ECON 4AA3 Bubble Research

McMaster University
ECON 4AA3
An Empirical Exploration of Bubbles
Gabrielle Di Bacco
400039413
April 22, 2020

Introduction
In recent years, larger than normal asset pricing swings have been observed in the stock
market.1
Although the stock market has conventionally been regarded as a volatile mar-
ket, recent years have pushed the bounds of even standard volatility. Notably, in the last
fifty years the world has experienced an unprecedented level of financial globalization that
may well help to explain the observed asset pricing swings.2
Previous work by Martin and
Ventura showcase episodes across the world that highlight a repeated pattern of large asset
price booms, followed by sharp reversals.3
The interest here, therefore, lies in establishing
whether these episodes mark normal business cycle activity or something more. Disen-
tangling the business cycle trend from atypical volatile behaviour in the asset market is
therefore an area of further research. Referred to as a bubble, these episodes mark a pe-
riod wherein volatility is beyond even the normal scope of the market and often condensed
into a shortened time frame. Measuring the extent and scope of these bubbles remains a
challenging but important topic. As Martin and Ventura explain, the importance of this
topic lies in the direct e↵ect of these bubbly episodes on household wealth and the economic
recessions they nearly always lead to.4
Disentangling bubbles from normal business cycle
patterns and standard volatility, therefore, is of importance to households and the economy
as a whole.
Literature Review
A large amount of research exists in the area of bubbles or bubbly episodes, including
user guides for rational bubbles, theoretical conditions for the formation of bubbles, cause
and e↵ects of bubbles, and some classification. Before delving into the divide between nor-
mal business cycles and bubbles, an exploration of the existing research is in order. As
Doblas-Madrid puts forth, the general definition of a bubble as “. . . the gap between the
1
Alberto Martin and Jaume Ventura, “The Macroeconomics of Rational Bubbles: A Users Guide,”
Barcelona GSE Working Paper Series 989 (2018). https://doi.org/10.3386/w24234.
2
Moritz Schularick and Alan Taylor, “Credit Booms Gone Bust: Monetary Policy, Leverage Cy-
cles and Financial Crises, 1870-2008,” American Economic Review 102, no. 2 (2010): 1029–61.
https://doi.org/10.3386/w15512.
3
Martin and Ventura, “Users Guide,” 1.
4
Ibid., 1.
1

price and fundamental value” leaves the meaning of fundamental value open to interpre-
tation.5
This open definition will be used to guide the separation of business cycle trends
from bubbles. Previous work in bubbles also includes Martin and Ventura’s user guide for
rational bubbles. Being a technical overview of the theory of rational bubbles, the authors
present several ways in which bubbles may be incorporated into macroeconomic models.
Beyond giving a more theoretical background of rational bubbles, the authors make theo-
retical predictions as to the characterization of bubbles in terms of capital inflows and real
activity.6
Martin and Ventura also employ a small open economy model to show that asset
prices are driven by market psychology as well as by economic conditions. The authors also
identified some theoretical conditions for the formation of a bubble, including low interest
rates, a growth rate fast enough to be attractive, and a large supply of available investment.7
Other areas of research include those of Schularick and Taylor who link bubbles with
credit booms and busts and economic recessions.8
Providing a historical overview of a selec-
tion of developed countries reaching back to 1870, the authors indicate the post-World War
II shift in monetary response to financial crises. These responses included rapid growth in
credit as well as the decline of safe assets in bank portfolios. The authors argue that this
has led us to a new era of “. . . unprecedented financial risk.”9
Expanding upon the general
definition of a bubble and linking to historical data are Carvalho, Martin, and Ventura who
show that, up to three decades ago, wealth has remained close to the fundamental value
and any deviations occurring before the early 1990s were often small and short-lived.10
The
authors maintain that the last two decades have seen unprecedented deviations from the
standard fundamental value driven by the appearance and bursting of bubbles in the key
asset markets.11
A similar vein of research refers to monetary policy for a bubbly world
wherein authors Asriyan, Fornaro, Martin, and Ventura show, that similar to Martin and
5
Antonio Doblas-Madrid, “A Finite Model of Riding Bubbles,” Journal of Mathematical Economics 65
(2016): 154–62. https://doi.org/10.1016/j.jmateco.2015.06.009.
6
Martin and Ventura, “Users Guide,” 1-2.
7
Ibid., 3.
8
Schularick and Taylor, “Credit Booms,” 1045.
9
Ibid., 1033.
10
Vasco M. Carvalho, Alberto Martin, and Jaume Ventura, “Understanding Bubbly Episodes,” American
Economic Review 102, no. 3 (2012): 95–100. https://doi.org/10.1257/aer.102.3.95.
11
Ibid., 98.
2

