New article Mathematics in Trading: How to Estimate Trade Results has been published:
We all are aware of that "No profit obtained in the past will guarantee any success in future". However, it is still very actual to be able to estimate trading systems. This article deals with some simple and convenient methods that will help to estimate trade results.
We are often warned: "Cut the losses and let profit grow". Looking at
final trade results, we cannot draw any conclusions about whether protective stops
(Stop Loss) are available or whether the profit fixation is effective. We only
see the position opening date, the closing date and the final result - a profit
or a loss. This is like judging about a person by his or her birth and death dates.
Without knowing about floating profits during every trade's life and about all
positions as a total, we cannot judge about the nature of the trading system. How
risky is it? How was the profit reached? Was the paper profit lost? Answers to
these questions can be rather well provided by parameters MAE (Maximum Adverse
Excursion) and MFE (Maximum Favorable Excursion).
Every open position (until it is closed) continuously experiences profit fluctuations.
Every trade reached its maximal profit and its maximal loss during the period between
its opening and closing. MFE shows the maximal price movement in a favorable direction.
Respectively, MAE shows the maximal price movement in an adverse direction. It
would be logical to measure both indexes in points. However, if different currency
pairs were traded,we will have to express it in money terms.
Every closed trade corresponds to its result (return) and two indexes - MFE and
MAE. If the trade resulted in profit of $100, MAE reaching -$1000, this does not
speak for this trade's best. Availability of many trades resulted in profits, but
having large negative values of MAE per trade, informs us that the system just
"sits out" losing positions. Such trading is fated to failure sooner
Similarly, values of MFE can provide some useful information. If a position was
opened in a right direction, MFE per trade reached $3000, but the trade was then
closed resulting in the profit of $500, we can say that it would be good to elaborate
the system of unfixed profit protection. This may be Trailing Stop that we can
move after the price if the latter one moves in a favorable direction. If short
profits are systematic, the system can be significantly improved. MFE will tell
us about this.
For visual analysis to be more convenient, it would be better to use graphical representation
of distribution of values of MAE and MFE. If we impose each trade into a chart,
we will see how the result has been obtained. For example, if we have another look
into "Reports" of RobinHood who didn't have any losing trades at all, we will see that each trade had a drawdown
(MAE) from -$120 to -$2500.
Author: MetaQuotes Software Corp.
Great job Rashid,
I have a question.
How to calculate the Probability of Dependence, %, do you have the formula ?
About 68% of values drawn from a standard normal distribution are within one standard
deviation away from the mean; about 95% of the values are within two standard deviations
and about 99.7% lie within three standard deviations. This is known as the "68-95-99.7 rule" or the "empirical rule."
To be more precise, the area under the curve between −nσ and nσ is
where erf(x) is the error function. To 12 decimal places the first 6 values of the 1-, 2-, and 3-sigma points are
given in the following table:
For the example with 30 trades, I find the following results: Z -0.161776414
W 16, L 14, N 30, R 15, P 448
Can anyone confirm Z calculation is correct ?