Contagious Exuberance
By Aravindaan Natarajan
An asset bubble is akin to a pandemic, the only difference being that the latter involves the spread of mere pathogens whereas the former involves the spread of more contagious human emotions of fear and greed- nothing surmises the uncanny resemblance between the markets and pandemics better than the aforementioned lines.
What are asset bubbles? How are they related to pandemics? Does epidemic modelling hold the key to prediction of asset bubbles? Read on to unravel these questions and to delve deeper into what could be the next big innovation in the field of finance – a cross between epidemiology and finance.
Understanding Asset Bubbles
An asset bubble is said to be formed when the price of the asset rises to levels that are well above its intrinsic/fundamental value. This upward trend continues till the investors eventually realise this pricing anomaly and start selling the asset in a frenzy. This causes asset’s price to fall to abysmal levels thereby resulting in the bursting of the bubble.
Asset bubbles have traditionally been a much-studied topic in the financial world. Be it the 2008 Housing bubble or the dot com bubble of 2000, financial experts have devised various models for the prediction and identification of stock market bubbles.
But one thing which has eluded them is a method to determine the time when the bubble will burst i.e. a method to time the events in an asset bubble.
But why is it important to time the bubble? Asset bubbles are generally viewed as harbingers of large-scale financial devastation, but, to the smart investors, they also provide an opportunity of earning huge profits. However, this profit-making potential offered by asset bubbles is available only to those who are able to reasonably predict the time of its bursting. Let us try to understand this by the means of an example: Say, you have forecasted the formation of a bubble and therefore have shorted the market. However, the euphoria which had caused the bubble may persist longer than you expected, thus causing you enormous loss. As Keynes beautifully puts it “ the markets can stay irrational longer than you can stay solvent”. Therefore, the ability to predict the direction of the market without being able to time it is often of very little help.
It is in this very aspect of timing asset bubbles, that epidemiology may hold the key. Pandemics and asset bubbles have more than just contagion in common. In fact, the phases of a pandemic and those of asset bubbles share an astounding degree of resemblance as highlighted below.
Phases of Pandemics and Asset Bubbles- a comparison
Phases of a Pandemic
Phase 1: Investigation Interval
This phase involves the discovery of a new pathogen which potentially has a negative implication on human health.
Phase 2: Recognition Interval
In this phase, the case count starts increasing and clusters are formed. There is an increased possibility for person-to-person transmission.
Phase 3: Initiation Interval
This phase marks the beginning of community transmission.
Phase 4: Acceleration Interval
The vigour of spread of the pathogen increases manifold. It is during this phase that Public health officials may take stringent measures such as closing schools, encouraging social distancing, and offering antivirals or vaccines—if available.
Phase 5: Deceleration Interval
This final phase is marked by a consistent decrease in the number of cases.
Phases of a Bubble
Phase 1: Displacement
Similar to the discovery of a new pathogen in the first stage of the pandemic, the initial stage of a bubble involves the onset of a new paradigm, such as an innovative product or a technology that captures the people’s attention.
Phase 2: Boom
Prices of asset(s) which are positively affected by the new paradigm start to rise at first, then get momentum as more investors enter the market.
Phase 3: Euphoria
This is where the herd mentality sets in and caution is thrown to the wind. The market is thrown into a buying frenzy and asset prices skyrocket.
Phase 4: Profit taking
In this phase, the smart investors become aware of the impending burst of the bubble and make money by selling off positions.
Phase 5: Panic
Asset prices change course and drop as quickly as they rose. Investors and others want to liquidate them at any price. Asset prices decline as supply outshines demand.
How Epidemic Modelling can be used to time asset bubbles
Having identified the similarities between pandemics and asset bubbles, this section explains the basics of epidemic modelling and how it can be used to determine the time of bursting of asset bubbles.
The most commonly used epidemic model is the SIR (Susceptible-Infective-Removed) model. Under this model, the entire population is divided into 3 categories:
- Susceptible: People who have not yet been infected and hence are still prone to the disease.
- Infective: People who currently have the disease and can infect others.
- Removed: People who have recovered from the disease
For simplicity purposes, the model assumes the recovery rate/death rate remains constant (i.e. a constant proportion of infected people recover/die every day).
Similarly, the investors of a particular asset (which is in the midst of a bubble) can also be classified into 3 similar categories:
- Susceptible: Investors who have never owned that particular asset
- Infective: Investors who own the asset
- Removed: Investors who have bought and sold the asset during the course of the bubble
As the disease spreads or the bubble gets enlarged, people in the “susceptible” category move into the “infective category” and those in the “infective” category eventually move into the removed category.
The model mentioned above can be encapsulated by using the following equations:
Let S, I and R denote the number of people under the Susceptible, Infective, and Removed categories respectively.
Since, the recovery rate/death rate, which is nothing but the rate of change of people falling under the removed category is assumed to be equal to a constant proportion of infected people,
𝑑𝑅 = 𝑏𝐼 ; 𝑑𝑡
- I: number of infected people
- b: the proportion of the infected population which recovers every day
The rate of change in the susceptible population is directly proportional to both the number of susceptible people and infected people. However, as the disease spreads or the bubble progresses, the number of infected people increases (or conversely the number of susceptible people decreases). As a result, the rate of change in the susceptible population is negative.
Thus,
dS/𝑑𝑡 = −𝑎𝑆𝐼
- a: Proportionality constant
- S: The number of susceptible people
- I: The number of infected people
Now, the rate of change in the infected population is nothing but the difference between the rate of change in the susceptible population and the rate of change in the recovered population
𝑑I/dt = 𝑎𝑆I − 𝑏I
It is apparent that the disease will continue to spread or the bubble will continue to grow as long as the rate of change in the infected population is positive
i.e. dI/𝑑𝑡 > 0
i.e. 𝑎𝑆𝐼 − 𝑏𝐼 > 0
i.e. 𝑆 > 𝑏/𝑎
On the other hand, the epidemic / the bubble shrinks if
𝑆<𝑏/𝑎
Thus as the value of 𝑏/a nears the total susceptible population, the bubble can be viewed as 𝑎
nearing its bursting phase.
Conclusion
The aforementioned model is a hugely simplified one and merely aims to highlight the potential applications of epidemic modelling in the field of finance. The arguments and comparisons put forth in the above sections prove it beyond doubt that financial markets are much more dynamic and interlinked to other topics than may appear on the face of it. Will “biological finance” be the next biggest hybrid in academic circles? Food for thought…