JBManagement
course 4 of 4

Risk management in trading is a system of rules that determine how much to put into a trade, where to cap the loss and what share of capital may be lost over a period. Statistics from European regulators show that between 74 and 89 per cent of retail accounts lose money when trading CFDs. The main reason is not wrong forecasts but position sizes that are out of proportion to the capital. This course explains the mathematics behind this.

Open an account

lesson 4.1

Let us compare two accounts with the same deposit of 10,000 euros and the same entry accuracy of fifty per cent.

The first trader The first trader risks one per cent per trade, and the average profit equals two units of risk.

Over a hundred trades: fifty losses of 100 euros give minus 5,000 euros, fifty profits of 200 euros give plus 10,000 euros. The net result is plus 5,000 euros.

The second trader The second trader risks ten per cent per trade at a risk-to-reward ratio of one to one.

A run of ten consecutive losses — a statistically expected event at fifty per cent accuracy — is enough to wipe out the account, regardless of the quality of subsequent signals.

the first trader's result over a hundred trades at 1% risk per trade

consecutive losses are enough to wipe out the second trader's account at 10% risk

Conclusion: The same analysis with different risk management produces opposite results. Position size determines the outcome more strongly than forecast quality.

lesson 4.2

Drawdown is asymmetric. To recover what was lost you need to earn more than you lost, because you have to earn it on a reduced capital base.

DrawdownGain required to recoverValue
5%
5.3 %
10%
11.1 %
20%
25 %
30%
42.9 %
40%
66.7 %
50%
100 %
70%
233 %
90%
900 %
drawdown required gain gain above 100% (bar fully filled)

Formula: the required gain equals the drawdown divided by one minus the drawdown.

gain = drawdown / (1 − drawdown)

Practical implication A drawdown of up to ten per cent is recovered in the course of normal work. A fifty per cent drawdown requires doubling the capital, a task that takes most people years. This is precisely why the maximum permissible drawdown is set in advance and trading is stopped when it is reached.

lesson 4.3

The standard: no more than one to two per cent of capital in a single trade.

How many consecutive losses an account can withstand at different risk levels.

Risk per tradeLosses to −20%Losses to −50%
0.5%
1%
2%
5%
10%

At ten per cent risk per trade, seven losing trades in a row wipe out half the account. For any trading system, seven consecutive losses are a routine event.

Additional limits worth setting in advance.

  • Maximum daily loss of three to five per cent of capital. Once reached, trading stops for the day.
  • Maximum monthly loss of ten per cent. Once reached, take a break and review the statistics.
  • Maximum aggregate risk across all open positions of five to six per cent.

lesson 4.4

Formula: the size in lots equals the deposit multiplied by the risk percentage, divided by the product of the stop size in pips and the pip value per lot.

size (lots) = deposit × risk % / (stop (pips) × pip value)

Example one: Deposit 10,000 euros, risk one per cent, pair EUR/USD, stop 25 pips, pip value per lot 10 euros.

Permissible loss: 10,000 multiplied by 0.01 equals 100 euros.

Size: 100 divided by the product of 25 and 10 equals 0.4 lots.

Example two: The same deposit and the same risk, but a stop of 80 pips.

Size: 100 divided by the product of 80 and 10 equals 0.125 lots.

calculator

Position size calculator

Change the parameters and the size is recalculated. The default values match the first example.

Risk per trade against the 1–2% standard1.0%

Position size

0.4lots

10,000 × 1% / (25 × 10) = 0.4
Permissible loss
100 €
Losses in a row to −20%
22
Losses in a row to −50%
69
size = deposit × risk / (stop × pip value)

The key principle that changes the approach to trading. Size is the result of a calculation, not a decision. It depends on the size of the stop. With a wide stop the size decreases, with a tight one it increases. The monetary risk stays constant throughout.

The reverse order — choosing a habitual size first and placing the stop afterwards — means that the risk differs several-fold from trade to trade, and one losing trade cancels out the result of several winning ones.

lesson 4.5

The risk-to-reward ratio is the ratio of the potential loss to the potential profit.

