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MEASURING HOUSING AFFORDABILITYAND HOME PRICE EQUILIBRIUMRevisiting the Housing Bubble & Bustand HPI Modeling

by Andrew Davidson and Alexander Levin | J U N E 2 0 1 2

QuantitativePerspectives

QP © 2012 andrew davidson & co., inc.

Contents

Introduction 0 1

The Role of the Down Payment (Equity) 02

Rates and Risk 03

The Role of Option ARMs 06

Geographical Angle 07

National and Regional Market Composition 09

Affordability Index and HPI Equilibrium 1 0

HPI Equilibrium and a Demand-Supply Argument 1 1

Does Our Theory Agree with Practice? 1 2

Conclusion 1 3

© 2012 quantitative perspectives 01

One of the most complex and controversial subjects of home-price

modeling is the role of interest rates. For example, AD&Co’s second-generation

Home Price Index model (HPI2) utilizes rates as an indicator of affordability and as

a force of inflation. When rates grow, affordability, and therefore, home prices

decline. However, over a long period of time, higher interest rates paired with

higher income inflation will ultimately push housing values up. This pattern is

backed by empirical data (Levin [2011] ), which shows that the Home Price

Appreciation (HPA) rate is negatively correlated to the loan payment rate, both

immediately and for up to three to four years after: The correlation turns positive

after that.

Our model also assumes that with a rate move, HPI will eventually adjust fully to

a new equilibrium so that a borrower will continue to pay the same fraction of his

or her income. Nevertheless, we have found that economists have differing

opinions on the role of interest rates in HPI modeling. In some models, this link is

missing completely, whereas in others, a positive rather than a negative,

relationship is postulated.

The concept of HPI equilibrium is closely related to financing terms, which go

beyond a merely stated loan rate. It can be presented as a dragon having three

heads:

• Loan Rate

• Down Payment

• Mispriced Risk

We have analyzed the history of the mid-2000s housing bubble and the

subsequent decline to reveal the role contributed by each of the constituent

components. Our conclusions generally agree with some academic studies that

seek the root of the crisis in availability of credit stemming primarily from

unregulated non-agency securitization (e.g. Levitin and Wachter [2012]). This paper

previews some of the HPI modeling revisions we plan to introduce based on a

deeper analysis of funding historically available to borrowers.

“The concept ofHPI equilibriumis closely relatedto financingterms, which gobeyond a merelystated loan rate.”

Introduction

long with entering into a loan, borrowers

need to come up with equity or “borrow” a

down payment at a much higher rate. If we

blend the loan rate (payable on debt) with the equity

rates (applied to down payment), we may have a better

gauge of what the loan really costs. For example,

combining a traditional 20% down payment at a 25%

return-on-equity (ROE) rate (25.03% payment rate

assuming the 30-yr amortization) with an 80% debt at

a 6% rate (7.3% payment rate), gives us 10.8% of an

annual payment measured off the full price of a home.

If the loan rate drops to 4% (5.8% payment rate), then

the total combined cost will go down to 9.6%. In this

example, loan payments fall by 20% (from 7.3% to

5.8%), but the equity-adjusted cost moved down only

11% (from 10.8% to 9.6%), as seen in Figure 1.

Naturally, a stricter requirement for a down payment

will be shown as a higher equity cost on a borrower’s

balance sheet—even with an unchanged loan rate.

If, in the above example, we replaced the 20% down

payment with a 10% down payment, the total cost

would drop from 10.8% to 9.0% or by 16.4%. This gives

us a hint of what happened in mid-2000s (see Figure 2).

On the other hand, suppose that during the period of

falling interest rates the origination’s combined loan-to-

value (LTV) fell, much as it did from 2006 to 2010. Then

the drop in interest rates could be more than offset by

the increase in down payment costs. Thus, even in a

falling interest-rate environment, housing could

become less affordable.

02 © 2012 andrew davidson & co., inc.

