Taylor Subprime

8/13/2019 Taylor Subprime

1/25


2/25

6hin !$%%:' has argued that the interaction of securitisation and the growth of the repomarket stimulated and fuelled the growth of liquidity, and led to the development of a;shadow banking system< that became an ;inflating ballooneoch, $%%0'.

?ut there remains the question( what was the driving force in this ballooning system4This is the question that this paper attempts to answer. To do so requires ane+amination not 3ust of the particular market, but of the macro-financial structurewithin which market is embedded. ?ecause it is within that macro-structure thatgrowth of liquidity takes place.

Liquidity is an elusive concept. @n the one hand an asset is liquid if it can be

immediately e+changed for money without any significant change in price !a fire-saleis not a manifestation of liquidity'. 8inancial assets command a liquidity premiumdetermined by their market relationship to cash. Liquid markets are markets inhabited

by agents with heterogeneous motives and behaviour A when someone wants to sellsomeone else wants to buy. Bonversely, markets in which agents display relativelyhomogeneous behaviour are likely to be illiquid as, particularly in the face of e+tremeevents, all rush to sell, or to buy. 6o liquidity is an ad3ective, not a noun.

@n the other hand, aggregate liquidity is often characterised as if it were a measurablequantity. #drian and 6hin !$%%:, p. ' cite popular phrases such as ;a flood of globalliquidity< and ;e+cess liquidity< as metaphors embodying this quantitative image.

Liquidity is a noun. #drian and 6hin define aggregate liquidity today as ;the growthrate of financial intermediaries7 balance sheet< and relate that growth to thedevelopment of the repo market. This amounts to defining liquidity as ;the ability ofagents to command purchasing power by acquiring liquid liabilities


3/25

)n 1art @ne of the paper accounting matrices are used to e+amine the role of liabilityacquisition in national balance sheets that reflect different stages of the developmentof financial market structures. )n 1art Two a national balance sheet incorporatingsecuritised mortgages is the starting point for the construction of a simple model ofthe interaction between the financial sector and the housing market. )n 1art Three the

model is used, with some empirical findings on leverage in households and in thefinancial sector, to attempt an answer to the question of what has been the drivingforce in the e+pansion of sub-prime mortgage lending.

Part One: Financial structure and the expansion of liquidity.

# very simple monetary structure !perhaps representative of the early stages of thedevelopment of market economies, or of some developing countries today' is

presented in Table @ne.

)n normal times !one historically significant sort of ;abnormality< is considered below', the only private assets are the value of tangible capital pk K with K as thee+isting stock at historical or replacement cost and pk as its asset price. ; oney

possible to mobili e large sums of liquidity to buy stock. This is e+actly how the repo

and reverse repo markets have worked to the si e of balance sheets in the 8inance6ector.

Table Three: Stage Three

The use of repos and reverse repos by financial institutions as a source of liquiditywas analysed by insky ! 2&0', who demonstrated that the tight 56 monetary policyof the mid-&%7s led government bond houses to develop repurchase agreements inorder to finance the e+pansion of their balance sheets, despite the rise in short-terminterest rates 2. >epos can be depicted as a financial innovation which makes ;idle

+:- ; b # ) . '( b

Cere we assume that the rate of growth of the demand for housing depends +a- negatively on the price of housing ph +b- positively on the rate of return on housing 7 !the ratio between capital gains 2p h " / 31and the holding of houses ph31 " / 31 - +c- negatively on the rate of interest on mortgages r m +d- negatively on the leverage ratioof households !the ratio between their stock of mortgages 0 and their net worth '( h'and +e- negatively on the leverage ratio of banks !the ratio between their stock ofrepos ) and their net worth '( b'.

+a-, +b- and +c- correspond to the relationships suggested by economic theory withoutconsidering restrictions facing borrowers in the housing market. +d- and +e- aim to

describe the effect of credit rationing on the demand for housing/

. +e- is based on6hin7s !$%%:' analysis of the active management of balance sheets by financialinstitutions( decreasing leverage ratios induce a ;demand for e+tra assets Kwhich, inturn entails scouring for borrowers, even sub-prime ones


13/25

@n the supply side it is assumed, following "enny ! 222', that the rate of growth of built homes 2/ s ./ s31 is related positively to the ratio between the price of housing ph and the production cost of housing c !which is assumed to be constant'. This equationis in line of Tobin7s ? analysis of investment *

+@- 2/ s ./ s31 # 5 1 " ph31 .c

The rate of inflation in housing 2p h .p h31 is then determined by the difference betweenthe rates of growth of demand and supply. 6uch a price mechanism allows the modelto achieve a steady state when both supply and demand grow at the same rate. )n otherwords, if the rate of growth of unsold houses remains constant, so does the price ofhousing units.