Risk/reward ratioMinimum accuracy to break even
1 to 1over 50%
1 to 1.5over 40%
1 to 2over 33.3%
1 to 3over 25%
2 to 1over 66.7%
3 to 1over 75%

Formula: the minimum accuracy equals one divided by the sum of one and the ratio.

accuracy = 1 / (1 + reward/risk)

Hence an important conclusion: at a ratio of one to three you can be wrong in three trades out of four and not lose money. At a ratio of three to one you need accuracy above seventy-five per cent, and sustaining that level consistently is extremely hard.

A caveat on honest calculation. The ratio makes sense only if the target is realistic. Declaring a ratio of one to five by placing the take-profit at a distance price reaches one time in twenty is not an improvement of the ratio but self-deception. The target must rest on market structure: the nearest significant level, the boundary of a range, the measured target of a pattern.

lesson 4.6

Expectancy is the average result of one trade within a system. It is the only metric that determines whether the system makes or loses money.

Formula: the share of winning trades multiplied by the average profit, minus the share of losing trades multiplied by the average loss.

E = P(win) × avg. profit − P(loss) × avg. loss

Example Share of winners forty per cent, average profit 300 euros, average loss 100 euros. Calculation: 0.4 multiplied by 300 equals 120, minus 0.6 multiplied by 100 equals 60. The expectancy is plus 60 euros.

Each trade brings in 60 euros on average. With twenty trades a month the expected result is around 1,200 euros. Individual trades will be losers, and so will individual months. What matters is the distribution of results over a long series.

If the expectancy is negative, increasing the frequency of trades speeds up the loss of the deposit. This explains why activity by itself does not improve results.

Other metrics worth tracking.

Profit factor

The sum of profits divided by the sum of losses. Benchmark above 1.3.

Maximum drawdown

The largest decline from the account's peak. Benchmark up to twenty per cent.

Average profit in units of initial risk

Benchmark above 0.3.

Share of winning trades

Assessed only together with the risk-to-reward ratio.

lesson 4.7

Opening several positions does not always mean diversification. Many instruments move in sync.

Examples of stable relationships.

  • EUR/USD and GBP/USD have a high positive correlation.
  • EUR/USD and USD/CHF have a stable negative correlation.
  • AUD/USD and NZD/USD have a high positive correlation.
  • Gold and the dollar index are, as a rule, negatively related.

Having opened long positions in EUR/USD, GBP/USD and AUD/USD with one per cent risk each, you are in effect holding a single position against the dollar with three per cent risk.

Rule: treat the aggregate risk across correlated instruments as the risk of a single position. Cap the total risk across all open positions at five to six per cent of capital.

lesson 4.8

Recurring errors caused by the way the mind works, not by a lack of knowledge.

Disposition effect

The tendency to take profits quickly and hold losing positions for a long time. Psychologically, you want to lock in a profit while it is there and wait out a loss. The result: small profits and large losses, that is, a systematically deteriorating risk-to-reward ratio. This is probably the most expensive of the typical mistakes.

Confirmation bias

Seeking information that supports a decision already made and ignoring information that contradicts it. Shows up as cycling through indicators until one displays the desired signal.

Sunk cost fallacy

Holding a losing position with the justification "I have already lost so much, I can't close now". The loss incurred has no bearing on the position's prospects; only the current market situation matters.

Revenge trading

Immediately opening a new trade with an increased size after a loss in order to win the money back. The most destructive pattern of behaviour, because it combines an emotional decision with exceeding the permissible risk.

Gambler's fallacy

The belief that after a run of losses a winning trade is due. Each trade is independent; previous results do not change the probability of the next one.

Fear of missing out

Entering a move that has already happened out of fear of missing it. As a rule, this happens at the end of an impulse, at the least favourable price.

lesson 4.9

A journal is the only way to tell a working system from luck and to find the specific source of losses.

FieldPurpose
Date and time of entry and exitIdentify the hours when results are worse.
InstrumentFind the instruments where the system does not work.
DirectionCheck for a bias in one direction.
Size and risk in per centVerify compliance with the rules.
Entry, stop and target pricesAssess the planned risk-to-reward ratio.
Actual resultCompare the plan with the execution.
Reason for entryDetermine which setups are profitable.
Rule-compliance flagThe key field, see below.
Emotional stateFind the link between your state and losses.
Chart screenshotRestore the context during the review.