The Role of the Down Payment (Equity)

A

OLD NEW CHANGELoan Rate/Payment 6.0% / 7.3% 4.0% / 5.8% -20%Loan (Combined LTV) 80% 80%Equity Rate/Payment 25.0% / 25.03% 25.0% / 25.03%

Equity (down-payment) 20% 20%Total (Blended) Cost 10.8% 9.6% -11%

Figure 1. Computations of Total Borrower Cost for Two Levels of Loan Rate

Figure 2. Historical Combined LTV at Origination(US average, purchase) of Loan Rate

Pre-2008: Non-agency loans; 2008-11: Agency loans.Sources: Intex, Freddie Mac, AD&Co


The Role of the Down Payment (Equity) ( C O N T I N U E D )

Rates and Risk

A historical chart of blended financing rates would not

yield sufficient information without also considering

loan quality. A large pool of subprime borrowers that

is projected to lose 20% of its principal over a 5-year

average life can be viewed as losing 4% per annum.

If that pool has a 7% Weighted Average Coupon (WAC),

it will effectively be paying only 3%—if we attempt to

monetize borrowers’ economics (regardless of whether

the investor is protected by loan insurance or not).

Such a loan instinctively catches borrowers’ attention

even if they cannot assess their own credit risk

objectively. This example shows that an undervalued

risk may lead to a strong demand to buy homes.

It is the loss-adjusted rate that matters for modeling

the borrower incentive. Creating financing privileges

and loopholes for weak borrowers stimulates them and

inflates demands for housing.

Figure 4 presents impressive qualitative evidence that

the explosion of non-prime origination in the years

leading to the crisis coincides with the housing bubble.

During the housing bubble, the combined LTV rate on

non-agency loans used to purchase homes rose

significantly. That trend was reversed in 2008–2011 (the

data reflects agency loans used to purchase homes

rather than non-agency loans, given the lack of new

non-agency origination).

Using the concept of the equity cost, we can quantify

that the shift in down payments alone moved the

combined borrower cost down about 15% from 2000 to

2006 and up 22% since 2006. This dynamic, shown in

Figure 3, contributed to the HPI moves we observed.

Figure 3. Composition of the Total Borrower Cost (US average)


Rates and Risk ( C O N T I N U E D )

Figure 4. Non-Agency Origination by Loan Shelf

How can we determine whether or not credit risk was

correctly priced in newly originated loans? We conducted

the following historical study. For each non-agency

origination quarterly cohort, starting from 2000, we ran

our Credit OAS model to assess expected loan losses

and (after dividing by the projected WAL) annualized

them. This approach utilized our LoanDynamicsTM

Model (LDM) of borrower behavior and the risk-

neutralized (conservative) Home Price simulation

model. Results are shown in Figure 5.

Figure 5. Non-Agency Origination by Loan Shelf

A) Loss Adjusted Rate B) Annual Loss Rate

Figure 5 (Panel A) shows that, before 2004, risk-

adjusted rates had been strikingly similar among

Prime, Alt-A and Subprime loans, essentially showing

that the risk had been priced fairly. Since 2004, the

lower quality loans were underpriced, with the loss-

adjusted rate falling below that of top-quality loans.

We have further analyzed the cause of this

phenomenon. The change of ex-ante HPI outlook was

not found to be a material factor, but the large

percentage of Option ARMs (see the next section) and

high combined LTV loans were. Hence, the reduced

down payment standards affected both the equity cost

and the expected credit losses, effectively reducing the

borrower cost in each case.

With the loss component detected, we now can

compute the all-in cost rate (Figure 6):


Rates and Risk ( C O N T I N U E D )

Figure 6. All-In Cost of Borrowing (Non-Agency Loans)

The red lines in Figure 6 clearly depict the mid-2000s

“dent” in effective cost despite an increase in loan rates.

It was caused by the plummeted equity cost and the

increased loss expectation. The effect is seen to be

somewhat stronger in California, which originated more

Option ARMs and non-standard loans in general (see

the following sections). The existence of the dent in

financing cost history was postulated in our work on

HPI2 (Levin (2011] ) and shown to have matched the

actual HPI dynamics fairly well.

