Philosophy, anti-fragility & statistics
Martin Sewell
mvs25@cam.ac.uk
University of Cambridge
Anti-fragility and statistical thinking session
Royal Statistical Society 2013 International Conference
Newcastle
2–5 September 2013
Intuitive definition of antifragility
Nature of goods Post Office label
fragile
HANDLE WITH CARE
robust
antifragile
Source: Taleb (2012)
HANDLE CARELESSLY
Examples of antifragility
• Attraction?
• Switzerland?
• A biological population (via natural selection)?
• An economy made up of entrepreneurs?
No single entity is genuinely antifragile, but if a set of fragile entities are
subject to errors/volatility and the weakest are eliminated but the rest
recover, then the collective will become stronger, and may be
considered antifragile.
Financial definition of antifragility
• Antifragility means positive sensitivity to volatility.
• Vega is the derivative of the value of an option with respect to the volatility
of the underlying asset, i.e. vega measures sensitivity to volatility.
• Therefore antifragility means positive vega.
• All options have positive vega.
• A long straddle involves purchasing both the call option and the put option
on some underlying.
• If you believe that volatility is going to increase, buy a straddle.
• For a mathematical definition of (anti)fragility, see Taleb and Douady 2012.
Taleb’s central thesis
• Teleb’s central thesis is that we should purchase options.
• The implication is that options, in general, are undervalued.
• Financial markets are highly efficient (Fama 1970), so most of us are
concerned with options outside finance that are undervalued.
Taleb’s prescriptions
• Modify our man-made systems to let the simple—and natural—take their
course.
• Decrease downside risk, rather than increasing the upside.
• Avoid centralisation and debt.
• Do not attempt to predict the future.
• Try to benefit from shocks when they occur.
• In fat-tailed domains one should extrapolate some properties from history,
instead of interpolating.
• Prevent individuals from becoming antifragile at the expense of others’
fragility. Taleb speaks at length about ‘skin in the game’, this is the agency
problem.
Moment preferences
Moment
Preference
Mean
High
Variance
Low
Robustness
Skewness High
Antifragility
Kurtosis
Robustness
Low
Preference implies
Source of preferences: Scott and Horvath (1980), source of implications: Taleb and Douady (2012)
Heuristics and biases
• The theoretical Homo economicus (or Economic man) seeks only to
maximize his utility.
• The minds of human beings are adapted to seeking our ultimate goal
of reproduction (in the Pleistocene).
• The differences between the two lead to cognitive biases.
Heuristics and biases
Bias
Preference
Ambiguity aversion Antifragility
Status quo bias
Antifragility
Risk aversion
Antifragility
Loss aversion
Antifragility
Overconfidence
Fragility
Optimism
Fragility
Camerer and Lovallo (1999) found experimentally that overconfidence and optimism lead to excessive business
entry.
News
• Our ancestors lived without the luxury of the media, so would have only been
aware of events taking place within the environment of their own tribe.
• Therefore our minds evolved during a time when events that we heard about
could well affect us.
• We now have news, so are aware of events globally, and hear about many events
that do not affect us.
• News, by definition, is unpredictable (otherwise, it would have been reported
yesterday).
• If we cannot predict something, it will be a surprise.
• So news is surprising.
• So we are less likely to experience a black swan event than our minds have
evolved to believe.
Social discount rate
• When considering the possibility of black swan events, we need to
consider the concept of time, and to what extent we care about the
future.
• An individual’s discount function is hyperbolic and reaches 100% at
the end of their lifetime, whilst an equitable social discount function
should average the population’s individual discount functions (Sewell
2010).
Evolution and the long-term future
• Evolution is survivorship bias.
• Natural selection is blind to the future, but can the long-term, as well
as the short-term, past affect the future?
• Lineage selection acts to suppress selfish traits which, although
advantageous in the short-term, hinder the population over a longer
time scale, facilitating the persistence of nonselfish traits over the
longer term (Nunney 1999).
• Therefore, a black swan event in the distant past could influence the
future.
Future volatility
• Minsky claimed that in a capitalist economy stability is inherently
destabilizing.
• Taleb argues that reducing vulnerability to small shocks may increase
the severity of large ones.
• An analysis of the Dow Jones Industrial Average shows that the long
term trend in stock market volatility has been upwards since about
1960, so it could be that risk, in general, is increasing.
Science and academia
• Science is essentially applied Bayesian inference (Sewell 2012), so if
we wish to conduct science, we need probabilities.
• Science is about building models, which are abstractions of reality, so
inherently wrong, but potentially useful.
• Universities are necessarily ivory towers divorced from reality.
• In practice academic research is often based on trial and error.
• Economics is arguably the strongest, rather than the weakest, of the
social sciences.
References
• CAMERER, Colin, and Dan LOVALLO, 1999. Overconfidence and excess entry: An experimental approach. The American Economic
Review, 89(1), 306–318.
• FAMA, Eugene F., 1970. Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383–417.
• NUNNEY, Leonard, 1999. Lineage selection: Natural selection for long-term benefit. In: Laurent KELLER, ed. Levels of Selection in
Evolution, Monographs in Behavior and Ecology. Princeton, NJ: Princeton University Press, Chapter 12, pp. 238–252.
• SCOTT, Robert C., and Philip A. HORVATH, 1980. On the direction of preference for moments of higher order than the variance. The
Journal of Finance, 35(4), 915–919.
• SEWELL, Martin, 2010. The social discount rate: An evolutionary approach. Credexea meeting, Amsterdam, 20–21 June 2010.
• SEWELL, Martin, 2011. Human behaviour under risk and uncertainty: Are we really just conservative? envecon 2011: Applied
Environmental Economics Conference, London, 4 March 2011.
• SEWELL, Martin, 2012. The demarcation of science. Young Statisticians’ Meeting, Cambridge, 2–3 April 2012.
• TALEB, Nassim Nicholas, 2012. Antifragile: How to Live in a World We Don’t Understand. London: Allen Lane.
• TALEB, N. N., and R. DOUADY, 2012. Mathematical definition, mapping, and detection of (anti)fragility. arXiv:1208.1189 [q-fin.RM].