Detecting Asset Price Bubbles

August 12, 2017 | Author: Ruben Carlo Asuncion | Category: Economic Bubble, Statistical Hypothesis Testing, Risk, Valuation (Finance), Investor
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PSY (2013) explored detecting asset price bubbles using the S&P 500 and has been highly accurate. This is an explana...

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Fulcrum Research Notes – January 2014

Detecting bubbles in asset prices Ziad Daoud*

Juan Antolin-Diaz**

This note describes recent advances in econometric methodology which allow us to detect bubbles in asset prices. The method identifies bubbles as periods in which prices have explosive dynamics, and proposes a procedure to date the start and the end of bubbles in real-time. When applied to historical S&P 500 data, the method identifies nine episodes in which prices deviated from fundamentals; around half of these were booms, the rest were crashes. While the S&P 500 might seem over-valued at the present time according to some metrics, the method suggests that it is not experiencing explosive dynamics and therefore is not currently in a bubble. It is intuitively easy to see why: over the last couple of years, the S&P 500 Index returned 40%, broadly in line with its dividends which were up by 34% over the same period. This is not the behaviour of an asset whose price is greatly detached from fundamentals. The recent award of the 2013 Nobel Prize in economics

significantly deviate from their fundamental drivers.

to three academics may have surprised some. Few

Fama denies the possibility that bubbles exist, and

would question that, individually, the three laureates

suggests that large swings in asset prices can be

(Eugene Fama, Lars Peter Hansen and Robert Shiller)

explained by variations in risk premia.

are fully deserving of the award as their work on understanding asset prices has been hugely influential in academia and beyond. What was surprising, however, was that they won it jointly given that two of them, Fama and Shiller, hold diametrically opposing views on asset pricing. Take for example their views on asset return predictability. In a series of papers in the 1960s Fama showed that returns are essentially unpredictable and any attempt to exploit market predictability is unlikely to overcome transaction costs. Asset prices, according to Fama, follow a random walk, which makes sense in an environment with competitive trading among rational investors. Two decades later, however, Shiller showed that in some circumstances stock returns are in fact predictable: variables such as price-dividend ratio can predict a significant portion of equity variation. One can reconcile the two views by concluding that both are right, and that returns are unpredictable in the short-run (ie at a monthly frequency or higher) but they are predictable over the longer-run of several years. It is harder, however, to reconcile the views of the two laureates on whether asset markets can experience bubbles, defined as periods in which prices *[email protected]; **[email protected]

Shiller, on the other hand, made his name outside the confines of academia by correctly calling two recent bubbles: in the equity market in the 1990s and in the housing market in the 2000s. He views psychological factors such as animal spirits and fads as significant drivers of variation in the economy and financial markets. Until recently, empirical evidence on whether bubbles exist in asset prices has not been conclusive, partly due to

the

lack

of

a

well-developed

econometric

methodology to test this hypothesis. However, recent advances made by Peter Phillips, Jun Yu and their coauthors allow us to test this hypothesis with greater accuracy. These authors

empirically

characterise

bubbles as periods in which asset prices experience explosive dynamics, and develop statistical tools to detect and time-stamp the presence of such behaviour. Updating and extending the application of their method to the monthly S&P 500 price-dividend ratio series, nine episodes of bubbles are identified since the beginning of the 20th century. When the method is applied to other valuation metrics, such as Shiller’s cyclically-adjusted price-earnings ratio, similar dates for bubbles are detected.