Ventura and their user guide for rational bubbles, market psychology plays a role in bub-
bles.12
The authors also agree with proposal of increased volatility of asset prices over the
past three decades and link this volatility to asset scarcity.13
Blanchard and Watson also
refer to the notion of rational bubbles and the rational deviation of asset prices from their
fundamental value.14
The extent and duration of bubbles has been examined through both speculative and
rational models. As various authors explain, boom-bust episodes or bubbles in the asset
market can be interpreted as speculative buying on the part of asymmetrically informed
buyers hoping to sell to a greater fool.15 16 17
This is contrasted with the model of rational
bubbles explained by various authors. The rational bubble model builds upon the work
of Abreu and Brunnermeier whose model consists of a real shock initiating bubble growth
until a random t0.18
At this time, asymmetrically informed agents observe the fundamental
value and gauge whether to sell or to hold and sell later to a greater fool.19
Doblas-Madrid
built upon this model by implementing the rational agents subject to liquidity constraints.20
Martin and Ventura, in their user guide to rational bubbles, built upon this model further
by adding various market psychologies which agents are subject to, including individual
maximization and market clearing.21
Further work in rational bubbles includes the work of Diba and Grossman, who de-
ﬁne a rational bubble in terms of the divergence from the market fundamental value due to
12
Vladimir Asriyan, Luca Fornaro, Alberto Martin, and Jaume Ventura, “Monetary Policy for a Bubbly
World.” Barcelona Working Paper Series 921 (2019). https://doi.org/10.3386/w22639.
13
Ibid., 2.
14
Olivier, Blanchard and Mark Watson, “Bubbles, Rational Expectations and Financial Markets.” NBER
Working Paper 945 (1982), https://doi.org/10.3386/w0945.
15
Antonio Doblas-Madrid, “A Robust Model of Bubbles With Multidimensional Uncertainty.” Economet-
rica 80, no. 5 (2012): 1845–93. https://doi.org/10.3982/ecta7887.
16
Asriyan, Fornaro, Martin, and Ventura, “Monetary Policy,” 3.
17
Doblas-Madrid, ”Riding Bubbles,” 154.
18
Dilip Abreu and Markus K. Brunnermeier, “Bubbles and Crashes.” Econometrica 71, no. 1 (2003):
173–204. https://doi.org/10.2139/ssrn.296701.
19
Ibid., 174
20
Doblas-Madrid, ”Multidimensional Uncertainty,” 1846
21
Martin and Ventura, ”Users Guide,” 1.
3

