Stats in Risk
Probabilities were invented in 1600s. Kahneman showed that people round off their
probabilities to: won’t happen, will happen, or maybe. We are not good a judging how much insurance
we need. Robert Shiller points out that
with stats we are like the cultures that count one, two, and, many. They are able to remember hundreds of
different plants but they do not count.
In emergent theory outcomes are dependent on millions of
little things, independent events, that accumulate. Think of humans from DNA.
Unexpected events are often caused by a failure of the independence
of these events. For example changes in
the stock market indices should be random since market changes are based on
news, which is random and the indices cancel out individual stock risk. Are stock returns independent variables? They are until group think sets in.
Fat tail events complicate this model. In Finance, low probability shocks that
shouldn’t happen occur.This is why geometric returns are more useful. Outliers exist . Random shocks to the economy are normally
distributed. In nature the normal distribution is not the only distribution
that occurs and some
other distributions have fatter tails. -
Kurtosis
The Central limit
theorem is probably the most important theory of statistics. if you have independent identically
distributed random variables and they have a finite variance then the distribution of an average of these
variables converges to a normal distribution as the number is increased. The normal curve is so common because so many
things we observe are averages of separate events. Note that he normal distribution does not
have fat tails. This is why things work most of the time.
One reason that the normal distribution is so common because
most events we observe are an average of independent events. In a normal distribution the tails drop
off. It assumes the underlying
variables have a finite variance.
Other stat concepts include
Variance – is the sum of weighted probabilities of deviation
from the mean
And standard deviation = square root of the variance
Covariance - how two different random variables move
together?
Can be positive, negative,
or zero if unrelated
Correlation - is
scaled -1 to +1
P = cov(x,y) /(s1,s2)
Low covariance is important in reducing risk. We may not get expected return if the
observations are not independent.
In the Law of large numbers, which is another stat concept–
although there are a lot of independent shocks if they are independent, there is
not much risk. Variance goes to zero as
n goes to infinity. Insurance relies on
this.
Value at Risk
VaR was invented in 1987 to
measure corporate risk. Companies would
calculate that there is a 5% probability of
loosing a million dollars. It was found
not to work well in 2008.
CoVar was invented by
Brunnermier at Princeton. It is Value at risk of financial institutions conditional
on other institutions being under distress.
This is supposed to be a newer more accurate model
Majority rule can be a good way to decide the better of two
options. Intrinsic justifications do not
concern themselves with the quality of the decisions. Voting outcomes can track truth if three conditions
hold. The voters are better choosers
than random, are independent, and they vote sincerely. One problem is that people have preexisting cultural mindsets which
determine how they look at information or even what new information they
consider. Only ten percent of people
can explain what nano-technology is but 80% have an opinion on how safe it
is. Page argues that good decisions
depend on sufficient cognitive diversity of the group or having people use
different models to arrive at a solution. A smart diverse group of people is needed to get
to the right answer.
I am not sure how this ties to religion or even political
parties, which encourage uniformity of thought. Most people do not choose their political
party or religion.
Shiller Finance Lecture
wisdom of crowds
Scott Page wisdom of crowds