Detecting bubbles in asset prices More generally, the presence of bubbles in historical



equity prices, together with evidence from survey data

[(

) (

)]

on expected returns, suggests that variations in risk premia cannot be the main driver of these explosive

The equation says that the price-dividend ratio has a

episodes in asset prices, and that psychological or

fundamental value driven by expected future dividend

informational factors may be at play.

growth (the

The method also highlights that there is very little evidence in favour of the presence of a bubble in current equity prices despite elevated levels of valuation metrics relative to the their historical averages. It is intuitively easy to see why the method reaches such a conclusion: over the last couple of

term): the higher the expected future

dividend growth, the higher today’s stock price should be. The fundamental component is discounted by the required rate of return,

. This rate of return is related

to investors’ risk appetite and impatience so variation in these factors can also induce variation in the pricedividend ratio.

years, the S&P 500 Index returned around 40%,

In addition, today’s price can be high without a

broadly in line with its dividends which were up by

commensurate increase in dividends if investors have

34% over the same period. This is not the behaviour of

self-fulfilling beliefs that they will make capital gains

an asset whose price is greatly detached from

from ever higher future prices. This introduces the

fundamentals.

possibility of prices deviating from their fundamental

That said, failure to detect a bubble does not

value due to the presence of bubbles represented by

necessarily mean that a large price drop cannot take

the

place. For example, a high price-to-earnings ratio may

price behaviour where past price increases induce

reflect over-optimistic views about future earnings

people to buy more of the asset driving its current price

growth because investors may expect the recent

higher.

increase in the profit share in the economy to persist. Prices, then, can still experience significant corrections if these optimistic forecasts fail to materialise and the profit share reverts to its past historical average. The

term. This can be an outcome of extrapolative

The important implication of this discussion is that the presence of the bubble term in the pricing equation changes the dynamics of the observed price process in a way that can be tested econometrically.

fact that we do not detect a bubble does not therefore mean that there is no risk of low returns going forward.

Generally speaking, we deal with three classes of processes in this note: stationary processes which tend

Such sharp conclusions could not be reached by the early literature based on standard econometric tools. The traditional approach to test for bubbles and its drawbacks will be outlined later but first the next section explains how bubbles can be empirically identified.

Identifying bubbles in asset prices

to revert to their mean; random walks (or unit root processes) which do not mean revert but have a stochastic time trend instead (although their trend evolves in a gradual manner) 1; and explosive processes which are non-mean reverting and grow at exponential speed. Looking at the components of the pricing equation, dividend growth is likely to be stationary but the price-

The starting point for identifying bubbles is the standard pricing equation widely used in financial economics:

Fulcrum Research Notes – January 2014

1

A random walk is a process with the property that the best forecast for the value of the process in the next period is its value in the current period. It is popular in modelling economic time series because it conveniently leads to trends which are stochastic, ie ones that can slow down or accelerate randomly over time.

2

Detecting bubbles in asset prices dividend ratio can still be non-stationary if the

constants (usually long-term averages or steady

discount factor is time-varying. However, the degree of

states). With non-stationary processes, the validity

non-stationarity is different when bubbles are present

of the approximation is questionable as these

because bubbles have explosive dynamics – a higher

constants may not exist. It is therefore better to

degree of non-stationarity than the random walks

work directly with the level of price-dividend ratio

typically assumed for the fundamental component.

rather than its logarithm. But this necessitates the

Therefore, detecting explosive dynamics in the price-

need to develop econometric tools for explosive

dividend ratio is a clue that bubbles might be present.

processes, which have not been available until

To

summarise:

deviation

of

prices

from

recently because of their analytical complexity.

their

fundamental value introduces explosive dynamics in the price-dividend ratio. This forms the basis of the

3. Evans (1991) showed in a simulation study that when bubbles are present but followed by periodic

empirical bubble-detection method presented in this

crashes, standard unit-root procedures fail to

note. A version of this empirical characterisation of

detect them, even when they are substantial in

bubbles was also exploited by the earlier literature,

magnitude and volatility like the ones shown in

which is reviewed in the next section.

Figure 1, because collapsing bubbles make the time series appear mean-reverting.

The early literature

Figure 1. The Evans Critique

A significant body of empirical literature on detecting

300

bubbles was developed in the 1980s and early 1990s with mixed results. Because the econometrics for dealing with explosive time series

250

Collapsing bubbles

was not well-

developed, the typical approach in the early literature began by log-linearly approximating the pricing

200

150

equation presented in the previous section. Doing this, Craine (1993) showed that the presence of bubbles

100

changes the statistical behaviour of the logarithm of the price-dividend ratio from a mean-reverting process to a random walk. Standard econometric unit root tests, such as that of Dickey and Fuller, could then be

50

0

Time series which contain collapsing bubbles pass as stationary

applied to discriminate between the two hypotheses.

by standard unit root tests. The data shown here are simulated.