irrelevant variables.22
A review of previous literature also has a role for the classification
of bubbles according to the type of asset. Classification of bubbles by type of asset is re-
searched by Olivier, who models that bubbles on productive and unproductive assets will
have opposite e↵ects.23
The manner in which stocks are chosen is also a subject of interest.
As Greenwood and Nagel explain, age, as a proxy for investment experience, can be used to
explain the asset types chosen, and the resulting link to economic bubbles caused by naive
optimism.24
In a similar manner, Brennan postulates that the late 1990s dotcom bubble,
bursting in early 2000, was spurred on by overeager young investors with limited experi-
ence.25
Utilizing previous definitions of bubbles and their cause, e↵ects, and classification,
this paper expands upon the definition and understanding of bubbles and their cause and
e↵ects in a Canadian context.
Economic Concept
As a further exploration of bubbles and their various monetary e↵ects, we begin first
with the definition of a Di Bacco bubble, hereafter referred to as a DB bubble, followed by
an exploration of said bubbles and related definitions. In a similar manner to Kehoe and
Prescott in their book, Great Depressions of the Twentieth Century,26
a Di Bacco bubble
is defined according to two definitions.
1. There exists a period of growth wherein the asset price increases from T1 by
a minimum of a factor of five within a two-year period to some peak value, P.
2. Within one year of reaching peak value, P, the asset price will decline rapidly
to T2 and will lose, at minimum, half of its value within one year.
22
Behzad Diba and Herschell Grossman, “Explosive Rational Bubbles in Stock Prices?” American Eco-
nomic Review 78, no. 3 (1988): 520–30. https://doi.org/10.3386/w1779.
23
Jacques Olivier, “Growth-Enhancing Bubbles,” International Economic Review 41, no. 1 (2000):
133–52. https://doi.org/10.1111/1468-2354.00058.
24
Robin Greenwood and Stefan Nagel, “Inexperienced Investors and Bubbles.” Journal of Financial Eco-
nomics 93, no. 2 (2009): 239–58. https://doi.org/10.3386/w14111.
25
Michael J. Brennan, “How Did It Happen?” Economic Notes 33, no. 1 (2004): 3–22.
https://doi.org/10.1111/j.0391-5026.2004.00123.x.
26
Timothy J. Kehoe and Edward C. Prescott. Great Depressions of the Twentieth Century. Minneapolis,
MN: Research Department, Federal Reserve Bank of Minneapolis, 2007.
4

Figure 1: Graphical depiction of Di Bacco bubble
As seen in Figure 1, a DB bubble is defined graphically by the points T1, P, and T2.
These points reference the initial trough or starting point of the DB bubble, the peak of the
DB bubble, and the final trough or end point of the DB bubble. The variables rise duration,
fall duration, rise factor and fall factor are defined and outlined in Table 1.
Table 1 Description of variables
Variable Description
Rise duration Measures the duration (in months) of time period between initial trough
and peak
Rise factor Measures the factor by which the initial stock price increases during
the rise duration period
Fall duration Measures the duration (in months) of time period between peak
and final trough
Fall factor Measures the factor by which the peak stock price decreases during
the fall duration period
Note: Rise duration and fall duration are measured in months.
5

Given the definition for a DB bubble, an exploration of an asset market, the stock mar-
ket, may be done. After identifying bubbles in the stock market, a further analysis may be
utilized to explore the e↵ects of DB bubbles. This analysis includes both the location, the
magnitude, and the duration of DB bubbles to further explore and expand upon our under-
standing of bubbles and macroeconomic events. Even with the definition of a DB bubble
as described above, a further definition is needed to fully explore the data. Referred to as
a Di Bacco Megabubble (hereafter referred to as a DB megabubble), it is defined according
to the following definition.
1. A period containing volatility in excess of the DB bubble definition of volatility
wherein two or more DB bubbles overlap within the period; or
2. A period containing volatility in excess of the DB bubble definition of volatility
wherein two or more DB bubbles fall completely within the period.
Similar to the definition of a DB bubble, a DB megabubble is defined graphically (as
per Figure 2 and Figure 3) by the points T1, P, and T2 (highlighted in the figure in red).
As noted in the definition, there exists two or more overlapping DB bubbles or two or more
smaller DB bubbles within the larger DB megabubble.
Figure 2: Graphical depiction of overlapping Di Bacco megabubble
6

Figure 3: Graphical depiction of DB bubbles within Di Bacco megabubble
Utilizing the previous research in bubbles a number of hypotheses as to the cause and
e↵ect of bubble may be established. Similar to Martin and Ventura, we expect to see a large
number of bubbles occurring before the beginning of recessions or downturns in economic
growth. The o cial criteria for a recession are that there be at least two successive quarters
(six months) which show a drop in real GDP (federal bureau Canada). Although within
the last twenty years only one o cial Canadian recession has occurred, there have been
several other instances of large asset volatility and contractionary periods in the Canadian
economy.27
Notable periods that require further analysis include the dotcom boom-bust in the early
2000s, the 2007-2009 housing market crisis, and the gold and silver boom-bust episode in
2010-2011. In addition, a large proportion of bubbles are expected to be found in the more
volatile sectors, namely the energy, technology, and ﬁnancial sectors and subsectors. Given
the role of market psychology in creating and enhancing bubbles, we further hypothesize to
see a large proportion of bubbles occurring in connection to new and emerging technologies,
processes, and regulations, such as bitcoin, blockchain technology, and cannabis companies.
27
Mark S. Bonham, “Recession in Canada,” The Canadian Encyclopedia, August 8, 2017.
https://www.thecanadianencyclopedia.ca/en/article/recession.
7

