬀers to mitigate future default risk.

To summarise, our approach has demonstrated that there do appear to be turning points in the

relationship between default and originating levels of both OLTV and ORC. If minimising default risk

is the objective function of macroprudential supervisors, tailoring the measures to take into account

these non-linearities may be appropriate.

3.2 Diﬀerence by Multi-Loan Grouping

Section 3.1 provides an assessment of the relationship between default, OLTV and OLTI on an in-

dividual loan-by-loan basis. That may be an appropriate strategy when the borrower is likely to be

limited to a single dwelling purchase and any equity releases are controlled for (as we have done above).

However, with BTL investments, it is highly likely that many borrowers build up an investment port-

folio and have multiple loans across multiple properties. If this is the case, it may have implications

for macroprudential policy if the default risk on the multi-loan borrowers is diﬀerent. Furthermore,

the relationship between OLTV, ORC, and default may depend on the borrowers’ multiple loans or

portfolio in particular where built up housing equity from the portfolio is used to access new credit.

In our data, we are able to ascertain whether individual borrowers have more than one property as

well as numerous loans on those collaterals with the same institution.

We can therefore test whether

One limitation of our LLD is that we do not have a full borrower view of lending. Instead, we can only

evaluate the extent to which an investor has loans outstanding with the same institution. If it is expected that

borrowers are drawing down loans from multiple institutions then our research is not able to capture this.

there is a diﬀerence in default risk for the group of borrowers with multiple loans. If this is the case,

then further consideration must be given to addressing how our calibration assessment is reﬁned to

account for this heterogeneity in risk.

In table 4, we re-run the baseline model at the loan level as per column (4) of table 3 but now

include a dummy indicator that takes the value of one for borrowers with more than one loan in the

data (Multi-Loan). For brevity we only display the marginal eﬀect on the OLTV, ORC and Multi-Loan.

The coeﬃcient on this variable is statistically signiﬁcant and positive: borrowers with multi-loans have

a higher default risk than those with a single loan. The magnitude of the eﬀect indicates that such

loans have a 1.13 per cent higher probability of default. With a sample mean default rate of 2.2 per

cent, the default rate for multi-loan borrowers is nearly 50 per cent higher than single-loan borrowers

controlling for other factors that aﬀect loan risk at origination.

To explore whether the relationship between OLTV, ORC and default is also diﬀerent for this

group, we interact Multi-Loan with OLTV and ORC. The estimates are presented in column (2) of

table 4. The own eﬀects of OLTV and ORC remain signiﬁcant and carry the expected signs. However,

the interaction of Multi-Loan with both OLTV and ORC suggest that the impact of these variables is

greater for these borrowers: the eﬀect of a one per cent increase in OLTV (ORC) on default is 0.0003

(-0.007) for single-loan borrowers and 0.001 (-0.0273) for multi-loan borrowers.

Table 4: Marginal Eﬀects of Logit Model w/Multi-Loan

Dummy Interaction

ORC −0.0131

∗∗∗

(0.002)

OLTV 0.0005

∗∗∗

(0.000)

Multi-Loan 0.0112

∗∗∗

(0.001)

ORC (Single-Loan) −0.0069

∗∗∗

(0.002)

ORC (Multi-Loan) −0.0249

∗∗∗

(0.005)

OLTV (Single-Loan) 0.0003

∗∗∗

(0.000)

OLTV (Multi-Loan) 0.0009

∗∗∗

(0.000)

Standard errors in parentheses

∗

p < 0.05,

∗∗

p < 0.01,

∗∗∗

p < 0.001

3.3 Towards a Borrower Level Macroprudential Policy

Section 3.2 shows a signiﬁcant diﬀerence in the risk proﬁle of investors with multi-property portfolios

and as such modeling default risk at the loan level is ﬂawed given correlation in default risk between

Figure 4: No of Properties for Multi Property Borrowers

loans connected to the same borrower. Therefore, it makes sense that macroprudential policy in

residential investment is implemented at the borrower level. To address these considerations, we shift

from a loan level to a borrower view. The dataset is constructed at the origination of the most recent

loan drawdown with a portfolio view of LTV and RC considered. In the case of single loan borrowers,

there will be no change from earlier description but in the case of multi-loan borrowers, OLTV will be

calculated as the sum of all balance outstanding plus the new balance drawn over the total value of all

collateral at the origination of the most recent property purchase. Similarly, ORC will be calculated

as total rent over installments of all loans at the origination of the most recent property purchase.

