The Banking System in The Banking System in an Age of Turbulencean Age of Turbulence

Professor Willem H. Buiter, London Professor Willem H. Buiter, London School of EconomicsSchool of Economics

Professor Anne Sibert, Birkbeck, Professor Anne Sibert, Birkbeck, University of LondonUniversity of London

MSc Financial EconomicsMSc Financial Economics

Professor Anne SibertProfessor Anne Sibert

February 2011February 2011

Asset Price BubblesAsset Price Bubbles

Rational BubblesRational Bubbles

In this talk I am going to consider In this talk I am going to consider rationalrational bubbles, so it is worth digressing and bubbles, so it is worth digressing and reminding you what an economist means reminding you what an economist means by the term rational.by the term rational.

ExpectationsExpectations

• Suppose that market participants’ behaviour Suppose that market participants’ behaviour depends on their forecast of some future variable.depends on their forecast of some future variable.

• If an economist wants to model the behaviour of If an economist wants to model the behaviour of market participants, then he must make some market participants, then he must make some assumption about how the they form their assumption about how the they form their forecasts.forecasts.

• It is typical to assume that the market participants It is typical to assume that the market participants have have rational expectationsrational expectations..

• Rational expectations is a modelling technique. Rational expectations is a modelling technique. We use it because it is a good, if not perfect, We use it because it is a good, if not perfect, description of reality and it is relatively description of reality and it is relatively straightforward to implement.straightforward to implement.

Rational expectationsRational expectations

• (technical definition) If market participants (technical definition) If market participants have rational expectations then their have rational expectations then their forecast of a future variable is the forecast of a future variable is the statistical expectation conditional on all statistical expectation conditional on all available information.available information.

• (intuitive) Market participants with rational (intuitive) Market participants with rational expectations make the best possible expectations make the best possible guess using all available information.guess using all available information.

If market participants have If market participants have rational expectationsrational expectations

• They are correct on average.They are correct on average.• They do not make systematic errors.They do not make systematic errors.• They cannot be systematically fooled.They cannot be systematically fooled.• ““You can fool some of the people all of the time, You can fool some of the people all of the time,

and all of the people some of the time, but you and all of the people some of the time, but you cannot fool all of the people all of the time.”cannot fool all of the people all of the time.”

• In a scenario where nothing is random, market In a scenario where nothing is random, market participants with rational expectations have participants with rational expectations have perfect foresightperfect foresight. That is, their expectation of a . That is, their expectation of a future variable is the actual value of that variable.future variable is the actual value of that variable.

HistoryHistory

• The theory of rational expectations was proposed The theory of rational expectations was proposed by John Muth, a graduate student at Carnegie by John Muth, a graduate student at Carnegie Mellon, in the early 1960s.Mellon, in the early 1960s.

• It pretty much rendered obsolete in macro-It pretty much rendered obsolete in macro-economics the earlier theories based on economics the earlier theories based on adaptive adaptive expectationsexpectations. If market participants have . If market participants have adaptive expectations then their beliefs about the adaptive expectations then their beliefs about the future depend upon the past.future depend upon the past.

• Rational expectations theory was developed in the Rational expectations theory was developed in the late 1960s and 1970s. The most important late 1960s and 1970s. The most important contributors were Robert Lucas, Edward Prescott, contributors were Robert Lucas, Edward Prescott, Thomas Sargent and Neil Wallace.Thomas Sargent and Neil Wallace.

Non-Rational expectationsNon-Rational expectations• "Most, probably, of our decisions to do something positive, the "Most, probably, of our decisions to do something positive, the

full consequences of which will be drawn out over many days full consequences of which will be drawn out over many days to come, can only be taken as the result of to come, can only be taken as the result of animalanimal spiritsspirits - a - a spontaneous urge to action rather than inaction, and not as spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities." (John Maynard multiplied by quantitative probabilities." (John Maynard Keyes,Keyes,The General Theory of Employment Interest and The General Theory of Employment Interest and Money, Money, 161-162.)161-162.)

• ““But how do we know when But how do we know when irrational exuberance irrational exuberance has has unduly escalated asset values, which then become subject to unduly escalated asset values, which then become subject to unexpected and prolonged contractions as they have in Japan unexpected and prolonged contractions as they have in Japan over the past decade?” (Alan Greenspan, speech at the over the past decade?” (Alan Greenspan, speech at the American Enterprise Institute, 5 Dec 1996)American Enterprise Institute, 5 Dec 1996)

A model of house pricesA model of house prices

• Let R(t) be the amount it costs to rent one Let R(t) be the amount it costs to rent one unit of housing at time t.unit of housing at time t.

