Teacher guide - worked answers
Teacher copy - contains the answers. Use the separate student workbook for independent work. The marking notes assess only the stated hypothetical model.
E01 / worked answer
Sizing a yen pair for a euro account
Decision: Calculate the pip value in JPY, convert it to EUR, divide the EUR risk budget by the EUR loss per lot, and round the volume down to the allowed step.
Numeric target: 0.66 lots
Worked calculation
- Budget = 10,000 × 1% = 100 EUR.
- Pip value per lot = 100,000 × 0.01 = 1,000 JPY; 1,000 × 0.006 = 6 EUR.
- Risk per lot = 25 × 6 = 150 EUR. Theoretical volume = 100 / 150 = 0.666666… lots.
- Round down to 0.66 lots. Planned price-move loss = 0.66 × 150 = 99 EUR.
Explain the result
Pip size is a price increment; pip value is a monetary result. The account currency belongs in the final conversion.
A leverage setting does not change pip value at an unchanged contract and volume.
At 0.66 lots, the modelled loss at the stop is 99 EUR. Rounding to 0.67 lots raises it to 100.50 EUR.
Neither number is a guaranteed execution loss. Costs and adverse fills have deliberately been left out of this exercise.
Common mistake: Treating every standard lot as 10 units of the account currency per pip, or rounding the calculated size up and exceeding the risk budget.
Model assumptions
- All numbers are synthetic. The supplied JPY-to-EUR rate is fixed for the exercise.
- Linear 100,000-unit FX contract; 0.01 JPY pip; zero spread, slippage and commission.
https://forexmechanics.com/tools/decision-lab/#case=jpy-position
E02 / worked answer
Execution costs and net expectancy
Decision: Convert the additional cost from pips to R and subtract it once from gross expectancy; it applies to winners and losers.
Numeric target: -0.04 R per trade
Worked calculation
- Gross expectancy = 0.45 × 1.8 − 0.55 × 1 = 0.26R.
- Additional cost = 1.5 / 5 = 0.30R per trade.
- Net expectancy = 0.26 − 0.30 = −0.04R per trade.
Explain the result
A tight stop makes a fixed pip cost a larger fraction of R. Moving the stop can also change the strategy, its hit rate and its payoffs; the cost ratio alone cannot select a better stop.
For an already-net journal, deduct only costs that are genuinely additional to those outcomes.
The arithmetic changes from +0.26R gross to −0.04R net per trade under these fixed assumptions.
Changing discipline alone does not change this arithmetic. The assumed win rate, payoff distribution and measured cost would need a fresh, consistent assessment.
Common mistake: Keeping gross expectancy as the final result, charging costs only to losing trades, or subtracting a cost from both the payoffs and expectancy.
Model assumptions
- Synthetic two-average outcome model with constant inputs; not a forecast.
- The 1.5-pip cost is additional, charged on every trade and not already in the payoffs.
https://forexmechanics.com/tools/decision-lab/#case=execution-costs
E03 / worked answer
Shared dollar exposure
Decision: All three long base/USD positions contain negative USD legs, so the portfolio shares one dollar direction. Currency exposure and the sum of planned stop-loss budgets are separate measures.
Numeric target: -30000 USD exposure
Worked calculation
- Each base leg = 0.10 × 100,000 = 10,000 base units.
- EUR/USD USD leg = −10,000 × 1.10 = −11,000 USD.
- GBP/USD USD leg = −10,000 × 1.25 = −12,500 USD.
- AUD/USD USD leg = −10,000 × 0.65 = −6,500 USD.
- Net USD leg = −11,000 − 12,500 − 6,500 = −30,000 USD.
Explain the result
Shared currency exposure can be calculated without estimating historical correlations. It does not imply that the three pairs will move identically.
A coherent shock scenario specifies each currency relative to the same account currency. Stop triggers, gaps and broker netting rules require separate treatment.
The portfolio has a −30,000 USD quote leg against its three positive foreign-currency legs. This is an exposure measure, not a 30,000 USD maximum loss.
The separate planned stop-loss budgets sum to 300 USD. They are a different measure and do not establish a worst-case portfolio loss or independent outcomes.