This allows us to capture the cross subsidisation of house equity and rent growth used by borrowers

to increase their property portfolio. This is of particular importance in a macroprudential context as

this housing investment is driven by, and further contributes to, house price bubbles.

Table 5 presents summary statistics for key loan and borrower characteristics from the dataset

depending on whether or not the borrower has multiple properties. The diﬀerence between the mean

values for each group is also presented with tests of statistical signiﬁcance. Consistent with Table 4, the

default rate for multi-loan borrowers is more than twice that of single. While individual loan sizes are

not signiﬁcantly diﬀerent between the groups, as expected, porfolio value and gross income (includes

rent) are both signiﬁcantly larger. In terms of the main macroprudential lending instruments, while

there is a statistical diﬀerence between the groups for both, portfolio OLTV is less than 3 percentage

larger and portfolio ORC is 4 per cent smaller for single loan borrowers.

Table 6 replicates at the borrower level the logit speciﬁcation presented in table 3. Marginal

eﬀects are presented with standard errors robust to heteroskedasticity. Column 1 presents the basic

Table 5: Borrower Level Summary Statistics by Number of Loans

Single Loan Multi Loan Diﬀ % Diﬀ

(SL) (ML) from ML

Default (%) 1.5 3.1 1.6 51.6

∗∗∗

Loan Size (£) 115,740 116,919 1,179 1.0

Portfolio Purchase Value (£) 155,049 405,886 250,836 61.8

∗∗∗

Portfolio Current Value (£)

181,390 444,012 262,622 59.1

∗∗∗

Borrower Characteristics

Gross Income (£) 67,122 96,564 29,442 30.8

∗∗∗

Age (yrs) 43 45 2 4.44

∗∗∗

Loan Characteristics

Term (months) 255 248 -7 2.8

∗∗∗

Vintage (months) 92 88 -4 4.5

∗∗∗

Rate Type, IO (%) 84.3 92.9 8.6 9.3

∗∗∗

London (%) 9.7 8.5 1.2 14.1

Portfolio OLTV (%) 76.8 79.69 2.92 3.7

∗∗∗

Portfolio Originating Rent (£) 8,844 23,241 14,397 61.9

∗∗∗

Portfolio ORC (%)

1.14 1.19 0.05 4.2

∗∗∗

Notes: Signiﬁcant diﬀerence is based on t-tests on the equality of means.

∗

p < 0.05,

∗∗

p < 0.01,

∗∗∗

p < 0.001

Current valuation as of December 2013.

Originating rent cover deﬁned as the % of installment covered by rent.

speciﬁcation without controls for OLTV and ORC. Columns (2) and (3) introduce these variables in

a stepwise fashion while column (4) includes the full speciﬁcation. The ﬁndings hold with default is

increasing with LTV at origination and falling in original rent coverage.

If macroprudential policy was to reﬂect the higher default risk for multiple property loan portfolios

and a greater sensitivity to ORC and OLTV through lending limits, additional analysis on the interac-

tion and threshold eﬀects between portfolio size and the main policy tools is required. We undertake

the following: (i) estimate a borrower-level model which explores non-linearities between default and

OLTV/ORC and (ii) test how the single and multiple property portfolios diﬀers across originating

ORC and OLTV levels.

We address these questions by re-estimating the logit model at the borrower level including the

non-linear splines and the interactions of the spline variables with the ﬂag for borrowers with multiple

loans. All other controls and variables are included as in table 6. Figure 5 presents the predicted

probabilities of default across the values of OLTV and ORC for both single-loan borrowers (red) and

multiple-loan borrowers (blue). Standard error bands at the 5 per cent level are also presented.

In relation to OLTV, there is no statistically signiﬁcant diﬀerence in the default rates for the two

groups up to OLTV of approximately 60 per cent as the error bands cross. However, from 60 to

approximately 95 LTV, multi-loan borrowers have a statistically signiﬁcant higher default rate than

single-loan borrowers. The slope of both splines begin to increase between 75 to 80 OLTV indicating

considerably heightened risk of default for loans with LTVs above this point.