• Let P(t) be the amount it costs to buy one Let P(t) be the amount it costs to buy one unit of housing at time t.unit of housing at time t.

• Let I(t) be one plus the interest rate at on Let I(t) be one plus the interest rate at on bonds held between time t and time t + 1bonds held between time t and time t + 1

Simplifying AssumptionsSimplifying Assumptions

• Assume that people are risk neutral. That Assume that people are risk neutral. That is, they only care about the expected is, they only care about the expected return on investments.return on investments.

• Assume that there is no depreciation, no Assume that there is no depreciation, no transactions costs, no repairs, no tax transactions costs, no repairs, no tax considerations.considerations.

• Suppose that R(t) = R and I(t) = I: the Suppose that R(t) = R and I(t) = I: the rental price of housing and the interest rental price of housing and the interest rate are constants.rate are constants.

Investing in bonds vs. rental propertyInvesting in bonds vs. rental property

• People must be indifferent between buying People must be indifferent between buying houses as an investment and renting them houses as an investment and renting them out and investing their money in bonds. out and investing their money in bonds. Otherwise, they would only do one of these Otherwise, they would only do one of these things. Thus, the expected (forecasted) things. Thus, the expected (forecasted) returns on these two options must be the returns on these two options must be the same.same.

• If you invest one unit of money in a bond at If you invest one unit of money in a bond at time t, then you get I units of money at the time t, then you get I units of money at the start of time t + 1.start of time t + 1.

Returns to different investmentsReturns to different investments

• If you take one unit of money at time t, you If you take one unit of money at time t, you can buy 1/P(t) units of housing. You can can buy 1/P(t) units of housing. You can rent the house in period t (suppose the rent rent the house in period t (suppose the rent is paid at the start of the period) and you is paid at the start of the period) and you can sell the house at the start of period t + can sell the house at the start of period t + 1. At the start of time t + 1, you have [RI + 1. At the start of time t + 1, you have [RI + P(t+1)] / P(t) units of money.P(t+1)] / P(t) units of money.

• There is no randomness in our model so we There is no randomness in our model so we assume that market participants have assume that market participants have perfect foresight. Their forecasted value of perfect foresight. Their forecasted value of P(t+1) is P(t+1).P(t+1) is P(t+1).

Arbitrage conditionArbitrage condition

• If the returns on these two investments are If the returns on these two investments are equal we have: [RI + P(t+1)] / P(t) = Iequal we have: [RI + P(t+1)] / P(t) = I

• This implies: P(t+1) = IP(t) – RI.This implies: P(t+1) = IP(t) – RI.

• Note that this tells us how the house price Note that this tells us how the house price changeschanges over time, but it does not pin over time, but it does not pin down the down the levellevel and this causes rational and this causes rational bubbles to be possible.bubbles to be possible.

Example:Example:

• Suppose that R = £1,000 and I = 1.10.Suppose that R = £1,000 and I = 1.10.• Then we have P(t+1) = 1.1P(t) – 1,100.Then we have P(t+1) = 1.1P(t) – 1,100.• Suppose that P(0) = 20,000. Then P(1) = Suppose that P(0) = 20,000. Then P(1) =

20,900, P(2) = 21,890, P(3) = 22,979, P(4) = 20,900, P(2) = 21,890, P(3) = 22,979, P(4) = 24,177, …24,177, …

• Suppose that P(0) = 30,000. Then P(1) = Suppose that P(0) = 30,000. Then P(1) = 31,900, P(2) = 33,990, P(3) = 36,289, P(4) = 31,900, P(2) = 33,990, P(3) = 36,289, P(4) = 38,818,…38,818,…

• Suppose that P(0) = 5,000. Then P(1) = 4,400, Suppose that P(0) = 5,000. Then P(1) = 4,400, P(2) =3,740, P(3) =3,014, P(4)=2,215, …P(2) =3,740, P(3) =3,014, P(4)=2,215, …

Multiple outcomes are possibleMultiple outcomes are possible

• This scenario is similar to being told that This scenario is similar to being told that someone has driven 100 kilometers per someone has driven 100 kilometers per hour down the highway for the last hour hour down the highway for the last hour and then being asked where they are.and then being asked where they are.

