116
9 Bubbles, Crashes, Fat Tails and Lévy-Stable Distributions
orders that could not be satisfied and eventually the bubble burst in October 1987
leading to the Black Monday crash of 1987. Unlike the aftermath of the crash of
1929, recovery from the 1987 crash was swift and the stock market recovered and
reached its previous level within two years.
Just as recovery from the 1987 crash was in full swing, the prevailing optimism was
further enhanced by the fall of the Berlin Wall, the demise of the Soviet Union, and
the end of the cold war leading to a remarkable growth period during the 1990s. Partly
fueled by the newly emerging Internet and technology companies, which promised
large profits, the stock market grew at a remarkable pace to ever increasing heights of
the stock indices. There were a few hiccups along the way, such as Russia’s default
on foreign debt in 1998, which wiped out some hedge funds, but the overall trend was
upwards. This continued until speculators started to become cautious and attempts to
sell shares faced difficulties, which then led to the so-called dot.com crash of 2000.
In order to alleviate problems with lacking liquidity following the dot.com crash,
interest rates were lowered significantly in the US. At the same time political consensus emerged to stimulate the purchase of private homes, even for those previously not
eligible for mortgages. But the increased availability of mortgages led to increased
demand for housing, which led to higher prices for homes. Using the newly acquired
homes as collateral for the mortgage is possible as long as house prices rise. Around
2007, however, the demand for new homes decreased, which lowered the value of
homes, such that the home value did no longer cover the mortgages. The hard-pressed
home-owners were required to sell below price or default on their mortgage. The latter
happened on a large scale, which wiped out several banks, most notably the Lehman
brothers.
Note that none of the above crashes were caused by natural disasters, but rather by
speculation on a rising asset price. In the following section we will try to summarize
some observations about the underlying mechanisms of the bubble-crash sequence.
9.2 Bubble-Crash Mechanisms
Here we distill some observations pertaining to the speculative bubbles and ensuing
crashes from the preceeding section.
• The normal valuation of stocks as sum of discounted future earnings (see Sect. 3.6)
does not apply. Instead traders speculate on an increasing asset price and hope to
sell at higher prices than they bought the asset.
• Bubbles require liquidity to invest. Often the increasing stock value is used as
security for the borrowed money, which is called “leveraged purchase” or “bought
on margin.” Cheap money and low interest rates often accompany bubbles.
• Speculative bubbles and crashes appear to be inherently linked. First an unfailing
trust in an ever-increasing asset value (what A. Greenspan called “irrational exuberance” in 1996, which is also the title of Shiller’s book [4] on bubbles) drives
the bubble to ever-higher values. Losing faith in the continued increase of the
9 Bubbles, Crashes, Fat Tails and Lévy-Stable Distributions
orders that could not be satisfied and eventually the bubble burst in October 1987
leading to the Black Monday crash of 1987. Unlike the aftermath of the crash of
1929, recovery from the 1987 crash was swift and the stock market recovered and
reached its previous level within two years.
Just as recovery from the 1987 crash was in full swing, the prevailing optimism was
further enhanced by the fall of the Berlin Wall, the demise of the Soviet Union, and
the end of the cold war leading to a remarkable growth period during the 1990s. Partly
fueled by the newly emerging Internet and technology companies, which promised
large profits, the stock market grew at a remarkable pace to ever increasing heights of
the stock indices. There were a few hiccups along the way, such as Russia’s default
on foreign debt in 1998, which wiped out some hedge funds, but the overall trend was
upwards. This continued until speculators started to become cautious and attempts to
sell shares faced difficulties, which then led to the so-called dot.com crash of 2000.
In order to alleviate problems with lacking liquidity following the dot.com crash,
interest rates were lowered significantly in the US. At the same time political consensus emerged to stimulate the purchase of private homes, even for those previously not
eligible for mortgages. But the increased availability of mortgages led to increased
demand for housing, which led to higher prices for homes. Using the newly acquired
homes as collateral for the mortgage is possible as long as house prices rise. Around
2007, however, the demand for new homes decreased, which lowered the value of
homes, such that the home value did no longer cover the mortgages. The hard-pressed
home-owners were required to sell below price or default on their mortgage. The latter
happened on a large scale, which wiped out several banks, most notably the Lehman
brothers.
Note that none of the above crashes were caused by natural disasters, but rather by
speculation on a rising asset price. In the following section we will try to summarize
some observations about the underlying mechanisms of the bubble-crash sequence.
9.2 Bubble-Crash Mechanisms
Here we distill some observations pertaining to the speculative bubbles and ensuing
crashes from the preceeding section.
• The normal valuation of stocks as sum of discounted future earnings (see Sect. 3.6)
does not apply. Instead traders speculate on an increasing asset price and hope to
sell at higher prices than they bought the asset.
• Bubbles require liquidity to invest. Often the increasing stock value is used as
security for the borrowed money, which is called “leveraged purchase” or “bought
on margin.” Cheap money and low interest rates often accompany bubbles.
• Speculative bubbles and crashes appear to be inherently linked. First an unfailing
trust in an ever-increasing asset value (what A. Greenspan called “irrational exuberance” in 1996, which is also the title of Shiller’s book [4] on bubbles) drives
the bubble to ever-higher values. Losing faith in the continued increase of the