The old approach suffered from three shortcomings:

The Evans critique dealt a blow to the literature as it

1.

Even if the procedure worked perfectly, it would not be able to date the beginning and end of bubbles. At best, it would merely be able to state whether bubbles are likely to be present in the data.

2. Working with the logarithm of the price-dividend ratio requires approximating a relationship around

Fulcrum Research Notes – January 2014

showed the deficiency of the techniques available at the time. Subsequent research developed in different directions without converging to a consensus on either methodology or conclusion. In his survey of the literature, Gurkaynak (2005) summarised the state of research by concluding that “[f]or each paper that finds evidence of bubbles, there is another one that fits the data equally well without allowing for a bubble”.

3

Detecting bubbles in asset prices However, in a series of recent papers, Peter Phillips,

But if we measure persistence using all the data up to

Jun Yu and their co-authors developed a new battery of

that point, then we may fail to detect the true

methods that managed to overcome the shortcomings

explosiveness of the most recent observations. As in

of the traditional approach. Their test—explained in

the Evans critique, past collapsing bubbles may make

detail in the next section—also provides a real-time

the data look rather stationary.

dating procedure for bubbles and crashes in asset prices. It is designed to deal with levels directly as well as logarithmic transformations and, unlike standard tools, it successfully detects bubbles even when they are subsequently followed by crashes.

A new method for detecting bubbles The method of Phillips, Shi and Yao (2013), referred to as PSY henceforth, relies on the characterisation of bubbles as episodes in which the level of the pricedividend ratio experience explosive dynamics.

To overcome this, PSY propose measuring the degree of persistence over all backward-looking intervals of variable sizes—varying the start point of each interval but keeping the end fixed at the point of interest. The final test statistic is the maximum of these different persistence measures. The intuition behind the procedure is that while some subsamples which contain collapsing bubbles might understate the degree of persistence in the process (Subsample 1 in Figure 2), the procedure would also give rise to other subsamples (such as Subsample 2 in

In order to date the start and end of bubbles, PSY use a

Figure 2) which are very persistent because they do not

procedure which tests for the presence of explosive

contain past bubbles and their subsequent crashes. The

behaviour at each point in time, instead of running a

maximum

global test over the full sample.

determined by the latter group, and a large value is

persistence

statistic

would

then

be

evidence for the presence of a bubble. How does this procedure work? We have classified time series into three types of processes: stationary,

The method has many advantages: First, the backward

unit-root and explosive. These processes have differing

subsampling procedure is a clever way to handle the

degrees of persistence. A stationary process is not very

Evans critique, giving PSY’s method more power to

persistent: the impact of a shock today on the forecasts

detect bubbles than older approaches.

of its future values tends to die out eventually. Nonstationary processes, such as unit-root and explosive processes are very persistent: shocks to today’s value of the process changes our forecast of all future values, even those in the distant future. Explosive processes are the most persistent of all, since any shock tends to

Second, it provides a real-time tool for detecting bubbles. To determine whether an asset is going through a bubble or not, only current and past information is needed and there is no look-ahead bias involved.

get compounded exponentially. Therefore, the degree

Third, in addition to answering the question of

of persistence of the price process at the point of

whether bubbles in asset prices exist, the method also

interest is indicative of whether a bubble is present or

provides a live dating mechanism determining when

not.

they begin and end.

