Trading myths: ten common beliefs, tested with arithmetic

Leverage changes the size of the position a given sum can open. It does not change which way the price goes. A stake of 1,000 used in full at 1:100 answers for a position of 100,000. A move of 1% in favour is a gain of 1,000, which doubles the stake. A move of 1% against is a loss of 1,000, which is all of it.

The same 1% move at 1:10 is 100 either way: a tenth of the stake. Leverage multiplies the result in both directions by the same number, and it brings the point at which a position is closed by the provider nearer. More leverage is a larger outcome, with the sign undecided.

A win rate counts trades and ignores their size. Take a method that wins nine times in ten, gaining 10 each time, and loses once in ten, losing 100. Over ten trades it gains 90 and loses 100. It is right 90% of the time and loses money.

The figure that joins the two is expectancy: the win rate times the average win, less the loss rate times the average loss. Here 0.9 × 10 − 0.1 × 100 = −1 a trade. The worked example below takes the same sum further.

The opposite case is as easy to build. A method that wins only four times in ten, with each win twice the size of each loss, makes 4 × 2 − 6 × 1 = 2 units over ten trades.

For any ratio of win to loss there is a win rate at which a method only breaks even: one divided by one plus the ratio. At two to one it is one in three, about 33%. At one to one it is 50%. These are figures before costs, and they describe a sum, not a forecast: nothing says a method will achieve the win rate or the ratio written on paper.

An indicator is arithmetic on prices that have already printed. A three-period moving average of closes at 10, 11 and 12 is 11. Every number that went into it was known before it was drawn, and it contains nothing else.

An indicator can describe: that recent prices are above their average, or that the last move was fast. Whether what it describes tends to continue is a separate claim, which has to be tested and which a chart cannot prove by looking convincing in hindsight. Chart school gives the sum behind each indicator so that it can be seen for what it is.

A stop is an instruction to trade when a price is reached. Much of what looks like a hunt is the spread. A chart usually draws the bid. A stop on a short position is a buy order, and is triggered by the ask. If the chart’s high is 1.1000 and the spread is 2 pips, the ask reached 1.1002, and a stop at 1.1002 was filled although the line on the chart never touched it.

Spreads also widen when a market is thin or news is out, and a stop placed inside a market’s ordinary range will be reached by ordinary movement. Many traders place stops at the same obvious levels, so a price that gets there meets a cluster of orders.

None of this says misconduct never happens. Where it does, it is a matter for evidence and for a regulator. The arithmetic says only that a stop being reached is not, by itself, evidence of it.

An account of 100 that loses 50% holds 50. A gain of 50% on 50 is 25, which makes 75. To return to 100 the account must gain 50 on 50, which is 100%.

The gain needed is the loss divided by what is left. A 10% loss needs about 11%, a 20% loss needs 25%, and a 90% loss needs 900%. The further down an account goes, the steeper the climb back, which is why the size of a loss matters more than the count of losses.

The plan is to stake 1, and after each loss to double, so that the first win recovers everything and leaves a profit of 1. After ten losses in a row the stakes have been 1, 2, 4 and so on up to 512, and the total lost is 1,023. The eleventh stake is 1,024, placed in order to end 1 ahead.

The plan needs an account with no bottom and a provider with no maximum size. Every real account has both limits. The method does not remove the chance of a long run of losses. It collects many small gains and gives them back, with more, in one.

Take a method that aims for 10 pips and risks 10 pips, with a cost of 1 pip for each round trip. A win now brings 9 and a loss takes 11. To break even the method must win 11 times in 20, which is 55%, where without costs it needed 50%.

The shorter the distance a trade aims for, the larger the share of it that costs take. One pip is a tenth of a 10-pip target and a hundredth of a 100-pip target. A cost that is negligible for one way of trading can be the whole edge of another.

Suppose a rule with no merit at all has a 5% chance of looking good on a given stretch of past prices by luck alone. Try twenty unrelated versions of it. The chance that at least one looks good is 1 − 0.95 multiplied by itself twenty times, which is about 64%.

A search through many settings will usually find something that worked, whether or not anything real is there. What separates the two is how the rule was chosen, and how it does on prices it was never shown.

With a win rate of 50%, the chance that five particular trades in a row all lose is 0.5 multiplied by itself five times: about 3%. That sounds rare. But in a series of 100 such trades there are many places for a run of five to begin, and at least one such run is more likely than not.

What a streak does to an account depends on size. Five losses in a row at 1% of the balance each leave about 95% of it. At 10% each they leave about 59%. A streak is ordinary in any series of uncertain outcomes, and the question it raises is less whether the method has failed than whether the account was sized to live through it.