+ - 2p h .p h31 # " +2/ d ./ d 31 8 2/ s ./ s31 -

The shadow ban%ing syste!

The ne+t step is to consider the behaviour of the ;shadow banking system< and itsinteraction with the housing market. Cere, it is assumed that all purchases of housingunits 2/ d "ph are financed through mortgages(

+D- 20 # 2/ d "ph

oreover, all mortgages are securitised through the chain of financial institutions presented in 1art @ne. 8rom a macroeconomic point of view securitisation consists oftaking sub-prime mortgages 0 off the aggregated balance sheet of the banks, placingthem in a separate special purpose vehicle, and receiving in return mortgage-backedsecurities S whose price p s is correlated with the price of housing !the ultimatecollateral'. This is captured in equation !2' in which the price of securities p s is

proportional to the price of housing ph. The issue of mortgage-backed securities isderived directly from the amount of new mortgages created !equation %'.

+E- p s # " p h

+153$- 2S = 20.p s

# consequence of securitisation is, as shown in ! ', that a rise in the price ofhousingMsecurities now leads to a rise in the net worth of banks and thus to a decreasein their leverage ratio.

+11- '( b = p s"S 8 > Z 8 )

* "enny7s ! 222' version is in terms of difference between price and cost( NCMC - O P% Q P !p h- - c'.This tends to force price and cost toward equality. The ratio is a more general formulation.

/


14/25

@n the supply side of the housing market, it is assumed that non-financial firms !that build housing units and produce investment and consumption goods' are also financed by the banking system without any restriction. )n other words net borrowing financeswhatever part of firms7 investment is not covered by profits(

+163$iii- 2 = G f 8 P f

The banking system has two sources of liquidity that allow it to finance the housingmarket. The first source is the savings of households collected by the financialsystem. )n this model savings can be collected only in the form of bank deposits & > and banks apply a spread between the various rates of interest on loans !rates ondeposits r d , mortgages r m and corporate loans r l ' in order to reali e profits P b1@ (

+193iii- P b = r m31 " 0 31 r l31" 31 8 r d31 " > 31

This first source of liquidity is not necessarily sufficient to cover the needs of thehousing market, especially since banks are forced by the central bank to hold reserves

Z in proportion to the amount of deposits(

+1:- Z # H " >

The second source of liquidity is repurchase agreements, repos. #s e+plained earlier,repos between the various financial institutions enable a global increase in liquiditythrough a rise in the velocity of circulation. Cowever these intra-sector repos do notappear e+plicitly in the macro model since repos and reverse repos offset each other inthe aggregated balance sheet of the shadow banking system. The e+pansion of reposand reverse repos is endorsed by the operations of the Bentral ?ank to sustainliquidity in short-term money markets. #ccordingly, growth of the net repo position inthe ?anking 6ystem is balanced by counter-party transactions by the Bentral ?ankclearing the repo market !on mortgage backed securities 0 ' at the rate of interest of itschoice r p, so providing an endogenous demand for repos : . Thus, through repos, thecentral bank provides whatever liquidity is required by banks at the rate r r 2

+1


15/25

+1@- C # c " +( r d31"> 31 8 r m31"0 31 -

+1 3i- 2> # I = ( 3 C r d31"> 31 3 r m31"0 31

'on(financial fir!s.

The behaviour of non-financial firms is also quite rudimentary. )nvestment consistssolely of the number of newly built houses, implying that no investment is necessaryfor producing consumption or investment goods(

+1D- G f # 2K # L " 2/ s

)n the same way, wages are a proportion of the cost of newly built houses.

+1E- ( # M " +2/ s " c-

1rofits of firms, that appeared in equation ! $', are given by the following accountingidentity(

+653$ii- P f = 2/ "p h C G f 8 ( 8 r l31 " 31

)losure of the !odel.

