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DECIPHERING THE FINANCIAL
CRISES 2007-0?
Millenium Bridge,London,UK
Millenium Bridge, 6/10/00
The opening day:
Soon after the crowd
streamed on to
Millennium Bridge,
the bridge started to
sway from side to
side.
Many pedestrians fell
spontaneously into
step with the bridge’s
vibrations,
inadvertently
amplifying them.
The Wobbly Bridge
Attempts to limit the
number of people
crossing the bridge.
Long queues, but
dampened neither
public enthusiasm for
something of a
white-knuckle ride,
nor the vibrations
themselves.
Unexpected lateral
vibration (resonant
structural response)
caused the bridge to
be closed after two
days.
Diagnosis
Trouble was at 1
hertz (one complete
cycle per second)
Walking pace is
approximately two
steps per second (2
hertz)
Although most force
exerts down when
walking, there is
small sideways force
every two steps (1
hertz)
Positive Feedback
The bridge's movements lead
to 'positive feedback‘:
Synchronous Lateral
Excitation.
The natural sway motion of
walking caused small
sideways oscillations.
In turn people on the bridge
sway in step.
Increasing amplitude of
bridge oscillations
Reinforcing the effect.
Probability of Coordination
What is the probability that a thousand people walking at
random end up walking exactly in step, and remain in lock
step thereafter?
• If individual steps are independent, then probability is close
to zero.
• But if there is a coordinating mechanism, the probability is
close to 1 under the right conditions
Bridge moves → Adjust stance
↑
↓
Further adjust stance ← Push bridge
Millenium Bridge Analogy
Bridge moves
Pedestrians
adjust stance
Millenium Bridge Analogy
Prices and measured
risks change
Banks adjust
balance sheet
Endogenous Risk
Risk from shocks generated and amplified within the system
(feedback effects)
In contrast to exogenous risk, from shocks that originate from
outside the system (storms, earthquakes)
Positive Feedback
Preconditions for feedback:
• Marking to market
— Sensitivity of equity cushion to price changes
• Risk management that depend on market variables
— Sensitivity of equity cushion to risk measures
• Sensitivity of price and risk to portfolio changes
— Uniformity of trading positions among participants
Leverage Cycle
Banks increase leverage
Upwards
Balance sheets
strengthen
Balance sheets
expand
Asset prices rise
The Run on Repo
How did breakdown in housing market lead to systemic crisis in
financial sector?
The Panic of 2007-2008 was run on the Repo market, which
stopped functioning, leading to massive deleveraging of
participants.
The run occurred with failure of Lehman Brothers in 09/08. “Non
rescue” forced lenders to reevaluate default probabilities of
banks and freeze Repo markets.
Uncertain about solvency of counterparties, worry about liquidity
of collateral bonds; if all firms hold cash, collateral decline in
price to find buyers.
Leverage Cycle
Banks reduce leverage
Downward
Cycle
Balance sheets
weaken
Balance sheets
contract
Asset prices decline
Postscript
The problem was fixed
by the retrofitting of 37
fluid-viscous dampers
(energy dissipating) to
control horizontal
movement and 52 tuned
mass dampers (inertial)
to control vertical
movement.
This took from May 2001
to January 2002 and cost
£5m.
The bridge was
successfully re-opened
on 22 February 2002.
The bridge has not been
subject to significant
vibration since.