Optimal trading elements
While the MPS is self-evident given the parameters placed on it by the analysis, discrete algorithms can be used to generate the MPS and define the optimal transactions and trades more efficiently. "Optimal trading elements" (below) describe the properties needed to study an optimal trade.
We begin the analysis by specifying a cost for building the MPS. This is not the trading cost (applied later) but a money goal filter. For example, if it is equal to $75 per transaction per contract, then each trade (two transactions) will seek a profitable price change exceeding 2 * $75 = $150. The final MPS is evaluated along with trading cost, for instance $7.64 per transaction, per contract or 2 * $7.64 = $15.28.
We can record the optimal trading elements from many sessions and subject them to statistical analysis. For instance, we can evaluate empirical distributions and sample moments of profits and durations. The value of this analysis should be clear. The best typical profit can be used to take an actual profit or set a trailing stop order tighter to the current price. The typical best duration can be used to identify when a current trade is not acting as expected (see "Optimal trade analysis," below).
The number of ticks and volume are liquidity characteristics of the optimal trading elements. They indicate how quickly transactions can be executed and how large they can be. Slippage or execution of limit orders critically depends on this.
The terms a- and b-increments denote the smallest time and price increments between neighboring ticks. The c-increments (differences between the first in the current and last price in the previous sessions) are not in the list of intraday trades. Building a-, b- and price distributions uncovers the time-price microstructure of the optimal trading elements ("Market Profile and the distribution of price," June 2011).
Directional efficiency (DE) is a new geometric and economic concept involving fractal properties of a price path (see "Optimize your MPS," last page).
Analyzing trading elements
In the table, there are 374 trading elements recorded from five business days before Memorial Day 2011. They returned from $142.13 to $933.22 per contract after commissions and fees. Lean hogs presented 18 elements, the least, while wheat provided the most with 110. This confirms an opinion of many professional intraday traders that success comes from many trades with relatively small profit from each trade. The expectation of thousands of dollars from an intraday position often leads to losses (usually after giving up a solid winner).
Many trades lasted from 200-300 seconds to one-two hours. Some trades took just a few seconds, perhaps because a quick liquidation was necessary to avoid a big loss. Trades stagnating for two to three hours are found for the E-mini S&P 500 (results of optimal trades in S&Ps and bonds are included online).
MP and MPS are objective market properties. They could be used as building blocks for creating profitable pattern recognition strategies. Quantitatively expressing the main law of the speculative market, they stand out as fundamental notions. Being well defined and oriented on specified trading goals, they introduce the optimal trading element — a powerful complement to modern trend and volatility analysis. They provide an analytical view of the best trades and reveal new horizons for studying repetitive market properties, the understanding of which is a clear path to trading success.