The model is now closed. The ;missing identity< is the accounting balance of thecentral bank(

+$i- Z )"

This identity reflects the fact that base money Z is supplied to the economy throughrepos ) to private banks. 9hen the model is solved numerically, identity !vi' isalways verified, confirming ;stock-flow consistency


16/25


17/25

The kind of instability that such a positive feedback in the price of housing maygenerate may be illustrated in terms of equations describing the interaction betweenthe leverage ratio of households and the price of housing(

h p # f p + d / N s / - # f p + ph N ;h - +61-

h # f ; + 0 N h( ' - # f ; + ph N ;h - +66-

Equations +61- and +66- correspond to a generic form of differential equation. Cerewe do not try to solve the model numerically or to determine the e+act form of theseequations $%. >ather our emphasis is on determining which conditions can generate anunstable regime similar as the one observed with simulations. To do so, suppose that4 : is high enough to generate a positive feedback in the price of housing(

h p . ph 5

#nd note that equation ! ' means that the leverage ratio has a negative impact on thedemand for housing and thus on ph(

h p . ; h O 5

Equation ! ' also implies that the leverage ratio behaves in a self-stabili ing fashionsince an increase in the leverage of households reduces the supply of mortgages(

h . ; h O 5

)n the steady state h p # h # 5 with positive critical values ph ! 5 and ; h ! 5 , theform of the Jacobian matri+ J is(

J +g 5! , l ! - # 11 5 16 O 5 61 Q 66 O 5

with >et +J- # 11R66 8 61R16 r +J- # 11 66

6ince the main-diagonal product 11R66 is negative, the system will only avoid asaddle-point with et !J' S % if the off-diagonal product 61R16 is also negative !and

higher than 11R66 in absolute value', that is, if 61 is positive. Thus, when the price ofhousing feeds back positively into itself, a ;household-led< financial crisis wouldrequire that h . ph 5 . )n this case, if the trace of the Jacobian matri+ is

positive $ , the model can generate a divergent tra3ectory similar to the one that appearsin the phase diagram of 8igure Two. 6tarting from A, the price of housing willincrease and the leverage ratio of households fall !due to capital gains' until the ! ph N

; h - tra3ectory crosses the isocline of the leverage ratio in B. Then the leverage ratio

$% 5sing equation !0', one can show that h p depends on d / and s / and thus, according toequations ! ' and ! ', on ph and ; h"5sing equation !/', one could show that ; h depends on 0 and h( '

and thus, according to

equations !:' and !&', on ph and d / , that is on ph and ; h"$ )f the trace of is negative the model will still generate a stable tra3ectory, even if 61 is positive.

0


18/25

starts to increase due to the rise in mortgages !allowed by a higher net worth' but the price of houses still increases until C . #t that point the demand and the price ofhousing begin to fall !due to the negative impact of higher leverage ratios $$' whichleads to further increases in the leverage ratio !due to negative capital gains' till .#round that point a debt deflation may occur.

Figure Two: * households(led financial crisis.

)n short, the financial crisis that the model generates for a relatively high value of 4 : iscaused by both a positive feedback in the price of housing and a pro-cyclical leverageratio of households.

)s this a plausible scenario4 )n particular, is it realistic to assume that the leverageratio of households can respond positively to a rise in the price of houses4 )ntuitively,the direct effect of a rise in the price of houses seems rather an increase in the networth of households !due to capital gains' and thus a decrease in the leverage ratio.The only way for the leverage ratio to rise would be that mortgages increasesubstantially in response to this increase in their net worth !as represented by the highvalue assigned to 4 : '.

Cowever, some basic empirical analysis, following of #drian and 6hin !$%%0' wouldtend to contradict this hypothesis. )n Table 6even are displayed estimates of how therates of growth of the debt of 56 households and 56 financial institutions responds to

$$ Equation !$ ' can be written as follows(

h p # " T34 1" ph31 84 : " ; h31 8 1"ph31 .c UV

@n top of the normal negative demand and supply responses of h p to ph, there is a positive effect of ph through ; h which attenuates as ph gets bigger. The attenuation helps e+plain why the solutiontra3ectory ultimately crosses the h p # 5 isocline and provokes a crisis in 8igure $.

#

?

B

ph

;h

# 5

# 5

:


19/25

the rates of growth of their net worth or equity capital. )n the case of households, anincrease in net worth has a very limited impact on the rate of growth of debt.

Table Se"en: 4e"erage beha"iour 1/556(78863Source: Federal 9eser"e Federal ;eposit E9 0.09;90D 0.0;=9D 0.09CD? 0.0CE?>?R-squa%ed& 0.0>E> 0.0D9>C> 0.0EE;=D 0.90E0>= 0.0?09E=

So rceF !,6 !685 !685 (5A S,5

dlog (deb "

T*is table reports regressions o arterl% irst di erences o t*e logarit*m o debt on irst di erences o t*e logarit*m o e it%. 6ebtdi erence bet)een assets and e it%. T*e investment banks col mn reports a panel regression or ive investment banksF Bear StSac*s< e*man Brot*ers< $erril %nc*< $ organ Stanle%.

