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107

Current Return Calculations In the trading room, people seldom take a full exposure at once. The traders like to build their positions in steps (gearing steps). In such cases, it is useful to introduce an auxiliary variable, the average price p paid for achieving the current exposure (gearing). This variable simplifies the computation of the return of a position built in steps. After a new deal with index i, the average price depends on the type of transaction as follows:

Pi-\ if \gi \ < and gjgi-i > 0

Pi =

gi [*L0=1 + f] if \gi\ > Ift-il and gigi-x > 0 Pi if gigi-\ < 0 or gi = 0

undefined

if gi=0

(11.1)

where and gi are the previous and current gearings, respectively, pi is the current transaction price, and j is the average price before the deal. In the initial case, when the current gearing is neutral, the average price p is not yet defined. If we start from a neutral position = 0 or reverse a position gigi-i < 0, the price to build the position is simply the current price p,. If the new position is built on top of a previous position, then we need to compute the average price paid from the price paid for each fraction of the full position. If the new position is just unfolding part of the previous position, then the average price paid for the position does not change. It is simply either profit taking or stop loss.

The average price ~p is needed to compute a quantity central to a trading model, the return of a deal,

n = <* , - gi) (£- - l)

( .2)

where the gearing g\ is equal to 0 if the model takes aji opposite position (gigi-1 < 0) and gi otherwise. There are deals with no return: those starting from a neutral gearing, - 0, and those increasing the absolute value of the gearing while keeping its sign.2 In these cases, Equation 11.2 does not apply (whereas Equation 11.1 applies to all deals).

The current return, rc, is the unrealized return of a transaction when the current position is off the equilibrium (gi 0). If pc is the current market price required

2 The example below demonstrates the accounting of a trading model of USD-CHF, where CHF is the home (numeraire) currency and USD is the foreign exchanged currency. The trading model is played with a limit of 100 CHF. The usual practice for the capital flow in foreign exchange trading is that it is started from a capital of zero with credit limit. This is what is assumed here. All of our return calculations are expressed in terms of the home currency. In other words, the returns are calculated in terms of DEM for USD-DEM, CHF for USD-CHF, FRF for USD-FRF, and JPY for DEM-JPY.

for going back to neutral, generalizing Equation 11.2 yields the current return,

rc = gd* - 1) ( . )

Gearing Calculation A gearing calculator lies at the heart of a trading model. The gearing calculator provides the trading model with its intelligence and the ability to capitalize on movements in the markets. The gearing calculator also provides the trading model with particular properties. These include the frequency of dealing and the circumstances under which positions may be entered.

In other words, the gearing calculator is the real model. In contrast, the other trading model components form a shell around the gearing calculator, providing it with price data, detecting if the stop-loss is hit, and examining the trading recommendations made by the gearing calculator. The gearing calculator reevaluates its position every time a new price quote is received from the data-vendors. (As previously noted, a filter validates each price beforehand in order to eliminate outliers and other implausible data.)

The gearing calculator employs two kinds of ingredients: a set of indicators, which are produced from the input price data, and trading rules, which are functions of the past dealing history, the current position, and other quantities such as the current unrealized return of an open position.

The models described here give a recommendation not only for the direction but also for the amount of the exposure. In our models, the possible exposures (gearings) are ±, ±1 (full exposure) or 0 (no exposure).

Recommendation Maker The fact that the gearing calculators indicators and rules suggest entering a new position does not necessarily mean that the model will make such a recommendation. Whether it does or not depends on various secondary rules that then take effect.

These rules constitute the deal acceptor. This determines whether the deal proposed by the indicators is allowed to be made. The prime constraint is the timing of the proposed deal. First, no deal other than a stop-loss deal (see Section 11.2.1) may take place within a few minutes of a deal already having occurred. This is to prevent overloading a human dealer who may be following the models. Second,

 Time Gearing Current position in CHF Current position in USD Dont care 35.71 -100 69.04 (33.33 more) 10.46(69.04*1.6 more)

In the example above, the trading lots in CHF arc always 50 (half gearing step) or 100 (full gearing step) when increasing the (long or short) position, whereas decreasing the position means selling the full current USD amount (when going to neutral) or half the current USD amount (when going from gearing 1 to 1/2). There can be other accounting conventions, but they hardly differ numerically.

the gearing calculator may make a recommendation to enter a new trading position but this recommendation can be followed only if the local market is open.

The quality of the most recent price imposes another constraint. A stringent filter determines if a given price is suitable for dealing. This is to ensure that recommended deals are made only with genuine prices rather than extraneous data. The deal acceptor permits a new deal only with a price passing the deal-filter.

If the gearing calculator suggests entering a new position but the deal acceptor decrees otherwise, the suggestion is simply ignored. Eventually, when timing and other factors are right, the gearing calculator will suggest entering a new position and the deal acceptor will approve.

Stop-Loss Detection Besides being passed on to the gearing calculator, the filtered price quotes are also sent to the stop-loss detector. The stop-loss detector is triggered if the market moves in an unexpected direction. That is, if the model enters a trading position because it anticipates the market to move in a certain direction but in fact the market then moves the other way, the stop-loss may be hit. The trading model defines a stop-loss price when a position is entered. If the current price - that is, the most recent price - moves below the stop-loss price (for a long position) or above the stop-loss price (for a short position), the stop-loss is said to be hit. Hitting the stop-loss causes a deal to close the current open position (i.e., return to the neutral position). In effect, the stop-loss prevents excessive loss of capital when the market moves in an unexpected direction. The stop-loss price may change when a new position is entered or as the current price changes (see Section 11.2.1). The current stop-loss price is displayed on the user-agent.

For 24-hr markets like FX, a stop-loss deal may occur at any time, even outside local market hours. In this case, the assumption is that a position that is kept open outside market hours is handled by a colleague present in another market-place who will deal appropriately if the stop-loss is hit. Should this happen, no further change in position occurs until the local market opens once again.

Stop-Profit Control The concept of stop-profit is associated with that of stop-loss. The stop-loss price starts to move in parallel with the current price once a trading model has achieved a potential profit (3% or slightly less in FX market) since entering the latest position. In other words, being in a situation whereby the model could realize such a gain by immediately entering a neutral position causes the stop-loss price to start moving. The difference between the stop-loss and current prices is kept constant as long as the current price continues moving in a direction that increases the potential profit of the open position. That is, the stop-loss price moves as a ratchet in parallel with the current price. The stop price is allowed to move only during opening hours. It is never adjusted when the market is closed.

The model then enters a neutral position if it detects prices slipping backward. This allows a model to save any profit it has generated rather than lose it when the market abruptly turns. This one-directional movement of the stop-loss price allows the model to capitalize on a price trend.

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