Table 6: Marginal Eﬀects of Logit Model

Baseline OLTV ORC Full

Ln(Loan Balance) 0.0115

∗∗∗

0.0105

∗∗∗

0.0101

∗∗∗

0.0091

∗∗∗

(0.001) (0.001) (0.001) (0.001)

Ln(Additonal Balance) 0.0016

∗∗∗

0.0020

∗∗∗

0.0016

∗∗∗

0.0019

∗∗∗

(0.000) (0.000) (0.000) (0.000)

Loan Age 0.0000 0.0000 −0.0001 −0.0000

(0.000) (0.000) (0.000) (0.000)

IntType, Variable −0.0061 −0.0043 0.0017 0.0040

(0.003) (0.003) (0.004) (0.005)

Loan Term −0.0000 −0.0000

∗

−0.0000 −0.0000

∗

(0.000) (0.000) (0.000) (0.000)

Pay Type, IO 0.0104

∗∗∗

0.0092

∗∗∗

0.0124

∗∗∗

0.0114

∗∗∗

(0.002) (0.002) (0.002) (0.002)

Multi-Loan 0.0106

∗∗∗

0.0107

∗∗∗

0.0119

∗∗∗

0.0121

∗∗∗

(0.001) (0.001) (0.001) (0.001)

Borrower Age −0.0002

∗∗

−0.0001

∗

−0.0002

∗

−0.0001

∗

(0.000) (0.000) (0.000) (0.000)

PropType, Apt 0.0057

∗∗∗

0.0053

∗∗∗

0.0055

∗∗∗

(0.001) (0.001) (0.001)

Region Controls

East Anglia −0.0038 −0.0041 −0.0034 −0.0040

(0.002) (0.002) (0.002) (0.003)

London −0.0103

∗∗∗

−0.0083

∗∗∗

−0.0103

∗∗∗

−0.0077

∗∗

(0.002) (0.002) (0.002) (0.002)

North East −0.0162

∗∗∗

−0.0140

∗∗∗

−0.0152

∗∗∗

−0.0112

∗∗∗

(0.002) (0.002) (0.002) (0.002)

North West −0.0004 −0.0014 0.0001 −0.0005

(0.003) (0.003) (0.003) (0.003)

Scotland 0.0025 0.0008 0.0028 0.0017

(0.002) (0.002) (0.002) (0.002)

South East −0.0041 −0.0052 −0.0034 −0.0017

(0.003) (0.003) (0.003) (0.003)

South west −0.0179

∗∗∗

−0.0185

∗∗∗

−0.0172

∗∗∗

−0.0166

∗∗∗

(0.002) (0.002) (0.002) (0.002)

Wales −0.0116

∗∗∗

−0.0098

∗∗∗

−0.0110

∗∗∗

−0.0088

∗∗∗

(0.002) (0.002) (0.002) (0.002)

West Midlands −0.0031 −0.0038 −0.0036 −0.0044

(0.003) (0.003) (0.003) (0.003)

York-Humber −0.0036 −0.0053

∗

−0.0037 −0.0048

(0.002) (0.002) (0.002) (0.002)

Macro Prudential

OLTV 0.0004

∗∗∗

0.0004

∗∗∗

(0.000) (0.000)

ORC −0.0117

∗∗∗

−0.0114

∗∗∗

(0.002) (0.002)

Standard errors in parentheses

∗

p < 0.05,

∗∗

p < 0.01,

∗∗∗

p < 0.001

Figure 5: Diﬀerential in Default Rates by OLTV and ORC for Single and MultiLoan Borrowers

As the spline of multi-loan borrowers is a level-shift higher, it is potentially the case that these

borrowers should be subject to tighter LTV caps on all loans after the ﬁrst so as to bring the risk back

towards that of single-loan borrowers. Our results would suggest that LTV caps could be calibrated

between 75 to 80 per cent for the borrowers ﬁrst investment mortgage but that the LTV on the portfolio

for any subsequent loan should be tighter to build more resilience for portfolio borrowers.

For ORC, the ﬁndings are somewhat similar. For low levels of ORC, the default risk of multi-

loan borrowers is considerably higher than that of single-loan borrowers. The diﬀerence becomes

statistically insigniﬁcant between the two groups at between 1.15 and 1.20 ORC. Overall, the default

risk falls with ORC for both groups until it ﬂattens out at approximately 1.5. The results suggest that

a calibration for single-loan borrowers of approximately 1.5 ORC and a tightening on further loans

added to the portfolio would be appropriate to build in buﬀers for borrowers to withstand shocks.