The relationship between quarterly changes in total household assets and quarterlychanges in leverage as measured in the 8low of 8unds account for the 5nited 6tates

between 220 and $%%0 is illustrated in 8igure Three. #s shown by #drian and 6hin!$%%0' in a similar chart based on data from 2 / to $%% , there is a strong negative

relationship between total assets of households and their leverage$/

. Cence it wouldappear to be unreasonable to impose the parameter values on the model that would berequired to generate a ;households-led< financial crisis.

Figure Three: *ssets and le"erage growth rates of &ouseholdsSource: Federal 9eser"e.

$/ )n figure Three, the leverage of households is defined, following #drian and 6hin !$%%0', as the ratio

of assets A to net worth ' . This leverage ratio is of course interchangeable with the one we used in ourmodel !debt > on net worth ' '. )ndeed #MF O # M !# A ' O Q M !# - ' O Q MF. Thus, when theleverage ratio of 8igure Three decreases, so does the one we used.

2


20/25

-.0?

-.0;

.00

.0;

.0?

.0=

.0>

.90

-.090 -.00C .000 .00C .090 .09C

dlog/leverage1

d l o g

/ a s s e t s

1

* ban%(led financial crisis.

?y contrast with the above case the second type of unstable regime that the model cangenerate, for high values of P &, provides a plausible representation of the recent sub-

prime mortgage crisis.

Figure Four: +nstable regi!e for , 0 8.> 1cloc%wise tra2ectory3

0.>?

0.>>

0.D;

0.D=

9.00

9.0?

9.0>

-; 0 ; ? = > 90 9;

,3@B@0

P@

S / B a s e

l i n e

1

$%


21/25

#s shown in figure 8our, simulations show that unstable regimes obtained for highvalues of P & can be interpreted, in some cases $*, as arising from the interaction

between the price of securities p s and the leverage ratio of the banking system ; b6


22/25

supply of mortgages that depresses the price of securities and leads to even weaker balance sheets and to a possible debt deflation.

#s argued by #drian and 6hin !$%%0' this is a plausible scenario for the sub-primecrisis since the data suggest that there is a strongly pro-cyclical leverage ratio for the

financial institutions which enter in the securitisation chain, in particular investment banks $0(

Figure Fi"e: *ssets and le"erage growth rates of fi"e in"est!ent ban%sSource: Securities =xchange )o!!ission *drian and Shin 178863

-.90

-.0C

.00

.0C

.90

.9C

.;0

-.; -.9 .0 .9 .;

dlog/leverage1

d l o g

/ a s s e

t s 1

Bear Sterns

-.0?

.00

.0?

.0>

.9;

-.B -.; -.9 .0 .9

dlog/leverage1

d l o g

/ a s s e

t s 1

Goldman Sac*s

-.B

-.;

-.9

.0

.9

.;

-.B -.; -.9 .0 .9 .;

dlog/leverage1

d l o g

/ a s s e

t s 1

e*man Brot*ers

-.;

-.9

.0

.9

.;

-.B -.; -.9 .0 .9 .;

dlog/leverage1

d l o g

/ a s s e

t s 1

$erril %nc*

-.9C

-.90

-.0C

.00

.0C

.90

.9C

-.; -.9 .0 .9 .;

dlog/leverage1

d l o g

/ a s s e

t s 1

$organ Stanle%

5sing data from the 8ederal eposit )nsurance Borporation it may be shown thatcommercial banks have a similar behaviour !see 8igure 6i+' $: . oreover theregressions presented in Table 6even suggest that there is a positive relationship

between the rates of growth of debt and equity for a number of financial institutions $2.

Figure Six: *ssets and le"erage growth rates of co!!ercial ban%sSource: Federal ;eposit


23/25


24/25

9eferences

#drian Tobias and Cyun 6. 6hin, $%%0, ;Liquidity and Leverage


25/25

#nniversary of Lombard 6treet >esearch, ?ank of England, 9ednesday $:July.

9icksell, "nut, 2/&, ectures on Political Iconomy , =ol. )), London( acmillan.

Documents

Taylor Subprime