Methodology
For further exploration the definition of a DB bubble is applied to a stock exchange
whereby the rise and fall of asset prices may be measured through the movement of stock
prices. Although a large variety of countries have experienced bubbles, this paper will fo-
cus on one market in particular: the Canadian-based Toronto Stock Exchange (TSX). The
TSX was selected for further examination due to its large and diversified presence in the
Canadian economy and its longevity in the world markets. The TSX Venture Exchange
(TSXV) was excluded from analysis as it deals mainly with emerging companies, which are
more prone to asset fluctuations. The TSX Alpha Exchange was also excluded as it lists
both TSX and TSXV securities. Even with the exclusion of these two branches the TSX
retains over 500 listings in four main sectors. Since some of the greatest episodes of asset
fluctuations have occurred in the last twenty to thirty years, the definition of a DB bubble,
as stated above, is applied to all listings on the TSX for the period between January 1, 2000
and December 31, 2019.
Listings for the TSX are readily obtained from the TMX website and the dataset in-
cludes all current listings as of January 2020. Companies which experienced a bubble with a
peak forming within the given time period but with the initial trough, T1, occurring before
January 2000 will be included in the dataset. After compiling a dataset of TSX listings, the
search engine Yahoo! Finance was utilized to obtain historical data on the high and low
stock price for the relevant months.
Given the twenty-year time span, data was collected on a month-to-month interval.
Variables include the month and year of observation, the stock price in CAD, and the sector
and various subsectors. The sectors include the five main categories of the TSX; energy,
mining, technology, diversified, and real estate, as well as subcategories within each sector.
Due to the repetition of the real estate sector within the diversified sector, the two sec-
tors were combined under the title of the diversified sector. Repeated listings within the
diversified and energy sector were also removed to ensure no companies were double counted.
8

Observations were collected for each ticker symbol symbol and excluded all subsidiaries
of the companies due to a lack of available data. Date and stock price information were
collected at three dates; T1, P, and T2, which correspond to the trough occurring within two
years previous to the peak, the peak, and the trough occurring within one-year post-peak.
For the points T1 and T2, the low for the month for the stock price was recorded, while for
the peak value, the high for the month for the stock price was recorded. This ensures the
maximum factor of increase and decrease between troughs and peak is recorded.
Using the points T1, P, and T2, as previously outlined, the date and stock price at
which these points occur were used to calculate both the factor of increase and decrease, as
well as the rise duration and fall duration of DB bubbles. The definition of these terms is
referenced in Table 1. Additional information on the sector and subsectors, as well as and
overall time frame in which the DB bubble occurred in was obtained and recorded.
Data
A total of 785 companies listed on the TSX were examined and found to contain a total
of 496 DB bubbles. Of these 496 DB bubbles, 55 were defined to be DB megabubbles, with
an average of 0.63 DB bubbles occurring per company and 0.07 DB megabubbles occurring
per company.
Table 2 Sector DB bubble and DB megabubble counts
Sector Companies DB Bubbles DB Megabubbles
Diversified 313 41 2
Energy 122 56 4
Mining 211 287 36
Technology & Innovation 139 112 13
Totals 785 496 55
9