All-In Borrower Cost = Loan payment + Loss rate (negative) + Equity cost


The Role of Option ARMs

Figure 7 depicts origination by loan type and shows two

prominent periods that saw 10%+ negative amortization

ARMs. First, they were Cost of Funds Adjustable Rate

Mortgages (COFI ARMs), designed to match banks’

liabilities. Negative amortization was an innocent by-

product feature arising from the mismatch between

frequent interest resets and less frequent payment

resets. In contrast, the second wave of “negam”

innovation was malignant by design. Homeowners-to-

be had incentive to increase their debt in the hope of

selling homes later at a higher price and paying off the

loan.

Figure 7. Non-Agency Origination by Loan Type

The negative amortization volume also has a

remarkable coincidence with HPI booms and busts,

although it remains a chicken-and-egg dilemma.

Option ARMs could only be offered with confidence that

home prices would grow. The low-cost financing they

offer propels HPI further. Once the HPI reached its

peak, Option ARMs stopped being offered. Their death

caused HPI to decline deeper as new homebuyers could

not afford the prices paid by previous owners who used

Option ARMs.


The housing bubble and bust were most prominent in

California, Nevada, Florida and Arizona. Figure 8,

taken from Levin [2010], shows the connection between

these HPI anomalies and the proliferation of

“affordable” lending programs. It is evident that the

four states that experienced the largest plunge are

those that abused the affordable lending programs

(Nevada, Arizona, Florida and California).

Overall, the correlation between affordable lending and

HPI decline is evident although other factors may have

played a certain role, too (e.g. severe stumbling of the

automotive industry in Michigan). Berkovec et al.

[forthcoming, 2013] also argue that the first and most

important explanatory factor in matching bubble and

bust by region is the loan’s features, which evade

normal amortization.

Geographical Angle

Figure 8. Affordable Lending versus HPI Decline

Figure 9 demonstrates the last quarter-century history

of non-conventional origination in California and its

relationship to HPA. This state was the motherland of

COFI ARMs in the second half of 1980s and it had the

Option ARMs share exceeding 20% of its 2005-2007

loans. The COFI ARM origination can be linked to a

modest HPI decline in the 1990s, but the proliferation

of Option ARMs was really poisoned.

Green line=Share of Option ARMs + IO ARMs for non-agency Prime + Alt-A originations during 2002-06

Red line=Decline from the peak to first trough (2009Q1)


Geographical Angle ( C O N T I N U E D )

Figure 9. Non-Agency Origination by Loan Type versus HPA in California


Before we proceed to reporting our actual results that

explain historical events via change of housing

affordability, we need to pay attention to the mortgage

market’s composition in the areas in question. We

should account for the shares of government (GNMA)

loans, conforming (GSE) loans and non-conforming

(non-agency) loans. Those main loan types have

existed for many years, but different regions featured

their distinctly differing and dynamically changing

shares. For example, California loans had been mostly

non-conforming due to their size until 2008.

Figure 10-US reports on the composition of the

national mortgage market and blended costs we

assessed for GNMA, GSE and non-agency loans. Figure

10-CA shows the same for California where

composition has obviously shifted in recent years with

the increase of the conforming limit. In compiling data

for these charts, we neglected credit risk underpricing

for GNMA and GSE loans and utilized origination data

from the Mortgage Market Statistical Annual [2012].

Although this may seem to be a frivolous shortcut to

avoid complexity, the quality of GSE loans has been

very high as of late and the points paid by borrowers to

obtain FHA loans may be viewed a fair compensation

of the high-LTV related credit risk1.

National and Regional Market Composition

Figure 10-US. Loan Origination Composition and Blended Cost (US)

A) Composition B) Cost

Figure 10-CA. Loan Origination Composition and Blended Cost (CA)

A) Composition B) Cost

__________________1At the time of this writing, we have not analyzed the credit risk of government loans.

Having computed an all-in borrower cost, we are

now in position to define the Affordability Index, or

equivalently, affordability-based home price

equilibrium. Affordability Index is the ratio of

household income to the annual borrowing cost:

Affordability Index = Income / (All-In Cost * HPI)

HPI equilibrium is defined as the HPI level that keeps

the Affordability Index constant using the above

formula. We depict the Affordability Index relative to

its 2000 level (i.e. in 2000 earned dollars) in Figure 11.

