Wall Street New York City ### `  ``   This article suggests that the trading stock market has some tendency towards ``   equilibrium. Appropriate portfolio structure, however, is the primary means of ``   handling volatility. ``   `` ``   I do not believe that a human system can ever be analyzed satisfactorily ``   In simple mechanical terms, and that at some point the complexity of the``   level of abstraction must begin to move towards the complexity of the ``   subject matter. In particular we cannot ultimately avoid economic models``   which take explicit notice of the nature of the economic system as an ``   information...process, very different from the simple dynamic system of            ``   the physical world. `` ``                                                  Kenneth E. Boulding``                                                  Research in Economics``                                                         (1958)`

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#### The market maker uses an algorithm to calculate the price of an order, (w):

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`                         P t+1 = f(P t,w)`
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`                              where: P t is the current price.`
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Function (f) is an increasing function of the order size; the larger the buy order, the higher the price must be to clear the market. This order has an impact upon the market approximated by the equation:

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`                         p t+1 ~ w/lambda + p t `
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`                               where: p t = log P t.`
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`                                      For the sake of simplicity, all the                                                              `
`                                      following price and value calculations               `
`                                      are carried out in terms of logarithms. `
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`                                      w is the order size. `
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`                                      lambda is the market's liquidity.`
`                                      this is mainly of concern to market `
`                                      makers and traders.`
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#### In the case of a whole market comprised of a market maker and many trading decisions, the future price of a security will be, summing the transactions:

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`                                         n`
`   (1)        p t+1 = p t + (1/lambda) * SUM [w (i) (p t, p t-1, ...I t)] + N t+1                  `
`                                       i = 1`
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`                   where:  lambda, as before, is market liquidity.`
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`                           i is the ith market transaction.`
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`                           w is the order size.`
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`                           (p t ,p  t-1 ,...I t) is an investment                                                                                                 `
`                           strategy that utilizes the information available  `
`                           in the economy, I t. This is very well stated.`
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`                           N t+1 is a random term; it can include `
`                           unanticipated events.`
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#### Utilizing the investment strategy (p t, p t-1,...I t), value investors make a common assessment of value (V t) in relation to price.* They buy stock if the price is less than the estimated value and sell stock if the price exceeds this value. The amount of stock held is approximated by an equation related to the perceived mispricing:

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`                   X t+1 = c(v t - p t) `
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`                        where: X t+1 is the amount of stock held. `
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`                               c is a constant proportional to trading capital.                                     `
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`                               v t = log V t. `
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#### The change in the logarithm of price, caused by a market consisting only of value investors and the market maker is:

 change p t+1 = c/lambda * (change v t - change p t) + N t+1

#### Momentum investors buy stocks if the price is going up and sell stocks if the price is going down. Momentum investors hold stocks according to the formula:

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`                X t+1  =  c(p t - p t-theta)`
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`                      where: theta is the time scale used to measure a                   `
`                             trend.`
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