As per Table 2, the distribution of DB bubbles is not uniform across the four sectors,
with the mining and technology & innovation sectors amassing the largest proportion of the
bubbles. Between the two sectors, they account for 80.44% of the DB bubbles and 89.09%
of the DB megabubbles while occupying only 44.58% of the total number of companies. As
a more accurate measure of the total market, however, the quoted market value (QMV) is
obtained for each sector as calculated as a proportion of the total market value of the TSX.
As per Table 3, only a small minority of the market value, at 21.68%, is held by the mining
and technology & innovation sectors. The vast majority of the quoted market value of the
TSX is held by the diversified sector, accounting for nearly 60% of the total value.
Table 3 Quoted market value according to sector
Sector Quoted Market Value ($CAD) Proportion of QMV
Diversified 1,816,672,336,913 59.74%
Energy 565,101,740,634 18.58%
Mining 359,966,253,213 11.84%
Technology & Innovation 299,028,772,378 9.84%
Totals 3,040,769,103,138 100
Within each sector the counts for DB bubbles and megabubbles may also be split be-
tween the various subsectors. As per Table 4, the diversified sector contains a total of
thirteen subsectors with a total of six subsectors containing DB bubbles or DB megabub-
bles. Of the 41 bubbles within the diversified sector, 30 DB bubbles are contained within
two subsectors: diversified, subsector financial services and diversified, subsector industrial
products & services. In the energy sector, as per Table 5, there are a total of four subsectors
with all but one of the DB bubbles existing in two subsectors: industrial products & services
and oil & gas. Within the mining sector there are two subsectors, as per Table 6, although
98% of the companies exist within one subsector. Lastly, the technology & innovation sector
contains 3 subsectors with 18 subsubsectors, as per Table 7. Of the three subsectors, the
life science subsector contains just over 60% of the total amount of DB bubbles.
10

Table 4 Diversified sector and sub-sectors
Sector Companies Bubbles Megabubbles
Diversified Communications & Media 23 - -
Diversified Consumer Products & Services Consumer Discretionary 48 5 -
Diversified Consumer Products & Services Consumer Staples 23 2 -
Diversified Financial Services 75 13 -
Diversified Industrial Products & Services Agriculture 4 - -
Diversified Industrial Products & Services Forest Products & Paper 12 3 1
Diversified Industrial Products & Services Mining Services 3 - -
Diversified Industrial Products & Services 68 17 1
Diversified Real Estate Diversified 7 - -
Diversified Real Estate Industrial/O ce/Retail/Residential 33 - -
Diversified Real Estate Real Estate Development and Services 3 1 -
Diversified Real Estate Real Estate Operating Companies 8 - -
Diversified Real Estate Specialized 6 - -
Totals 313 41 2
11

Table 5 Energy sector and sub-sectors
Energy Industrial Products & Services Energy Services 35 15 -
Energy Oil & Gas 67 40 4
Energy Technology Energy Services 1 - -
Energy Utilities & Pipelines 19 1 -
Totals 122 56 4
Table 6 Mining sector and sub-sector
Mining 206 289 36
Mining Agriculture 5 - -
Totals 211 289 36
12

Table 7 Technology & innovation sector and sub-sectors
Technology & Innovation Clean Technology Energy E ciency 5 9 1
Technology & Innovation Clean Technology Low Impact Materials and Products 9 3 1
Technology & Innovation Clean Technology Renewable Energy Equipment Manufacturing and Tech 1 - -
Technology & Innovation Clean Technology Renewable Energy Production and Distribution 14 4 -
Technology & Innovation Clean Technology Waste Reduction and Water Management 1 - -
Technology & Innovation Life Sciences Biotechnology 18 28 4
Technology & Innovation Life Sciences CBD 1 - -
Technology & Innovation Life Sciences Healthcare Facilities and Equipment 4 8 1
Technology & Innovation Life Sciences Healthcare Services and Supplies 4 1 -
Technology & Innovation Life Sciences Healthcare Technology 2 2 -
Technology & Innovation Life Sciences Medical Marijuana 15 17 5
Technology & Innovation Life Sciences Pharmaceuticals 13 12 -
Technology & Innovation Technology Blockchain/Cryptocurrency 1 - -
Technology & Innovation Technology Communication Technology 8 12 -
Technology & Innovation Technology Hardware & Equipment 9 5 1
Technology & Innovation Technology Internet Software & Services 8 2 -
Technology & Innovation Technology IT Consulting & Services 5 1 -
Technology & Innovation Technology Software 21 8 -
Totals 139 112 13
13