Fulcrum Research Notes – January 2014

4

Detecting bubbles in asset prices

Box 1. Testing for persistence and explosiveness in time series The building block of both the old literature and the new method is unit-root tests, the most well-known of which is the one by Dickey and Fuller. Specifically, if one assumes that the time series the Dickey-Fuller method tests if

is a random walk by examining whether

follows an autoregressive model, then in the regression

(1) This is done by calculating a standard t-statistic (the estimate of β divided by its standard error), but rather than comparing it to a quantile of the t-distribution as in standard regression analysis, it is compared to a quantile from the Dickey-Fuller distribution. The early literature on testing for bubbles relied on such unit-root testing procedure, where

represented the

logarithm of the price-dividend ratio. When bubbles are present, the logarithm of the price-dividend ratio would behave like unit-root process and

; while if there are no bubbles, the series should be stationary and

.

The method of Phillips, Shi and Yao (2013) differs from the old literature in the way it characterises bubbles and implements unit-root testing. Under their procedure, bubbles are present,

represents the level of the price-dividend ratio and when

is greater than one, while when they are not,

is at most equal to one.

Moreover, as explained in the main text, instead of running one unit-root test over the full sample, PSY test for unit root at each point in time, which allows them to date the entry into and exit from bubbles. How does testing at each point work? Suppose we want to test whether there is a bubble at the 100th observation. Rather than running a Dickey-Fuller test using all the 100 available observations, PSY calculate t-statistics for each of the intervals that end with the 100th observation such as {1, 2, …, 100}, {2, 3, …, 100} up to {65, 66, …, 100} (a minimum number of observations is needed to run the regression (1) and calculate the resulting t-statistic. In this paper, this minimum number is set to 36). Finally, PSY take the maximum over all these 65 t-statistics and compare its value to a quantile from their distribution.

Fulcrum Research Notes – January 2014

5

Detecting bubbles in asset prices Figure 2. Illustration of the bubble detection method on the S&P 500 real price-dividend ratio 250

[1] We want to test for the presence of bubbles at this point ...

230 210

[2] Subsample 1: The persistence of this interval is diluted by the crash of 1974 and the subsequent recovery ...

190 170 150 130 110

[3] Subsample 2: The persistence of the process over this subsample is high due to its recent explosive trajectory ...

90

[4] The Phillips, Shi and Yu (2013) procedure uses the maximum degree of persistence over all backward subsamples to identify bubbles, so will be determined by Subsample 2

70 50 1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

Source: Fulcrum Asset Management, Price-dividend data from Robert Shiller’s website.

Finally, PSY deal directly with levels of price-dividend

these were of the irrational exuberance variety when

ratio as opposed to logarithmic approximations which

investors’ optimism drove equity markets higher than

may or may not be valid with non-stationary time

justified by fundamentals, including:

series, overcoming another of the shortcomings of the old approach.



started in September 1928 and ended with the

Having described the procedure, the next section updates and extends PSY’s application to identify

great crash of October 1929. 

historical bubbles in the S&P 500, and to answer the question whether we are living through an equity



Bubbles and crashes in the S&P 500

Robert Shiller’s website. The sample spans the period from January 1871 to December 2013. Applying PSY’s method to the data, nine episodes of stock market bubbles are identified since the beginning of the 20th century (shaded areas in Figure 3). Five of

Fulcrum Research Notes – January 2014

The second post-war boom from September 1954 to April 1956.



to dividend ratio for the S&P 500 Index obtained from

The boom which started immediately after World War 2 in October 1945 and ended in June 1946.

bubble now.

The data used in this section are the monthly real price

The stock market boom in the 1920s. The bubble

The mid-1980s bubble starting in March 1986 and ending with Black Monday in October 1987.



The dot-com bubble of the second half of the 1990s. This is by far the longest episode of exuberance lasting around six years from July 1995 to August 2001.

The other four episodes when prices were divorced from their fundamental value were stock market crashes, possibly driven by excessive pessimism, including:

6

Detecting bubbles in asset prices Figure 3. Historical bubbles in the S&P 500 real price-dividend ratio (Shaded areas = bubble) 90 80 70 60 50 40 30 20 10 0 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Note: Last observation is December 2013. Source: Fulcrum Asset Management, Price-dividend data from Robert Shiller’s website.

