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1.2 Capital and markets

[ SLIDE capital - markets - random walk || VIDEO modem - LAN - DSL ]

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:

  1. 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.
  2. 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.
  3. Investors have an interest in putting their wealth to work for the larger benefit of the society and will sometimes make a profit.
  4. 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.

Virtual market experiments: the random evolution of market prices
  1. Reduce the value of the Volatility parameter and test how you can affect the ``amount of randomness'' in the price increments. Taking one step at a time, verify that you cannot predict with any certainty whether the next movement of the price will go up or down.
  2. Increase the value of the Drift parameter to add a small, positive or negative but systematic and predictable drift to the price increments.
  3. Raise the number of independent Walkers to 100 and higher to verify how a Monte-Carlo simulation can be used to compute a large number of possible realizations of the market that all start from the same present value.

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/N. 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= $ \int_a^b p(S) dS$ .

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.

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