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1.2 Capital and markets
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capital -
markets -
random walk ||
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Most of the ideas discussed in this course derive from one particular
model of the society called capitalism.
At the core lies an idea that capital
(indeed any kind of asset such as money,
raw material, even patents) owned by an individual
(the investor) can be lent to another
(the entrepreneur) to produce a
certain number of goods or services.
The separation of roles played by the owner and producer is not granted
for example in feudal, communist or family based societies, where the
suzerain, the state or the father
respectively are as much the owners as the chief producers of goods.
With no implied judgment for choosing one particular model, this
separation of interests does however lead to a number of interesting
characteristics:
- Entrepreneurs with little resources but good ideas can realize
projects for the larger benefit of the society and are rewarded
for their work with a regular income.
- Investors have an independent judgment of what they consider good
ideas, which reduces the likelihood that powerful individuals with
bad ideas allocate large resources to realize projects that have
little but self-interest.
- Investors have an interest in putting their wealth to work for the
larger benefit of the society and will sometimes make a profit.
- The mutual interest and also the competition between investors
and entrepreneurs can, via regulations, be used to maximize the
efficiency of reaching certain goals the society wants to pursue
- such as the growth in the
gross domestic product (GDP) that
measures the total amount of goods produced in a country.
By helping entrepreneurs to realize their ideas, investors take a certain
risk that their initial assets (the
investment) will be consumed without
producing the expected return:
to statistically compensate for more frequent losses, investors demand
a larger return from a risky investment. This is apparent in all the
assets that constitute the savings of an individual, which are commonly
called portfolio.
An important feature of capitalism is the markets, where investors exchange standardized
assets in the form of securities, for a
market price (the spot price) that is openly
disclosed to all the participants in the market.
Examples include the well known stock markets
(such as the New York Stock Exchange
NYSE,
the European Virtual Exchange
VTX)
and less well know exchanges (such as
the New York Mercantile Exchange
NYMEX,
the New York Commodity Exchange
COMEX, or
the Chicago Board of Trade
CBOT)
where raw material are traded (such as cattle, oil, gold).
The spot price of a security depends on the consensus reached via offer
and demand from the sellers and the buyers: if everything goes well for
the investors, it slowly drifts in time at
a rate that reflects the growing value of this security.
Uncertainties in the valuation lead to different opinions and are the
source of price fluctuations: quantified as the standard deviation of
normalized increments measured over a period of time, the fluctuations
are called volatility and play a
central role in the description of any security.
Combining the effects from drift and volatility, the spot prices are said
to evolve in a stochastic manner, i.e.
they never follow any quite predictable pattern: rather, they look like
the random walk that was first described
in biology, when Brown observed the motion of small particles under a
microscope and is illustrated with horizontal motions in the
VMARKET applet below.
VMARKET applet: press Start/Stop
to simulate the evolution of a daily closing price in a volatile market.
The horizontal position of the red dot measures the value of an asset:
it starts from the present value (price initially known to be 10) and
evolves in a stochastic manner as Time goes by.
Observe how the red dot jumps to the left (price drop) or the right
(rise) in an unpredictable manner, reproducing in a simulation what
could be a possible realization of the market.
In a first reading, you can simply forget about the black line and
completely discard the vertical dimension: it has been introduced
only to distinguish different dots and has no particular meaning.
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Masters: probability of an outcome.
Even if one cannot predict with certainty the evolution of a random
variable such as a spot price, it is often possible to say at least
what are the
possible realizations and to
attribute a probability to a certain
outcome.
Assuming that the drift and the volatility of an asset are known over a
period of time, the experiments above suggest that a computer can simulate
possible realizations with random walkers, by adding small increments to
an initial value that is known.
Monitoring the evolution of a large number of walkers N, the probability
of the chosen outcome can then be estimated by dividing the number of
realizations n that satisfy this outcome by the total number of walkers,
P=n/N; the relative precision of the estimate is e~1/ÖN.
This procedure can be used to estimate the probability of winning in a
market (exercise 1.04) and, more generally, of expecting a price in an
interval [a,b]:
quants view this as an approximate integral over the probability distribution
P=
.
Not all the trades are openly disclosed in exchanges: non-standard
deals are generally carried out
over-the-counter (OTC) by a
broker, who's job as a
market maker
is to determine a fair price that will match buyers with sellers,
while keeping a small fraction of the money for himself in
transaction costs.
Neither are the trades always for investment purposes: markets are
inhabited by speculators who bet
on the price evolution, hedgers who
seek protection to reduce the investment risk and
arbitrageurs who try to exploit
small price differences to make immediate and risk free profits.
Financial regulations try to guarantee a fair treatment for all the
participants in an open market. Clearinghouses, via a deposit in cash,
ensure that the deals are carried out according to the contracts:
clearing margins are particularly
important when a party enters an obligation toward another some time in
the future: instead of buying (i.e. go long)
a security in the hope that the price will rise, this allows members of
a clearinghouse to sell short a security,
i.e. sell something for future delivery that they do not currently own,
in the hope that they will be able to buy it more cheaply later.
Private investors generally have access to the markets through a bank
or a Internet broker who will carry out market operations on their
behalf, generally charging a fixed fee
plus a commission around 1-2% of
the value of the deal, which have both to be added to the total
transaction costs.
Because of the risk of defaulting on a deal, securities that carry
an obligation are often not accessible to the private investors;
chapter 2 will show how a put option can be used instead to
earn money in falling markets.
SYLLABUS Previous: 1.1 How to study
Up: 1 INTRODUCTION
Next: 1.3 The risk and
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