Figure 4. Historical bubbles in the S&P 500 real cyclically-adjusted price-earnings ratio (CAPE) (Shaded areas = bubble) 50 45 40 35 30 25 20 15 10 5 0 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Note: Last observation is October 2013. Source: Fulcrum Asset Management, CAPE data from Robert Shiller’s website.

Figure 5. Degree of support for the bubble hypothesis (Shaded areas = bubble) 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Notes: Higher values indicate stronger support from the data for the presence of bubbles. Shaded regions are constructed as the periods in which the support metric exceeds the 0.95 threshold. Last observation is December 2013. Source: Fulcrum Asset Management, CAPE data from Robert Shiller’s website.

Fulcrum Research Notes – January 2014

7

Detecting bubbles in asset prices  

The banking panic which started in August 1907

that there is little support in the data for the bubble

and ended in February 1908.

hypothesis2.

The stock market crash which began in August 1917 and ended in April 1918.



The brief stock market crash of 1974, which lasted from July to December.



The financial crisis originating in October 2008 and ending April 2009.

Delving a little deeper into what the 0.2 figure means, recall that the logic of statistical hypothesis testing is such that the null hypothesis of no bubbles is maintained unless there is strong evidence against it. A threshold for the degree of support for bubbles is then set so that a bubble is called if its degree of support

Figure 4 shows bubbles in S&P 500 using an

exceeds the threshold. The lower the threshold, the

alternative metric: Shiller’s cyclically-adjusted real

easier it is to detect bubbles, but also the higher is the

price-to-earnings ratio (CAPE). The chart highlights

probability of incorrectly discovering a bubble when

the same episodes as the price-dividend ratio with one

there is not one. This note uses the conventional

notable difference in the 1920s where CAPE started

threshold of 0.95 in order to limit the false discovery

behaving explosively before the price-dividend ratio.

rate to 5%.

What does the method say about whether or not the

To put the latest reading in context, it would require a

equity market is currently in a bubble?

big drop in our standards of controlling the likelihood of erroneously calling a bubble when one does not in

Carrying out the test using either of the two metrics

fact exist (from 5% to over 80%) to accept the presence

suggests that we are not going through an equity

of bubbles in current equity prices. Evidence in

bubble, and it is fairly clear why this is the case. Since

support of bubbles is so weak that in order for us to call

2009, both the price-dividend ratio and the CAPE have

a bubble now, we would have to conclude that equities

been moving sideways (albeit at a higher level than

have been in a virtually continuous bubble over the

historical average) rather than upwards in an explosive

whole sample period!

manner. Over the last couple of years, the price of the Figure 6. Actual and simulated Cyclically-Adjusted Price to Earnings ratio (CAPE) under a bubble scenario

S&P 500 Index moved up by around 40%, broadly in line with its dividends which were up by 34% over the same period. This is not the stuff of bubbles where

45

price movements are completely divorced from

40

fundamentals.

35

One way to quantify this observation is given in Figure

30

5 which plots the strength of evidence in favour of the

25

bubble hypothesis. In statistical terms, the metric is

Simulated CAPE ratio under a bubble scenario

Actual CAPE

20

the complement of the test’s p-value, and the larger it is (within a range from zero to one), the stronger is the

15

evidence for being in a bubble. The latest reading of the

10 1988

support metric is quite low at less than 0.2, suggesting

1992

1996

2000

2004

2008

2012

Source: Fulcrum Asset Management, CAPE data from Robert Shiller’s website.

2

Data for the CAPE ratio is only available up to October 2013 as of the writing of this note. If we extrapolate earnings the metric would rise slightly to 0.33

Fulcrum Research Notes – January 2014

8

Detecting bubbles in asset prices To illustrate this point further, it may be useful to

been detected by the econometric method used in this

consider how the S&P 500 Index would have behaved

note.

if it had been in a bubble. Given the 34% move in dividends over the last couple of years, it would have taken at least a 100% move in the S&P 500 over the same period for its behaviour to be considered explosive and for a bubble to be detected. This would have taken the index beyond the 2,500 mark by September 2013 (when its actual value was around 1,700). Such a move would have also taken valuation metrics to high levels only exceeded by the peak of the dot-com bubble. As Figure 6 illustrates, had such a bubble occurred, Shiller’s CAPE would have been