• We know where the person is relative to We know where the person is relative to where they were an hour ago, but to where they were an hour ago, but to answer the question we need to know answer the question we need to know where they started out.where they started out.

Some Possible Outcomes:Some Possible Outcomes:

The horizontal axis is time; the vertical axis is the house price.

There are many outcomes, There are many outcomes, depending on P(0)depending on P(0)

• Some of them have prices becoming Some of them have prices becoming negative: clearly these are not equilibria.negative: clearly these are not equilibria.

• Some of the have prices going to infinity: Some of the have prices going to infinity: these are possible equilibria: these are possible equilibria: bubblesbubbles..

• One of them has a constant price.One of them has a constant price.

Note that the environment is constantNote that the environment is constant

• In this model of house prices, we take the In this model of house prices, we take the (gross) interest rate I and the rental price R as (gross) interest rate I and the rental price R as given. They are the given. They are the dependentdependent, or , or exogenousexogenous, , variables.variables.

• We want to use these exogenous variables to We want to use these exogenous variables to solve the model for the solve the model for the independentindependent, or , or endogenousendogenous, variable, the house price., variable, the house price.

• Note that exogenous variable are constant. This Note that exogenous variable are constant. This suggests that it is reasonable for the suggests that it is reasonable for the endogenous variable to be constant. Guess that endogenous variable to be constant. Guess that the house price is a constant: P(t) = P.the house price is a constant: P(t) = P.

Substitute this into the arbitrage Substitute this into the arbitrage condition: condition:

• P = IP – RIP = IP – RI

• Solve for P: P = RI / (I – 1) = 11,000Solve for P: P = RI / (I – 1) = 11,000

• It turns out that this has an economic It turns out that this has an economic interpretation: It says that the price of a interpretation: It says that the price of a house should be equal to the discounted house should be equal to the discounted present value of the rental payments.present value of the rental payments.

Boundary ConditionsBoundary Conditions• Equations that relate the value of a variable at time t + 1 to its value Equations that relate the value of a variable at time t + 1 to its value

at time t are called at time t are called difference equationsdifference equations. . • The problem I gave with the car is similar. There, we wanted to find The problem I gave with the car is similar. There, we wanted to find

the location of a car given its speed (how fast its location is the location of a car given its speed (how fast its location is changing). This type of equation is a changing). This type of equation is a differential equationdifferential equation..

• Both types of equations have an infinite number of solutions. With Both types of equations have an infinite number of solutions. With the car example, we pick out the solution we want by appealing to the car example, we pick out the solution we want by appealing to some additional information: where the car started. Mathematicians some additional information: where the car started. Mathematicians call this a call this a boundary conditionboundary condition..

• Here, we are not going to use P(0) (where we started) to pick out Here, we are not going to use P(0) (where we started) to pick out the right solution. Instead we are going to reason that if the the right solution. Instead we are going to reason that if the fundamentals are constant, the solution we want is the only one fundamentals are constant, the solution we want is the only one where the price is constant.where the price is constant.

• More generally, when the fundamentals are changing we will pick More generally, when the fundamentals are changing we will pick out the single solution that depends just on the fundamentals. All of out the single solution that depends just on the fundamentals. All of the others will have the price going to infinity because of the others will have the price going to infinity because of self-self-fulfilling expectationsfulfilling expectations..

Another way to see thisAnother way to see this

• Consider the equilibrium condition: P(t+1) Consider the equilibrium condition: P(t+1) = IP(t) – RI.= IP(t) – RI.

• I am going to graph this and use the result I am going to graph this and use the result to show that a bubble can exist.to show that a bubble can exist.

P(t)

P(t+1) P(t+1)=IP(t)-RI

P(t+1)=P(t)

P(0) P(1) P(2)

This is related to coordination games

• Suppose that two players are confronted with four tiles

• They simultaneously select a tile.

• If they select the same tile, they each get £1,000. Otherwise, they get nothing.

Player 1 sits here Player 2 sits here

Nash equilibriumNash equilibrium

• Both players select the same tile.

• But, how would a Nash equilibrium result in this game?

Try the game again

• Suppose that two players are confronted with four tiles

• They simultaneously select a tile.

• If they select the same tile, they each get £1,000. Otherwise, they get nothing.

Player 1 sits here Player 2 sits here

Choosing the snazzy tile is focalChoosing the snazzy tile is focal

• I conjecture that the likely outcome is a Nash equilibrium where the players pick the tile that is different.