If home prices exactly followed the cost of borrowing

and income, the Affordability Index would stay

constant. In Figure 11, we see that our All-In cost was

much less volatile than the standard measure

advocated by the National Association of Realtors,

(NAR) that considers only loan payments. Equivalently,

our affordability-linked HPI equilibrium, unlike the

standard one, was a much better predictor of HPI

trends and levels (Figure 12). We observe that the

AD&Co HPI equilibrium was quite predictive of actual

home prices, although other factors also contributed to

the HPI dynamics. Such factors are classified by our

HPI2 model as “HPA jumps” (non-systematic

randomness) and “HPA diffusion” (systematic

randomness). For example, the HPI equilibrium derived

straight from our affordability index would understate

the housing bubble both in the US (on average) and in

California. It can be explained by the fact that we

excluded forward HPA expectation from affordability

thereby ignoring speculative optimism. Not

surprisingly, home prices overgrew objective

equilibrium in the mid-2000s.


National and Regional Market Composition ( C O N T I N U E D )

As seen from Figure 10, the cost of conforming loans

has been notably stable despite interest-rate volatility

because the combined LTV at origination was lower

when rates were lower, thereby inflating the equity cost

and offsetting the decline in loan cost.

As for the loans guaranteed by GNMA, we see their

rates falling as well, but without an equity cost offset;

the original LTV has been quite stable, in the narrow

range of 93 – 95, over the last decade.

Affordability Index and HPI Equilibrium

Figure 11. Affordability Index


In general, HPI volatility has been stronger in densely

populated areas, such as major MSAs. For example, the

HPI volatility measured for the Composite of 25 largest

Metropolitan Statistical Area (MSAs) is almost twice as

large as the HPI volatility for the US; San Francisco and

Los Angeles are more volatile than the state of

California; the New York MSA is more volatile than the

state of New York (Levin, [2011] ). Below we argue that

these observations can be backed by demand-supply

curves for the housing market. In essence, the ability

to meet growing demand by new construction reduces

potential HPI appreciation. In contrast, areas lacking

free land (e.g. dense MSAs) can see HPI moving stronger

in each direction. We illustrate this important point

using Figure 13 depicting hypothetical demand-supply

(y-axis) against HPI (the x-axis).

Affordability Index and HPI Equilibrium ( C O N T I N U E D )

HPI Equilibrium and a Demand-Supply Argument

According to the NAR, we are living in a time of record-

high affordability2; the Standard HPIeq lines in Figure

12 concur. The AD&Co Index does not share this view.

Once we consider currently existing high down

payment and credit requirements, the HPI equilibrium

is found just above currently observed home prices.

Figure 12. HPI and Constant Affordability HPI Equilibrium

__________________2http://www.realtor.org/news-releases/2012/03/housing-affordability-index-hits-record-high

Figure 13. Demand-Supply Curves

Aside from the fact that the shape of HPI equilibrium

we constructed resembles the actual bubble-decline

pattern, we would like to mention some other facts

supporting our views.

(1) In recent years, loan origination shifted from GSEs

to GNMA, the Federal Housing Administration (FHA), in

particular. This GNMA-sponsored, high-LTV, origination

has grown to approximately 25% of total3. We are still

researching the exact financial terms of FHA loans, but

it is evident that the low down-payment requirement

made those loans popular.

(2) According to our All-In cost formula and its

translation into Affordability Index, the relative role of

interest rates is higher when the role of equity cost is

lower. As seen from Figure 6, in 2006, loan payments

constituted close to 100% of the total cost (with the

equity cost being essentially offset by risk

underpricing). Today’s loan payments constitute only

50% of the total cost and are rather modest by

historical standards. This explains why the record-low

interest rates do not impress borrowers and do not

propel home prices up.

(3) Using a similar line of thought, with the small

equity cost of the mid-2000s, the relative importance of

risk-adjusted loan rates was high. Therefore, risk

underpricing played a strong role in borrower decisions.

