**OTE properties**

With our stop-and-reverse MPS, a BOTE always follows a SOTE and vice versa. Monitoring the arrival of ticks, it is easy to detect the advent of a new OTE. However, new ticks can affect other properties of the OTE, such as profit and duration. As for the profit, the following three scenarios exist after the initial tick of an OTE is detected: 1) The profit of the current OTE will grow, 2) the current OTE will be replaced by a new one of the opposite type or 3) the session will terminate.

The financial difference between the ticks is double the filtering cost (f-cost) minus the transaction cost (t-cost) per contract. Because the ending tick is unknown in advance, the result will depend on how frequently and how far OTE profits grow after the initial tick. The answer is given by empirical distributions of OTE profits, and under other equal conditions, it depends on the f-cost.

The number of OTEs depends on what we set as our filtering cost. The greater the f-cost, the fewer OTEs for a trading session. If the f-cost becomes too large, this number becomes zero. With a zero f-cost, the profit is maximized. We do not consider this case, however, because all computations are done with t-cost = $7.40, which is less than the f-cost. By applying MPS algorithms to individual trading sessions, we ignore the potential of the c-increments. This corresponds to intraday trading, where all positions are opened and closed in a single session.

If we set the f-cost to $49.99, we consider price moves exceeding 2 * $49.99 = $99.98 as significant. This produces a sequence of alternating BOTE and SOTE with a price differential corresponding to this dollar amount. On a chart, they appear as adjacent time intervals, where the starting and ending ticks mark local minimum and maximum prices.

Then, the OTEs are evaluated using the t-cost. Because live cattle’s minimum tick is 0.025, or $10, each filtered-out OTE will have a price differential of $100 or larger. Because of the t-cost, the smallest OTE profit will be equal to $100 – 2 * $7.40 = $85.20. Other possible profit values are obtained by adding $10 to this amount: $95.20, $105.20, …

Because of discrete prices, it is sufficient to examine the t-cost $7.40 and other values with the increment of $5: $9.99, $14.99, ..., $124.99. The last will target price moves of $250 or larger. The 801 moves of this magnitude are found in 225 electronic sessions over our testing data. The mean (801/225 = 3.56) indicates that a trader should be prepared to get at least three moves exceeding $250 in a single electronic session for the most liquid contract (see “OTE means,” below).