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108 11.2.2 Simulated Trader The simulated trader allows the system to control continuously its performance by simulating a trade every time the trading model gives a recommandation. In the following, we shall describe the different part that composes the simulated trader. Opportunity Catcher The trading model may make a deal recommendation in two distinct ways. One, the gearing calculator may make a recommendation that is then authorized by the deal acceptor. Two, hitting the stoploss price activates the stoploss detector. Whichever way a deal comes about, the opportunity catcher is activated. The opportunity catcher manifests itself on the useragent as an eyecatching signal for the FX dealer to buy or sell according to the recommendation. While he or she is actively dealing, the opportunity catcher in the trading model collects the transaction price with which to deal, either the median bid price if going from a longer position to a shorter one or the median ask price if going from a shorter position to a longer one. This search for the transaction price lasts for 2 or 3 min depending on the currency, the assumption being that a quoted price has a lifetime of about 2 or 3 min even if it is superseded by later quotes. After the 2 or 3 min search period, a second signal appears on the useragent signifying that the trading model has made a simulated deal using the transaction price found by the opportunity catcher. The FX dealer then concludes his or her dealmaking activities and waits until the trading model produces another recommendation.3 Bookkeeper The bookkeeper executes simulated deals on behalf of the trading model. It keeps track of all deals that have been made and evaluates statistics demonstrating the performance of the trading model. The bookkeeper computes a set of quantities that are important for the different trading rules like the following: The maximum return when open, which is the maximum value of rc from a transaction i to a transaction / + 1 reached during opening hours, The minimum return when open, which is the minimum value of rc from a transaction / to a transaction i + 1 reached during opening hours. In this section we describe some of the important variables that need to be watched for deciding on th£ quality of a specific model. These are the following: The total return, Rt, is a measure of the overall success of a trading strategy over a period T, and is defined by As a point of detail, the opportunity catcher is not activated for a stoploss deal occurring outside market hours. In this case the trading model deals directly. A human trader following the model should then make a corresponding deal for himself as quickly as possible. (11.4)
where is the total number of transactions during the period T, j is the jth transaction and ry is the return from the j,h transaction. The total return expresses the amount of profit (or loss) made by a trader always investing up to his/her initial capital or credit limit in his/her home currency. The cumulated return, Cr, is another measure of the overall success of a trading model wherein the trader always reinvests up to his/her current capital, including gains or losses Cr = l\ (I + rj)  I . (11.5) 7 = 1 This quantity is slightly more erratic than the total return. The maximum drawdown, Dj, over a certain period T = t  to, is defined by DT = max( R,a  R,b \ t0 < ta < tb < tE ) (11.6) where Rta and Rtb are the total returns of the periods from to to ta and tb, respectively. The profit over loss ratio provides information on the type of strategy used by the model. Its definition is Pr NT{r:\r: >0)  = 1 1 (11.7) where Nr is a function that gives the number of elements of a particular set of variables under certain conditions during a period T. Here the numerator corresponds to the number of profitable deals over the period T and the denominator is the number of losing deals over the same period. 11.3 RISK SENSITIVE PERFORMANCE MEASURES Evaluating the performance of an investment strategy generally gives rise to many debates. This is due to the fact that the performance of any financial asset cannot be measured only by the increase of capital but also by the risk incurred during the time required to reach this increase. Returns and risk must be evaluated together to assess the quality of an investment. In this section we describe the various performance measures used to evaluate trading models. The annualized return, Rt,a, is calculated by multiplying the total return (Equation 11.4) with the ratio of the number of days in a year to the total number of days in the entire period.4 In order to achieve a high performance and good 4 If it is the annualization of one particular return (for one trade going from neutral to neutral), one simply needs to multiply the return by the ratio of 1 year in days to the time interval from neutral to neutral. Usually, the annualization of the total return is calculated for all the trades during a whole year. This is simply the sum of all trade returns not annualized during the whole year. If at the end of the year there is an open position, the current return of your open position is added to the total return.
acceptance among investors, investment strategies or trading model performance should provide high annualized total return, a smooth increase of the equity curve over time, and a small clustering of losses. The fulfilment of these conditions would account for a high return and low risk. In addition to favoring this type of behavior, a performance measure should present no bias toward lowfrequency models by including always the unrealized return of the open position and not only the net result after closing the position. Already in 1966, Sharpe (1966) introduced a measure of mutual funds performance, which he called at that time a rewardtovariability ratio. This performance measure was to later become the industry standard in the portfolio management community under the name of the Sharpe ratio, Sharpe (1994). Practitioners frequently use the Sharpe Ratio to evaluate portfolio models. The definition of the Sharpe ratio is ( .8) where r is the average return and a} is the variance of the return around its mean and is an annualization factor,5 depending on the frequency at which the returns are measured Sharpe (1994).6 Unfortunately, the Sharpe ratio is numerically unstable for small variances of returns and cannot consider the clustering of profit and loss trades. There are many aspects to the trading model performance; therefore, different quantities have to be computed to assess the quality of a model. In the section on the bookkeeper, we already described some of the important variables that need to be watched for deciding on the quality of a specific model. Here we introduce the two risksensitive measures that are the basic quantities used in further sections to analyze the behavior of trading models. 11.3.1 Xeffi A Symmetric Effective Returns Measure As the basis of a risksensitive performance measure, we define a cumulative variable Rt, at time t, as the sum of the total return Rt of Equation 11.4 and the unrealized current return rc (Equation 11.3) of the open position. This quantity reflects the current value of the investment and includes not only the results of previously closed transactions but also the value of the open position (marktomarket). This means that Rr is measuring the risk independently of the actual trading frequency of the model. Similar to the difference between price and returns, the variable of relevance for the utility function is the change of R over a time 5 , = \/12 for monthly frequency. 6 Here the Sharpe ratio refers to the calculation of the returns in the expressed currency and the variance is computed with monthly returns. The monthly returns are the total return achieved to the end of the month (sum of all returns up to now, including the current return of the open position) minus the total return achieved at the end of the previous month.
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