• Perhaps the equilibrium that depends solely on the fundamentals is focal too.

• How would any of the uncountably infinite number of equilibria arise?

The existence of bubbles is a generic The existence of bubbles is a generic property of financial asset marketsproperty of financial asset markets

• Consider the arbitrage condition for stock and Consider the arbitrage condition for stock and bonds.bonds.

• Let Q(t) be the time-t price of stock and let D be the Let Q(t) be the time-t price of stock and let D be the dividend, which I assume is constant.dividend, which I assume is constant.

• Then, you can take one unit of money and buy Then, you can take one unit of money and buy 1/Q(t) units of stock. At the end of the period you 1/Q(t) units of stock. At the end of the period you get a dividend D/Q(t) and you can sell the stock for get a dividend D/Q(t) and you can sell the stock for Q(t+1)/Q(t). Q(t+1)/Q(t).

• For investors to be indifferent between stock and For investors to be indifferent between stock and bonds we need I = [Q(t+1) + D] / Q(t) or Q(t+1) = bonds we need I = [Q(t+1) + D] / Q(t) or Q(t+1) = IQ(t) – D. If you try some examples you will see that IQ(t) – D. If you try some examples you will see that there are bubbles in this case as well.there are bubbles in this case as well.

Exchange RatesExchange Rates

• Demand for a particular currency depends Demand for a particular currency depends positively upon how much it is expected to positively upon how much it is expected to appreciate.appreciate.

• All of the fundamentals (the exogenous All of the fundamentals (the exogenous variables) may be constant, but if people variables) may be constant, but if people think that the currency will appreciate, they think that the currency will appreciate, they buy more of it than they otherwise would.buy more of it than they otherwise would.

• As a result, the currency appreciates: As a result, the currency appreciates: beliefs are self fulfilling.beliefs are self fulfilling.

The problem with financial asset The problem with financial asset pricesprices

• The price of a financial asset today typically The price of a financial asset today typically depends upon what market participants depends upon what market participants believe the price will be tomorrow.believe the price will be tomorrow.

• If they believe the price will go up (even If they believe the price will go up (even though the fundamentals are constant), then though the fundamentals are constant), then they demand more than they otherwise would they demand more than they otherwise would and, as a result, the price goes up. Their and, as a result, the price goes up. Their expectations are self-fulfilling. The result is a expectations are self-fulfilling. The result is a bubblebubble..

Market participants do not need to Market participants do not need to believe a bubble will last foreverbelieve a bubble will last forever

• The bubbles I have described are a bit The bubbles I have described are a bit unrealistic. Market participants believe that they unrealistic. Market participants believe that they will last forever and they do.will last forever and they do.

• Most historical episodes that have been Most historical episodes that have been described as bubbles have the price collapsing described as bubbles have the price collapsing at some point.at some point.

• The theoretical model works if people correctly The theoretical model works if people correctly believe that there is some chance that the price believe that there is some chance that the price will collapse in each period and that as time will collapse in each period and that as time goes to infinity the bubble will certainly have goes to infinity the bubble will certainly have collapsed.collapsed.

Canonical BubbleCanonical Bubble

• In Feb 1637 tulip In Feb 1637 tulip prices in the prices in the Netherlands soared Netherlands soared until the price of a until the price of a tulip could be 10 tulip could be 10 times the annual times the annual earnings of a skilled earnings of a skilled craftsman. They craftsman. They quickly plummeted.quickly plummeted.

Source: Wikipedia

RacehorsesRacehorses

• The price of yearlings The price of yearlings seems far to high seems far to high relative to their future relative to their future earnings.earnings.

• In 1985 a yearling In 1985 a yearling named Seattle Dancer named Seattle Dancer sold for $13.1 million.sold for $13.1 million.

• Only half of all good Only half of all good quality yearlings win a quality yearlings win a race. They are sold as race. They are sold as parents of future parents of future yearlings.yearlings.

Other supposed examples:Other supposed examples:

• Famous early bubbles: The South Sea Famous early bubbles: The South Sea and Mississippi Company Bubbles of and Mississippi Company Bubbles of 1720.1720.

• Japanese real estate and stock market Japanese real estate and stock market (1986 – 1990)(1986 – 1990)

• Dot-com bubble (mid 1990s – 2001)Dot-com bubble (mid 1990s – 2001)

• Various residential housing bubblesVarious residential housing bubbles

Can monetary policy makers tell Can monetary policy makers tell if a bubble exists?if a bubble exists?