Common mistake: Assuming different pair names imply independent outcomes, or treating the signed currency exposure as a maximum possible cash loss.
Model assumptions
- Synthetic prices and positions; all conversion rates refer to one illustrative instant.
- The three 100 USD stop budgets are stipulated separately. Currency exposure is not a cash balance or a loss bound.
https://forexmechanics.com/tools/decision-lab/#case=usd-concentration
E04 / worked answer
Order of returns and maximum drawdown
Decision: The same multiplicative factors produce identical final equity in this model, while their order can change the running peak and maximum drawdown.
Numeric target: 19 %
Worked calculation
- Sequence A equity: 10,000 → 11,000 → 12,100 → 13,310 → 11,979 → 10,781.10 USD.
- Peak = 13,310 USD; subsequent trough = 10,781.10 USD.
- Maximum drawdown = (13,310 − 10,781.10) / 13,310 × 100 = 19%.
Explain the result
Peak-to-trough maximum drawdown differs from loss measured only against starting capital. Include the initial account value when tracking the peak.
Resampling can investigate conditional sequence risk, but independent resampling can lose dependence. Moving blocks preserve some local ordering, not every feature of a changing market.
Both sequences finish at 10,781.10 USD, a 7.811% gain in this model. Sequence A reaches 19% maximum drawdown; Sequence B reaches 10.9%.
A path-dependent constraint can therefore distinguish two sequences with the same final balance. The five invented trades do not describe a real strategy distribution.
Common mistake: Measuring every decline against the starting account instead of the running peak, or assuming equal win rates force identical drawdowns.
Model assumptions
- All five observations are invented, net of any already-included costs; extra cost is zero.
- The 10% risk fraction is an arithmetic illustration, not a recommended or safe threshold. No deposits, withdrawals or execution variation.
https://forexmechanics.com/tools/decision-lab/#case=backtest-sequence
E05 / worked answer
Cleaning a mixed journal export
Decision: Retain A-01, one B-02 and D-04. Exclude the confirmed accidental duplicate and the planned target; retain the legitimate losing trade.
Numeric target: 0.6666666667 R per trade
Worked calculation
- Valid IDs: A-01, B-02 and D-04. Valid sample size = 3.
- Total realised net R = 1 − 1 + 2 = 2R.
- Mean net R = 2 / 3 = 0.666666…R, or 0.667R to three decimal places.
Explain the result
Exclusions need reasons and an audit trail. Do not remove legitimate losing trades simply because they make the mean smaller.
Real exports can contain partial fills and reused order IDs. Define the unit of analysis before deciding what counts as a duplicate.
The cleaned mean is 0.667R from three completed trades. Averaging all five rows would mix realised results with a plan and a duplicate.
Three invented trades are enough to demonstrate data cleaning, not to establish an edge or a reliable future win rate.
Common mistake: Averaging every numeric R cell, double-weighting the copied loss, or removing a legitimate losing trade while cleaning the file.
Model assumptions
- The file is synthetic. The duplicate is explicitly known to be an accidental copy.
- The completed R values are realised and already net. The planned +2R is a target, not an outcome.
https://forexmechanics.com/tools/decision-lab/#case=journal-quality
E06 / worked answer
Free margin and stop-loss risk
Decision: Margin is collateral based on notional value and the supplied leverage model. Planned stop-loss risk is calculated separately from volume, stop distance and pip value. Free margin subtracts both existing and new margin from current equity.
Numeric target: 2166.666667 USD
Worked calculation
- New notional = 0.50 × 100,000 × 1.10 = 55,000 USD.
- New margin = 55,000 / 30 = 1,833.333… USD.
- Post-position free margin = 5,000 − 1,000 − 1,833.333… = 2,166.666… USD, or 2,166.67 USD.
- Separate planned price-move loss = 0.50 × 20 × 10 = 100 USD.
Explain the result
Use current equity rather than replacing it with an old account balance. Current used margin and new-position margin must refer to consistent account units.
Higher leverage changes collateral in this model at a fixed notional position; it does not change the cash value of a 20-pip move.