3.4 Robustness Checks: The Case of Current Shocks and Other Borrower

Income

To test the robustness of our ﬁndings, we undertake a range of additional checks. First, we control for

the current house price of the collateral and the current rent coverage ratio. The main literature on

commercial mortgage default highlights that it is current equity or current rent coverage that matter

for default (Grovenstein et al., 2005; Archer et al., 2002; Goldberg and Capone, 2002). That is, when

borrowers are hit with shocks to the asset value (house price falls) or shocks to the cash ﬂows (declines

in the rent), they may exercise the underlying option to default. This is particularly the case if the loan

enters negative equity or if the rent no longer covers the monthly installment. As our model is based

on determining default using originating values of LTV and RC, it does not capture these dynamics.

It is important that we undertake a robustness check to test that our ﬁndings are not altered by these

omitted factors.

Second, we control for the borrowers non-rental income. In many cases, BTL investors may not

be professionals but are borrowers who purchase a single investment property for example as part of

a pension plan or for a single investment. If fact, our data suggest that many BTL borrowers have

single loans. In these cases, the household may see the BTL income as part of the normal household

income ﬂow and intertwine the BTL returns with other borrower income. If BTL rent receives a shock,

the borrower may choose to substitute other income to avoid a default on the BTL payments. This is

more likely to be the case if the BTL rent only accounts for a small share of total gross income thus

the shock would be more manageable.

To control for both of these inﬂuences, we employ a number of tests. First, to capture the current

position of equity and aﬀordability, we calculate the change in house prices and rent between origination

and December 2014 (the date of our data drop from the institutions). Using data on the current

installment of the loan, we then include the updated RC and the change in house prices in the full

model.

The results are presented in table 7. Column (1) presents the main model again while column

(2) includes the current values for house prices as well as the current RC ratio. The current RC ratio

is negative and signiﬁcant as expected: higher rent coverage currently lowers the default probability.

We do not ﬁnd an eﬀect of the change in house prices. However, this may not be surprising as

many borrowers in our data experienced increases in house prices during the period and are unlikely

to exercise the option to default in these circumstances. It is more likely that borrowers who are

experiencing negative equity or facing house price falls will default. To assess whether borrowers who

experienced such declines have a higher default rate, we replace the change in house price variable with

a dummy which takes the value of one if the borrower had a price decline. The results are presented

in column (3). The variable is positive and statistically signiﬁcant indicating that suﬀering a property

price fall increases the default rate by 0.0004, a 2 per cent increase given the sample average default

rate of 0.02. Importantly for our assessment of the origination conditions, both OLTV and ORC are

still statistically signiﬁcant and signed as expected. Similarly, the predicted probabilities of default

are much higher for lower levels of ORC.

Our ﬁnal robustness check is to control for other borrower income, we include the share of rental

income in total borrower income to capture the degree to which there is available ﬁnancial capacity

to manage falls in rent or periods of vacancy through the use of other ﬁnancial resources. It must

be noted that in our data we do not observe the other borrower income after origination so the ratio

We do not include the current LTV ratio given the endogeneity between current LTV and default. Please

see Kelly and McCann (forthcoming) for details.

uses origination values of both series. The results are presented in column (4). While the variable is

insigniﬁcant in the speciﬁcation, our main ﬁndings on OLTV and ORC remain. Column (5) includes

all robustness checks simultaneously. More broadly, our ﬁndings appear to be robust to the inclusion

of these additional variables. The ﬁtted splines also maintain their original shape. This suggests that

our calibration of macroprudential policies using originating values of LTV and RC are appropriate

and informative for supervisors in their attempt to build resilience from the borrower and the bank

perspective.