• “Some economists, reluctant to let go of the comforting world of rational expectations, still tell us it is impossible for a central bank – or anyone else, for that matter – to call a bubble. This is baloney. When looking at house prices, just look at price-to-rent and the price-to-income ratios, sales volumes and credit statistics, and you know everything you need to know. Almost everything else central bankers do is more difficult than calling a housing bubble.”

• Wolfgang Münchau, Why Central Banks should Prick Bubbles,” Eurointelligence, 27 Oct 2009

Do bubbles exist? Do bubbles exist? Can we tell when?Can we tell when?

• Testing for bubbles is difficult. An Testing for bubbles is difficult. An econometrician must first specify a model. If a econometrician must first specify a model. If a rise in the price of a financial assest cannot be rise in the price of a financial assest cannot be explained by the model, the econometrician explained by the model, the econometrician might claim that it is a bubble. But, it could just might claim that it is a bubble. But, it could just be that the model is misspecified.be that the model is misspecified.

• Apparent bubbles might be due to non-Apparent bubbles might be due to non-stationary fundamentals. Examples are stationary fundamentals. Examples are hyperinflations that be explained by money hyperinflations that be explained by money growth.growth.

There is no conclusive There is no conclusive evidence of a bubbleevidence of a bubble

• Consider our model of house prices. If we Consider our model of house prices. If we let rents and the interest rate be time let rents and the interest rate be time varying we could solve it to find that the varying we could solve it to find that the non-bubble equilibrium price is equal to non-bubble equilibrium price is equal to the present discounted value of rental the present discounted value of rental payments.payments.

• We could test to see whether discounted We could test to see whether discounted rental prices explain house prices.rental prices explain house prices.

The null hypothesis is thenThe null hypothesis is then

• No bubblesNo bubbles

• The simple model of fundamentals is The simple model of fundamentals is correct.correct.

Recall that the simple model assumed no Recall that the simple model assumed no transactions costs, no maintenance costs, transactions costs, no maintenance costs, no depreciation, no tax considerations, no no depreciation, no tax considerations, no uncertainty, risk neutralityuncertainty, risk neutrality

Rejecting the null hypothesis:Rejecting the null hypothesis:

• There is a bubble.There is a bubble.

• Or, the model is not specified properly.Or, the model is not specified properly.

• Clearly adding uncertainty and risk Clearly adding uncertainty and risk aversion is necessary to have a really aversion is necessary to have a really sensible model and this makes the model sensible model and this makes the model way more complicated: I can’t use a way more complicated: I can’t use a simple arbitrage condition.simple arbitrage condition.

Was the tulip mania a bubble?Was the tulip mania a bubble?

• The tulip mania was popularized by Charles The tulip mania was popularized by Charles Mackay in 1841 in his the book Mackay in 1841 in his the book Extraordinary Popular Delusions and the Madness of Crowds. It is the classic example of a bubble: if it wasn’t . It is the classic example of a bubble: if it wasn’t a bubble, what was? But was it a bubble?a bubble, what was? But was it a bubble?

• At the time, tulips had just been introduced into At the time, tulips had just been introduced into Europe from the Ottoman Empire. The valuable Europe from the Ottoman Empire. The valuable ones owed their beauty to a mosaic virus.ones owed their beauty to a mosaic virus.

Garber (1990) argues that the tulip Garber (1990) argues that the tulip mania was not a bubblemania was not a bubble

• Cultivating tulips with the virus took years and Cultivating tulips with the virus took years and could not be done from seeds. This suggests could not be done from seeds. This suggests that the few early bulbs with the virus should that the few early bulbs with the virus should have been very expensive and that as bulbs have been very expensive and that as bulbs accumulated, the price should have fallen.accumulated, the price should have fallen.

• The data is not goodThe data is not good• There was also a spike in the prices of common There was also a spike in the prices of common

tulips, but Garber dismisses this as a winter tulips, but Garber dismisses this as a winter drinking game of the lower classes.drinking game of the lower classes.

Sun spotsSun spots• Sun spots are variables that are not fundamentals but affect Sun spots are variables that are not fundamentals but affect

prices anyway because of self-fulfilling expectations.prices anyway because of self-fulfilling expectations.• Example: Henry Kaufman: an economist who used to work for Example: Henry Kaufman: an economist who used to work for

Solomon Brothers and was famed for his interest rate Solomon Brothers and was famed for his interest rate forecasts.forecasts.

