Trading is attractive because markets provide huge profit opportunities in short periods of time. The maximum profit strategy (MPS) provides a quantitative measure of this opportunity relative to frequency and size. A market’s MPS is the sequence of optimal buy, sell and do-nothing actions that generates the maximum profit, with respect to trading times, prices, execution costs, capital, margins and government regulations.
MPS is an objective market property associated with any sequence of ticks. Positive and negative numbers are used to express long and short trades. A do-nothing, or non-action, is recorded as zero. This strategy is a hypothetical analytical tool that never loses money. (For a fundamental description of MPS and more on how it can be used to build real trading strategies, see “Trading system analysis: Learning from perfection,” November 2011.)
The optimal trading element (OTE) includes all the market properties associated with an optimal trade within an MPS. In actual application, a trader who is applying an MPS-based strategy “buys” and “sells” OTEs rather than futures contracts or shares.
MPS, OTE: A review
There are three types of MPS described in the November 2011 article. Here, we’re going to examine a stop-and-reverse approach, which alternates between long and short positions of the same size.
This system will be constructed by the l- or r-algorithm (see “Modeling Maximum Trading Profits with C++,” John Wiley & Sons, 2007). For example, let’s say that four consecutive time periods of live cattle futures prices are 123.025, 123.275, 122.900 and 122.875, while the cost of a transaction association with each price would be 7.40, 7.40, 7.40 and 7.40. Given this information, then the optimal trading strategy would be: 1, -2, 0, 1.
In English, the transactions are grouped into two trades: Buy, sell one to go flat, sell one to go short, do nothing, buy one to go flat. The buy OTE (BOTE) and the sell OTE (SOTE) are determined by the sign of the transactions. Their profits are $85.20 and $145.20, and their durations are t2 – t1 = 1 and t4 – t2 = 2. (Purely mathematically speaking, this would be (–123.025 * 1t1 – 123.275 * -1t2) * 400 – 2 * 7.40 + (–123.275 * -1t2 – 122.875 * 1t4) * 400 – 2 * 7.40 = $85.20 + $145.20 = $230.40).
MPS is an analytical tool used in hindsight. An MPS and the prices determining it are unknown in advance. However, signals from a pair of MPSs can be used for developing real trading rules (see “Idealized models for real profits,” May 2008). OTEs offer even more possibilities. Here, we’ll create an MPS employing an arbitrary filtering cost, or f-cost, approach and evaluate it with a smaller transaction cost, or t-cost.
Time and sales data are presented daily on the CME Group web site. The intraday ticks of real transactions of electronic trading were studied for the most liquid live cattle contracts. These included February, April, June, August, October and December 2011 and the February 2012 contracts.
The total numbers of sessions are 225 and there are 1,134,304 ticks. The electronic trading hours are 9:05 a.m. Monday to 1:55 p.m. Friday (Central time) with halts from 4 p.m.-5 p.m. each day. Each electronic transaction tick includes time, price and size.