A second possibility for the high price relative to (trailing) earnings is that investors expect high future earnings growth, perhaps because of a change in the structure of the economy and the way economic gains are split between firms and workers. Such structural change would prevent valuation metrics from reverting to their historical averages, and would not be detected by the method of this note because these changes tend to occur smoothly and gradually over time rather than in an explosive manner.

around 33 (compared to an actual value of 23.5),

Does it matter which possibility is more likely? Yes,

almost double its historical average, at which point the

because one would expect sharper price correction in

real price-dividend ratio would have been as high as 73

the case of bubbles than in the case of optimistic

when its realised level was 49.

earnings forecasts. However, it is worth emphasising

In contrast, The Economist (2013) has recently said that

that while recent price dynamics in the equity market do not seem to reveal bubble-like behaviour, it does not follow that prices cannot experience abrupt

“[Investors] should be wary of stock markets when

declines if over-optimistic earnings forecasts fail to

they look expensive relative to the long-term trend

materialise.

in profits. And that is the case with Wall Street at the moment; the cyclically adjusted ratio is 23.5, well above the long-term average.”

It is also worth noting that the switch from a nonbubble state to a bubble can happen over a short period of time if the equity price evolves in a manner

Proponents of the “bubble in equities” hypothesis tend

that is inconsistent with fundamentals. For example,

to point out the current elevated levels of valuation

we have conducted another simulation experiment in

metrics (the price-to-dividend ratio or CAPE) relative

which over the course of 2014, the S&P 500 Index

to their historical averages. The method used in this

returns 30% and both its dividends and earnings grow

note, on the other hand, detects rapid changes in

by 10% — a behaviour that mimics their performance

levels. The two things can give rise to different

in 2013. In that hypothetical scenario the method

conclusions since bubbles, as defined in this paper, are

concludes that the S&P 500 will be entering a bubble.

not synonymous with overvaluation as defined by traditional metrics.

Whether we are currently in a bubble or not, the existence of bubbles in the first place poses theoretical

So why are current valuation metrics such as price-to-

challenges for economists and different theoretical

earnings ratio high? In this note we have ruled out the

frameworks to account for the presence of explosive

possibility that there is a bubble in the sense that

behaviour in asset prices have been developed. The

prices are high today just because investors expect

next section outlines three views and shows that

future prices to be even higher, regardless of

empirical evidence may be inconsistent with one of

fundamentals. As argued earlier, this would have

them.

introduced explosive price dynamics which would have Fulcrum Research Notes – January 2014

9

Detecting bubbles in asset prices

What is the method actually capturing?

according to this theory are always rational, and they reflect investors’ attitude to risk. One might detect

The previous section has shown that explosive dynamics are recurrent in equity prices. There are at least three theories on the underlying forces which give rise to such behaviour.

explosive behaviour in asset prices, but one should not interpret that as deviation from fundamentals. Indeed, Phillips and Yu (2011) show that explosive behaviour could be a result of time-varying risk premia.

The first theory is psychological and is due to Akerlof and Shiller (2010). These Nobel Prize winning economists believe that variations in confidence drive variations in asset prices. The econometric method of PSY can be interpreted as empirically capturing the change in animal spirits, identifying episodes of overconfidence and panic by market participants which drive the swings in the price-dividend ratio.