• The name comes from a study by a 19The name comes from a study by a 19 thth-century British -century British economist William Stanley Jevons: he thought that sun spots economist William Stanley Jevons: he thought that sun spots really might affect agriculture.really might affect agriculture.

• Sun spots could also be fundamental variables that are given Sun spots could also be fundamental variables that are given too much weight, and because of self-fulfilling expectations, too much weight, and because of self-fulfilling expectations, are more important than they ought to be in determining are more important than they ought to be in determining prices: an example might be money supply numbers in the prices: an example might be money supply numbers in the United States when Paul Volcker was the Fed chairman.United States when Paul Volcker was the Fed chairman.

OvershootingOvershooting

• Suppose that goods prices are changed Suppose that goods prices are changed infrequently but that financial asset prices, infrequently but that financial asset prices, such as exchange rates, are changed such as exchange rates, are changed instantaneously.instantaneously.

• Then, because prices are sticky, a shock Then, because prices are sticky, a shock can cause the exchange rate to overshoot can cause the exchange rate to overshoot its equilibrium value.its equilibrium value.

A non-linear adjustment processA non-linear adjustment process

• Our very simple model of house prices yielded a Our very simple model of house prices yielded a linear solution. That is, when we graphed P(t+1) linear solution. That is, when we graphed P(t+1) = IP(t) – RI it turned out to be an upward sloping = IP(t) – RI it turned out to be an upward sloping straight line. The result was the prices go straight line. The result was the prices go monotonically off to infinity.monotonically off to infinity.

• But more complicated outcomes are possible. But more complicated outcomes are possible. We can get prices oscillating, either off to infinity We can get prices oscillating, either off to infinity or toward a steady state – even when the or toward a steady state – even when the fundamentals are constant.fundamentals are constant.

ChaosChaos

• It is even possible for macroeconomic It is even possible for macroeconomic models with no uncertainty and perfect to models with no uncertainty and perfect to exhibit chaos.exhibit chaos.

• Chaos is an adjustment process that is so Chaos is an adjustment process that is so “disorderly” as to appear random.“disorderly” as to appear random.

• The importance of this is controversial.The importance of this is controversial.

ExampleExample

• Suppose that equilibrium for some price Suppose that equilibrium for some price were given by x(t+1) = ax(t)[1 – x(t)] and were given by x(t+1) = ax(t)[1 – x(t)] and consider strictly positive starting values.consider strictly positive starting values.

• If 2 < a < 3, the equilibrium is a If 2 < a < 3, the equilibrium is a cobwebcobweb: it : it is stable with damped oscillations.is stable with damped oscillations.

• If 3 < a < 3.68: the price can oscillate with If 3 < a < 3.68: the price can oscillate with ever greater swings until the amplitude ever greater swings until the amplitude settles down to a cycle over two or more settles down to a cycle over two or more periods.periods.

When a becomes largeWhen a becomes large

• Chaos may emerge: there is no regular Chaos may emerge: there is no regular cycle or pattern.cycle or pattern.

• The outcome is highly sensitive to the The outcome is highly sensitive to the starting value or the precise value of a.starting value or the precise value of a.

Some stylised facts about booms Some stylised facts about booms and busts (from an IMF study)and busts (from an IMF study)

• Data from 19 industrialised countriesData from 19 industrialised countries

• Housing data from 1970 – 2002; equity Housing data from 1970 – 2002; equity data from 1959 – 2002data from 1959 – 2002

• Booms defined as a trough-to-peak rise in Booms defined as a trough-to-peak rise in the top quartile of rises; busts defined as a the top quartile of rises; busts defined as a peak-to-trough fall in the top quartile of all peak-to-trough fall in the top quartile of all fallsfalls

ResultsResults

• Equity price busts occurred about every 13 Equity price busts occurred about every 13 years, lasted for 2-1/2 years and where years, lasted for 2-1/2 years and where associated with price declines of about 45 associated with price declines of about 45 percent.percent.

• House price busts occurred about every House price busts occurred about every 20 years, lasted for 4 years and were 20 years, lasted for 4 years and were associated with price declines of about 30 associated with price declines of about 30 percent.percent.

ResultsResults

• A quarter of equity price booms were A quarter of equity price booms were followed by busts.followed by busts.

• Forty percent of house price booms were Forty percent of house price booms were followed by busts.followed by busts.