The rule-compliance field is the most informative. By splitting the statistics into trades taken by the rules and trades that departed from them, you often find that the system is profitable and the loss is created by impulsive trades outside the rules. This reframes the task: the problem is not the system but discipline.

Review: go through all the week's trades weekly, recalculate the metrics monthly and compare them with the previous period.

lesson 4.10

1.

Hypothesis

Formulate an assumption about recurring market behaviour. For example: after a breakout of the weekly high and a return to it, the move continues in the direction of the breakout.

2.

Rules

Describe the conditions for entry, stop placement, profit-taking and position size so that two different people applying them to the same chart would make the same decision. If a rule allows interpretation, it is not a rule.

3.

Backtesting

Test the system on at least one hundred trades over a historical period that includes different market conditions: trend, range, a period of elevated volatility. Calculate the expectancy, the profit factor and the maximum drawdown.

4.

Forward testing

Apply the system to the live market with the minimum size for one to three months. Historical results are almost always better than real ones, because in hindsight the outcome is known and the markup is unwittingly fitted to it.

5.

Live operation

Move to working size only after confirmation in forward testing. Increase the size gradually.

6.

Review

Revise the system on the basis of accumulated statistics, not after an individual losing trade. Changing the rules after every loss means there is no system.

A typical mistake is over-optimisation. A system with many parameters can always be tuned to show an excellent result on historical data. Such tuning describes past noise rather than a stable pattern, and it does not work in the real market. The fewer the parameters, the more robust the system.

Responsible trading

Trading CFDs with leverage carries a high risk of losing capital. A few principles worth adopting before opening an account.

  • Trade only with money whose loss would not affect your financial position or standard of living.
  • Do not trade with borrowed money, loans or funds set aside for essential expenses.
  • Do not treat trading as a source of regular income at an early stage.
  • Set a maximum permissible drawdown and stop when it is reached.
  • If trading starts to affect your sleep, relationships or work, that is a signal to take a break.

If trading has ceased to be a controlled activity and has taken on the features of compulsive behaviour — raising stakes to win back losses, hiding losses from family, trading with borrowed money — it makes sense to seek support from a professional. EU countries have free support services for problem gambling and financial behaviour.

Risk disclosure
self-check

Answered 0 of 80%

1.Why is risk management more important than forecast accuracy?

Incorrect. The correct answer is B

2.What capital gain is needed after a 50% drawdown to restore the original deposit?

Incorrect. The correct answer is B

3.What standard risk per trade is considered the most common for a professional approach?

Incorrect. The correct answer is C

4.What does position size primarily depend on when calculating the size of a trade?

Incorrect. The correct answer is C

5.What is the minimum risk-to-reward ratio that allows you to break even at an accuracy of about 33%?

Incorrect. The correct answer is B

6.What does the expectancy of a trading system show?

Incorrect. The correct answer is C

7.Why might opening several positions in different currency pairs not be true diversification?

Incorrect. The correct answer is B

8.Which bias occurs when a trader holds a losing position thinking "I have already lost too much, I can't close now"?

Incorrect. The correct answer is C

F & Q

The generally accepted guideline is one to two per cent of capital per trade. At ten per cent risk, seven losing trades in a row wipe out half the deposit, and such a run is a normal event for any system.

The size in lots equals the deposit multiplied by the risk percentage, divided by the product of the stop size in pips and the pip value. For example, with a deposit of 10,000 euros, one per cent risk and a 25-pip stop on EUR/USD, the size is 0.4 lots.

The main reason is a position size out of proportion to the capital and the absence of a loss limit. Secondary reasons are emotional decisions after a loss, holding losing positions and taking profits prematurely.

From one to one and a half upwards. At a ratio of one to two the system remains profitable at an accuracy above thirty-three per cent.

The average result of one trade: the share of winners multiplied by the average profit minus the share of losers multiplied by the average loss. A positive value means the system makes money over a long series of trades.

Yes. Without a stop-loss, the size of the loss is determined by the market, not the trader. Calculating position size without a known distance to the stop is impossible in principle.

At least one hundred trades on historical data plus one to three months of testing on the live market with the minimum size.

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