With the data collected for the DB bubbles, descriptive summary statistics for each sec-
tor are calculated to further explore the duration and magnitude of the factor increase and
factor decrease. The summary statistics include the median, mean, standard deviation and
minimum and maximum for the rise duration, rise factor, fall duration, fall factor, price 1,
price 2, and price 3. Note that the variables price 1, price 2, and price 3 refer to the stock
prices (in $CAD) as described above for T1, P, and T2, respectively.
Table 8 Descriptive statistics - all sectors
Variable Median Mean Std. dev. Min Max
Rise duration 18.00 16.00 7.42 1.00 24.00
Rise factor 8.52 22.10 189.52 5.00 4,220
Fall duration 10.00 9.00 3.12 1.00 12.00
Fall factor 3.24 4.62 6.35 2.00 122.32
Price 1 0.46 14.56 131.29 0.01 2,340
Price 2 4.93 157.01 1,586.30 0.10 32,145
Price 3 1.48 39.80 367.77 0.01 6,795
Table 9 Descriptive statistics - diversiﬁed sector
Rise duration 18.00 16.00 8.40 1.00 24.00
Rise factor 8.57 15.07 19.44 5.02 114.29
Fall duration 8.00 8.00 2.81 1.00 12.00
Fall factor 2.90 7.32 18.82 2.02 122.32
Price 1 0.85 5.45 14.07 0.02 70.00
Price 2 7.49 60.70 153.51 0.45 675.00
Price 3 2.55 10.12 23.33 0.06 112.00
Note: Rise duration and fall duration are measured in months
14

Table 10 Descriptive statistics - energy sector
Rise duration 21.00 17.91 6.36 4.00 24.00
Rise factor 7.91 14.18 21.94 5.00 157.50
Fall duration 10.00 9.39 2.67 1.00 12.00
Fall factor 3.17 3.72 1.87 2.01 10.45
Price 1 0.78 1.85 3.50 0.04 19.20
Price 2 8.64 14.34 21.34 0.34 120.78
Price 3 2.54 4.76 8.27 0.07 52.80
Table 11 Descriptive statistics - mining sector
Rise duration 18.00 15.98 7.60 1.00 24.0
Rise factor 8.76 13.02 13.80 5.00 126.25
Fall duration 10.00 8.82 3.11 1.00 12.00
Fall factor 3.09 4.20 3.19 2.00 31.60
Price 1 0.32 3.66 19.89 0.01 217.27
Price 2 3.00 31.98 155.47 0.10 1,792.00
Price 3 0.90 10.31 55.26 0.01 547.27
15

Table 12 Descriptive statistics - technology & innovation sector
Rise duration 15.00 14.36 6.84 1.00 24.00
Rise factor 9.05 51.89 397.67 5.00 4,220.00
Fall duration 10.00 9.02 3.42 1.00 12.00
Fall factor 4.09 5.17 4.55 2.00 36.76
Price 1 0.94 52.19 271.89 0.01 2,340.00
Price 2 9.44 584.01 3,303.40 0.19 32,145.00
Price 3 2.53 143.73 762.21 0.05 6,795.00
Analysis
Using the described dataset, a comprehensive analysis of the classification of DB bubbles
and DB megabubbles within a Canadian context is explored. Classification is first applied
according to sector, subsectors, and subsubsectors. Within the four main sectors in the
TSX dataset there are a total of 496 DB bubbles and 55 DB megabubbles. As seen in
Table 2, the distribution of DB bubbles and DB megabubbles is not uniform across the four
sectors. The mining sector, holding 287 or 57.86% of the total DB bubbles, has a larger
than would be expected share of DB bubbles. The mining sector also holds the largest share
of DB megabubbles at a count of 33, or 65.45% of the total DB megabubbles. Given that
the mining sector holds only 11.84% of the total quoted market value of the TSX, as seen
in Table 3, this suggests that the mining sector as a whole displays an excess of bubbly
characteristics and a high level of volatility in asset prices.
The large number of bubbles displayed in the mining sector is realistic given that the mining
sector is a cyclical industry and prone to large changes both positively and negatively. Given
the large number of factors at play in the mining sector, such as the ever-changing prices of
commodities, geographical considerations, legal regulations and political red tape, the high
number of DB bubbles and DB megabubbles in the mining sector is not unwarranted.
16