Fama’s

view,

however,

implies

that

investors’

expectations of future returns should be negatively correlated with the price-dividend ratio, which is not what we see in survey data. These show a positive and significant positive correlation as documented in Adam, Beutel and Marcet (2013). Surveys of expected returns therefore suggest – assuming that investors are responding truthfully to the surveys – that the detected

An alternative theory, due to Adam, Beutel and Marcet

explosive dynamics in equity prices are unlikely to be

(2013), uses informational restrictions on rational

merely driven by business cycle related variation in

investors rather than a behavioural explanation as the

risk premia. Instead, they are likely to represent

generator of bubbles. In this framework, investors do

bubble episodes in which prices are divorced from

not know the true fundamentals of the economy, but

underlying fundamentals which could arise because of

use variations in asset prices to learn about them. As

irrational investors driven by psychological factors of

asset prices rise, investors revise their estimates of the

fear and greed, or because of rational investors

economy’s fundamentals upwards leading them to

learning

invest more, driving prices further up. This continues

information.

in

an

environment

with

imperfect

until the wealth effect (investors are richer, and therefore want to consume more and invest less) starts to dominate the substitution effect (expected return on investment

is

higher,

making

investment

more

appealing relative to consumption), at which point investors

revise

down

their

estimates

of

the

fundamentals of the economy. From then onwards, both income and substitution effects lead to lower investment in the asset causing a sharp crash in its price. The third theory, due to Fama and elucidated in Cochrane (2013), explains bubbles and crashes by swings in investors’ risk premia. Sharp rises in prices can occur if investors suddenly become more risk tolerant and require a lower expected return for holding the asset. Conversely, as risk premia sharply reverse course, markets can experience crashes. Prices

Fulcrum Research Notes – January 2014

Conclusion This note has described a new econometric technique for determining the beginning and the end of bubbles in real-time. The method does not suffer from the disadvantages of traditional techniques, and shows that bubbles and subsequent corrections are a recurrent feature of equity prices. The method exploits different features of the price series compared with standard valuation methods such as the price-dividend ratio and Shiller’s CAPE, which focus on deviations of current valuations from their historical averages. Instead, the method used here relies on measuring the speed at which valuations increase or decline over time. In this sense, bubbles as characterised in this note are conceptually different from over-valuations. 10

Detecting bubbles in asset prices Since valuation metrics seem to have been stable in recent years, the bubble-detection method used in this note concludes that there is little evidence in favour of a bubble in the S&P 500. Meanwhile, the levels of these valuation metrics are elevated relative to their

Phillips, P. C. B., S-P Shi and J. Yu (2013), “Testing for Multiple Bubbles 1: Historical Episodes of Exuberance and Collapse in the S&P 500,” Working Paper. Phillips, P. C. B. and J. Yu (2011), “Dating the Timeline of Financial Bubbles During the Subprime Crisis,” Quantitative Economics, 2, 455-491.

historical averages, possibly indicating that prices are driven primarily by the expectation that the high earnings growth observed in recent years (compared with their long-term rate) will persist into the future. Despite the absence of any trace of bubbles, prices can still experience significant declines if these earnings forecasts turned out to be over-optimistic. For asset managers, being able to identify periods when asset prices are in a bubble in real-time has important implications for portfolio optimisation and hedging. Furthermore, successfully dating periods of excessive exuberance and panic is useful for testing how different strategies perform in these episodes relative

to

behaviour.

more We

moderate

are

periods

currently

of

undergoing

market such

assessment.

References Adam, K., J. Beutel and A. Marcet (2013), “Stock Price Booms and Expected Capital Gains,” Working Paper. Akerlof, G. and R. Shiller (2010), Animal Spirits: How Human Psychology Drives the Economy, and Why It Matters for Global Capitalism. Princeton University Press. Cochrane, J. (2013), “Bob Shiller’s Nobel,” available at bit.ly/1aEgYcN Craine, R., (1993), “Rational Bubbles – A Test,” Journal of Economic Dynamics and Control, 17, 829-846. The Economist (2013), “A Very Rational Award,” 19 October 2013. Evans, G. W. (1991), “Pitfalls in Testing for Explosive Bubbles in Asset Prices,” American Economic Review, 81, 922-930. Gurkaynak, R. S. (2005), “Econometric Tests of Asset Price Bubbles: Taking Stock,” Federal Reserve Board Finance and Economics Discussion Series, 2005-04.

Fulcrum Research Notes – January 2014

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Detecting bubbles in asset prices

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Fulcrum Research Notes – January 2014

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