Table 7: Robustness Checks: Marginal Eﬀects of Logit Model

(1) (2) (3) (4) (5)

Full Current House Other All

Model Price Fall Income

Multi Prop 0.0078

∗∗∗

0.0075

∗∗∗

0.0074

∗∗∗

0.0083

∗∗∗

0.0079

∗∗∗

(0.001) (0.001) (0.001) (0.002) (0.002)

OLTV 0.0003

∗∗∗

0.0002

∗∗∗

0.0002

∗∗∗

0.0003

∗∗∗

0.0003

∗∗∗

(0.000) (0.000) (0.000) (0.000) (0.000)

ORC −0.0139

∗∗∗

−0.0068

∗∗

−0.0054

∗

−0.0152

∗∗∗

−0.0067

∗

(0.003) (0.002) (0.003) (0.003) (0.003)

Current RC −0.0036

∗∗∗

−0.0037

∗∗∗

−0.0037

∗∗∗

(0.001) (0.001) (0.001)

∆ HP −0.0000

(0.000)

HP Fall 0.0004

∗

0.0004

∗

(0.000) (0.000)

Rent/Income −0.0023 −0.0020

(0.009) (0.009)

Standard errors in parentheses

∗

p < 0.05,

∗∗

p < 0.01,

∗∗∗

p < 0.001

4 Conclusions and Policy Implications

In this paper, we present a default model aimed at understanding the link between originating lending

conditions on debt-service-ratios and loan-to-value ratios and subsequent loan performance for residen-

tial investment (BTL) mortgages. We use a unique loan-level dataset for the UK which contains the

loans of Irish bank’s subsidiaries in that jurisdiction. This is one of the only loan-level datasets avail-

able for the UK which spans the period pre and post the ﬁnancial crisis. We provide two contributions

which can be a useful input into regulatory policy formation.

First, our empirical strategy speciﬁes a “double trigger” model which links mortgage default to

originating values of loan-to-value and rent coverage (our proxy for the debt-service-ratio) controlling

for a range of other loan and borrower characteristics. We ﬁnd default is increasing with LTV at

origination and falling in original rent coverage. To compare the magnitude of the eﬀects, a one

standard deviation increase in OLTV would increase the default rate by 28 per cent while a one

standard deviation decrease in ORC would increase default rates by 23 per cent.

To examine potential threshold eﬀects, we test how default changes across the OLTV and ORC

distributions by estimating the relationship between these variables and delinquency using a non-linear

cubic spline. For OLTV, it appears that for values below 75, there is no considerable variation in the

level of default. However, from 75 OLTV onwards, there is a very steep increase in the predicted

default rates. Regarding the originating aﬀordability channel, the eﬀects appear to taper out after

approximately 1.5 ORC with widening error bars after this level. These results provide empirical

evidence for the non-linear nature of default in these origination terms and may be a useful input for

the setting of OLTV and ORC limits in a macro prudential context.

Second, we investigate whether there are diﬀerences in the default rates between borrowers who

have one loan relative to those who have a portfolio of loans. We extend our empirical framework

to control for portfolio values of OLTV and ORC for borrowers with multiple loans outstanding. We

ﬁnd default rates double in the case of multi-loan properties, with signiﬁcantly greater sensitivity to

OLTV and ORC increases. We investigate how multiple property portfolio interacts with the threshold

ﬁnding and while there is no impact on the main ﬁndings of 75 and 1.5, there is strong evidence to

support tighter restrictions on second and subsequent properties.

A number of policy implications arise from our research. The impact of 2008-2009 ﬁnancial crisis on

mortgage delinquency rates resulted in the development of revised accounting standards (International

Financial Reporting Standards (IFRS) 9) for loan provisioning and a series of stress tests with a strong

focus on collateral valuation through an Asset Quality Review Process. The main aim of both is

ensuring a banking system adequate to absorb potential losses. These measures focus on the current

LTV ratios, as these form the major component of the loss given a default.

However, a broader suite of macroprudential measures on limiting LTV and aﬀordability at the loan

origination phase have been proposed since the onset of the crisis and introduced in many countries.

This is unsurprising given the rise in mortgage defaults, the link between the mortgage market and

the wider ﬁnancial turmoil and the link between credit conditions and housing asset inﬂation.

Macroprudential policies implemented at loan origination, such as restrictions on high LTV and

aﬀordability ratios, can provide buﬀers against adverse shocks. Lower originating LTV ratios will

provide greater resilience to house price falls while lowering originating ORC levels will provide a

buﬀer against aﬀordability shocks. Investment mortgages play a vital part of a functioning housing

market through the ﬁnancing of the provision of additional units for the rental sector. However, is

important to ensure that lending for housing investment is undertaken in a manner that does not

compromise ﬁnancial stability. Our ﬁndings may provide useful insights for policymakers attempting

to parameterise lending limits on investment mortgages.

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5 Appendix

Figure 6: Distribution of OLTV and ODSR