Although the mining sector occupies the bulk of the DB bubbles and DB megabubbles,
the technology & innovation sector also occupies a considerable amount at 22.58% of the
total DB bubbles and 23.63% of the DB megabubbles. Within the technology & innovation
sector all three subsectors have a share of the DB bubbles. Of the three subsectors the life
sciences subsector carries the majority of the DB bubbles, occupying 68 of the total 112 DB
bubbles in the technology & innovation sector, as per Table 7. Within the subsector there
are several smaller partitions or subsubsectors. Of key interest are the biotechnology, medi-
cal marijuana, and pharmaceuticals subsubsectors. Within the biotechnology subsubsector
there are a total of 28 bubbles and 18 companies, making for an average of 1.55 DB bubbles
per company. In a similar vein, the medical marijuana and pharmaceuticals subsubsectors
have an average of 1.13 and 0.92 DB bubbles per company, respectively.
The large number of bubbles in these life sciences subsubsector agrees with the hypothe-
ses set out that there would be a greater proportion of DB bubbles occurring in new and
emerging ﬁelds, such as biotechnology, medical marijuana, and pharmaceutical drug compa-
nies. Given that the vast majority of these companies are new or are constantly developing
and employing new technology and processes, the market psychology aspect of bubbles
comes into play. Agents looking to buy and sell assets may struggle to ascertain the true
fundamental value of them due to the relative newness of the assets and their fundamental
uncertainty associated with them. In the case of medical marijuana in Canada, the likely
driving force behind the upswing was increases in agent optimism due to changing legal
restrictions outlined in Canadian legislation Bill C-45. In a similar manner, the downturns
in these DB bubbles was likely due to agents recognizing the true fundamental value of the
asset over time and choosing to sell before gathering further losses.
This explanation of agents struggling to ascertain the true fundamental value of assets
is the likely explanation for the vast majority of bubbles in the technology & innovation
sector. Beyond the life sciences subsubsector there exist only two other subsubsector with
an average DB bubble value of 1.0 or greater. Of these two, energy e ciency and com-
munication technology, the introduction of emerging technologies and changing consumer
17

attitudes play a role in their growth.
Looking beyond to the diversified and energy sectors, no other subsubsector exists that
has an average DB bubble count of more than 0.60 DB bubbles per company. In the energy
sector, the industrial products and services subsector has an average of 0.43 DB bubbles per
company while the oil & gas subsector carries an average of 0.60 DB bubbles per company.
Although still a significant portion of the total amount of DB bubbles, the energy sector as
a whole is more stable than predicted in the hypotheses.
Lastly, given the large size and market value share of the diversified sector, a small pro-
portion of DB bubbles is not overly surprising. With a large market share and a diversified
portfolio, the diversified sector is better able to manage the business cycles of the economy
as well as any legal or political restrictions. In addition, the diversified sector in general
deals with longer term and more durable assets that have not changed in form or function in
recent years. The financial industry, which may well have been a sore spot in the diversified
sector, is also well protected through government support and a large number of financial
and legal safeguards.
Given the exploration of DB bubbles and DB megabubbles with regard to sector and
subsectors, further analysis may be applied according to the period of time over which
the DB bubble occurred. As seen in Figure 4, the DB bubbles found in the twenty-year
period are dispersed non-uniformly across the time period. In examination several columns
catch further attention: the years 2000, 2007, 2010-2011, and 2016-2017. With a uniform
distribution, we would expect to find approximately 25 DB bubbles per year. Within the
columns identified, there range between 38-60 DB bubbles per year, well above a uniform
distribution.
18

Figure 4: Number of DB bubbles according to sector and peak year
In the year 2000, a total of 48 bubbles reached peak value. DB bubbles were split across
all four sectors with the mining and technology & innovation sectors taking 19 DB bubbles
each and the energy and diversified sector coming in with 4 and 6 DB bubbles, respectively.
Although not o cially classified as a recession, the dotcom bubble bursting in early 2000
led to a contraction of economic activity in Canada, creating a ripple e↵ect beyond even
the technology sector.
The year 2007 is an o cially recognized recession with real GDP falling for a consecu-
tive two periods. Within this year a total of 47 DB bubbles occurred with 30 DB bubbles
occurring in the mining sector, strangely enough, and 9, 5, and 3 rounding out the tech-
nology & innovation, energy, and diversified sectors, respectively. Given that 2007 o cially
led into a recession the small number of DB bubbles, in comparison to other peak years, is
surprising. Even more surprising is the fact that the majority of the bubbles did not occur
in the financial sector but rather in the mining sector.
19