We think that, if originators were to offer subprime

loans today at a low rate, it would not lead to a

substantial surge in demand due to the severe equity

requirement.

Does Our Theory Agree with Practice?


HPI Equilibrium and a Demand-Supply Argument ( C O N T I N U E D )

Let us start with some demand curve, a decreasing

function of home prices (“starting D”). If financing

conditions improve, the line scales up (“increased D”).

How much will this improved affordability increase

home prices? The answer depends on the supply

curve. In large MSAs offering no or limited new

construction, that curve can be relatively flat (“flat S”).

This means that homeowners intending to sell homes

will do so no matter what the price is. Many of them

expect to buy another property so their gain on one

transaction offsets the loss on the other. Of course, a

perfectly flat curve is an over-simplification as there

will be some homeowners not selling at low price, e.g.

investors.

If new construction is possible, housing supply will

ultimately rise (“elastic S”). As seen in Figure 13, the

HPI shift will be larger in the case of a flat, or less

elastic, supply. It is therefore important not only to

measure housing affordability, but also to quantify its

role in formation of the HPI equilibrium, i.e. the

intersection of regional demand and supply lines.

The exact position of demand-supply lines is not going

to be known. However, we can assume that the HPI

equilibrium is formed using some parameterized

relationship and calibrate parameters using historical

data.

__________________3A rough estimate. Weighted average OLTV of GNMA loans has been 91%; combined OLTV is not available.


Mortgage rates alone do not paint a complete picture of

borrowers’ economics. The rates should be credit-

adjusted and blended with the cost of equity, i.e. down

payments. These factors, analyzed retrospectively, can

reveal the causes of housing boom and decline.

Proliferation of affordable lending programs such as

payment-reducing Option ARMs and non-prime loans,

high combined LTV loans with underpriced risk were

significant contributors to the crisis. With the demand-

supply argument, we showed that changing financing

conditions played larger roles in the formation of

housing prices in densely populated areas.

Our development of the next generation of AD&Co’s

HPI model (“HPI3”) is still underway, but the strength of

interest rates is likely to be reduced and made region-

dependent while remaining directionally unchanged.

Conclusion

J. Berkovec, Y. Chang and D. A. McManus, “Alternative Lending Channels and the Crisis in U.S. Housing Markets”,

Real Estate Economic, (upcoming) Volume 41, Issue 3, 2013.

A. Levin, “Home Price Derivatives and Modeling”, Chapter 17 in A. Lipton and A. Rennie (editors), The Oxford

Handbook of Credit Derivatives, Oxford University Press, 2011, pp. 604 – 630.

A. Levin, “HPI Modeling: Forecasts, Geography, Risk and Value”, 18th AD&Co Conference, New York, June 2010.

Levitin, Adam J. and Wachter, Susan M., “Explaining the Housing Bubble” (April 12, 2012). Georgetown Law Journal,

Vol. 100, No. 4, pp. 1177-1258; University of Pennsylvania Institute for Law & Economics Research Paper No. 10-15;

Georgetown Public Law Research Paper No. 10-60; Georgetown Law and Economics Research Paper No. 10-16.

Available at SSRN: http://ssrn.com/abstract=1669401 or http://dx.doi.org/10.2139/ssrn.1669401

Mortgage Market Statistical Annual, ”Inside Mortgage Finance, Volume I: Primary Market”, 2012.

Acknowledgement

References

We would like to thank Nadya Derrick and Herb Ray for compiling origination data, Levy He for automating and

furnishing results of historical Credit OAS analysis described in the Rates and Risk section, and Nancy Davidson and

Simone Davis for their editorial and publishing work.

QP © 2012 andrew davidson & co., inc.

QuantitativePerspectives

Andrew Davidson & Co., Inc.

65 Bleecker Street, Fifth Floor

New York, NY 10012

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We welcome your comments and suggestions.

Contents set forth from sources deemed reliable, but Andrew Davidson &

Co., Inc. does not guarantee its accuracy. Our conclusions are general in

nature and are not intended for use as specific trade recommendations.

© Copyright 2012 Andrew Davidson & Co., Inc.

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