The years 2010-2011, in comparison, are not a large surprise due to their recognition as
being years in which gold and silver prices fell. Given the large share of mining companies
listed in the TSX, a large number of mining DB bubbles would be predicted. This is what
is seen during those two years with 2010 and 2011 having 37 and 40 DB bubbles in the
mining sector, respectively.
The years 2016-2017 occupy the smallest of the peak years with a total of 38 DB bub-
bles occurring in each year. Although once again the mining sector plays a large role in DB
bubbles, the technology & innovation sector also carries a share, representing the period
during which medical marijuana companies reached peak value following legal changes.
A final method of analysis of DB bubbles and DB megabubbles lies in the analysis of
the factor and duration over which a DB bubble rose and fell. In reference to Tables 8-12,
the summary statistics for each sector’s DB bubbles and for the entire TSX as a whole were
calculated, along with the prices at the three key points. Of significance here is the median
values and any di↵erences observed between the four sectors.
Using an ANOVA test the mean values for the rise duration, rise factor, fall duration and
fall factor were computed and compared. The findings are summarized in Table 13 which
displays the mean values for the four variables across the four sectors. Of the tests ran, the
di↵erence in means of rise duration and di↵erence in means of fall factor were both found
to be statistically significant, both at the 5% level. In contrast, the di↵erence in means of
both the rise factor and fall duration were not found to be significant at any level. Given
the large di↵erences shown between the sectors in terms of number of DB bubbles this is
an unexpected finding. It is interesting to note that, despite a large number of DB bubbles
and DB megabubbles in the mining and technology & innovation sectors, the duration and
factor over which these DB bubbles rose and fell were similar to that of the bubbles found
in the other sectors.
20

Table 13 Mean value - ANOVA significance
Variable Diversified Energy Mining Tech. Significant P-value
Rise duration 14.36 15.98 17.91 16.00 Yes, 5% 0.02946
Rise factor 51.89 13.02 14.18 15.07 No 0.31170
Fall duration 9.02 8.82 9.39 8.00 No 0.20542
Fall factor 5.17 4.20 3.72 7.32 Yes, 5% 0.01344
Note: ↵ = 0.05
The results of the ANOVA may be subject to question due to the noisiness of the results
obtained, as referred to in the maximum and minimum values in Tables 8-12, as well as the
implementation of arbitrary cuto↵s in terms of the minimum and maximum values for rise
and fall duration and factor.
Conclusion
Upon review, the definition and classification of DB bubbles in the TSX market points to
a large number of episodes wherein the volatility exceeds standard business cycle volatility.
Within the data there were a total of 496 DB bubbles identified and classified out of 785
companies. The distribution of these DB bubbles across sectors is not uniform, even when
accounting for fraction of market value, with the mining and technology & innovation sectors
occupying a larger than expected share of bubbles. Upon classification according to sector
and subsector the resulting identification of DB bubbles in newly emerging technological
areas, sectors facing the easing of government and legal restrictions, and commodity-based
sectors agree with the hypotheses laid out at the beginning of this paper. Classification
according to time period led to large peaks in the number of DB bubbles in several key
years, including during the 2007-2009 recession, although the sorting of these bubbles by
sector was not always what the theory would have suggested for that period in time. Lastly,
the classification of DB bubbles according to their means for rise duration, rise factor, fall
duration and fall factor led to the surprising discovery that, although some sectors are
clearly more volatile than others, the magnitude and rate of volatility are often similar, if
21

not statistically indistinguishable from each each.
Further questions moving forward would relate to the examination of other, non-Canadian
markets. Given the TSX’s role as the stock exchange with the world’s largest number of
mining companies and given the large role the mining sector plays in DB bubbles, analysis
of additional markets and conﬁrmation and comparison of results would be beneﬁcial. In-
cluding the TSX Alpha, as well as delisted companies on the TSX, would also be crucial in
terms of eliminating statistical errors and biases.
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