The simple model leaves 2,166.67 USD of free margin after the new position, assuming equity does not change on entry. The separately planned price-move loss is 100 USD.
Those values do not reproduce broker margin tiers, hedging offsets, spread on entry, equity changes or close-out rules.
Common mistake: Treating required margin as the loss at the stop, or omitting existing used margin because it was committed before the new trade.
Model assumptions
- Synthetic linear FX contract and a simple 30:1 leverage model; not a statement of rules applying to a particular account.
- Equity is held constant at entry and additional costs, tiers and offsets are zero.
https://forexmechanics.com/tools/decision-lab/#case=margin-risk
E07 / worked answer
Realised loss after an adverse fill
Decision: Use the full 35-pip actual adverse move from entry to closing and add the round-trip commission once. The planned 20-pip distance is not an extra move to add.
Numeric target: 178.5 USD loss
Worked calculation
- Position pip value = 0.50 × 10 = 5 USD per pip.
- Actual price-move loss = 35 × 5 = 175 USD.
- Round-trip commission = 0.50 × 7 = 3.50 USD.
- Total loss = 175 + 3.50 = 178.50 USD.
Explain the result
Separate the trigger level from the realised fill. Evaluate the actual contract and any explicit execution protection separately.
Spread and slippage should not be added again if their effect is already contained in the entry-to-exit price distance being used.
The planned 20-pip loss plus commission was 103.50 USD. The supplied 35-pip execution produces a total loss of 178.50 USD, which is 75 USD more.
The example demonstrates a specified adverse fill. It does not predict how far any future gap or execution can move.
Common mistake: Using the planned stop as a guaranteed fill, adding the planned 20 pips to the full actual move, or charging price effects already included in the supplied execution distance again.
Model assumptions
- All prices and the adverse closing distance are invented and supplied as facts of this exercise.
- One round-trip commission of 7 USD per lot; no separate additional spread, slippage or financing charge.
https://forexmechanics.com/tools/decision-lab/#case=gap-execution
E08 / worked answer
Recovery from a drawdown
Decision: Divide the missing capital by the remaining account capital, because the recovery gain is measured from the smaller post-loss base.
Numeric target: 33.33333333 %
Worked calculation
- Missing capital = 10,000 − 7,500 = 2,500 USD.
- Required gain = 2,500 / 7,500 × 100 = 33.333333…%.
- A gain of 25% from 7,500 would reach only 9,375 USD.
Explain the result
Drawdown and recovery use different denominators. At a 50% loss, the same identity gives a 100% recovery requirement.
A deposit changes the capital available but is not a trading gain; keep cash flows separate in performance records.
The arithmetic recovery requirement is 33.33%, with no allowance here for subsequent costs, taxes or cash flows.
This is a percentage identity, not a forecast, a deadline or a reason to increase position risk.
Common mistake: Repeating the original loss percentage as the required recovery gain, or applying a universal rule that simply doubles every drawdown percentage.
Model assumptions
- Synthetic account values with no deposits, withdrawals or other cash flows.
- The calculation restores the starting nominal amount; it does not forecast the return attainable.
https://forexmechanics.com/tools/decision-lab/#case=drawdown-recovery
E09 / worked answer
Net R across two partial exits
Decision: Weight each exit by the volume actually closed, add the two cash results, deduct the single total commission and divide by the unchanged original price-risk amount.
Numeric target: 1.465 R
Worked calculation
- First partial gross P&L = 0.50 × 20 × 10 = 100 USD.
- Second partial gross P&L = 0.50 × 40 × 10 = 200 USD.
- Total net P&L = 100 + 200 − 7 = 293 USD.
- Net R = 293 / 200 = 1.465R.
Explain the result
Keep the initial risk definition fixed for a completed-trade R metric, even when volume changes later.
A broker may have minimum-ticket fees or a different charge convention. Those are deliberately excluded from this linear commission example.
The weighted gross result is 300 USD, or 1.5R. The stated commission reduces it to 293 USD, or 1.465R.
This comparison does not establish that partial exits outperform another management rule; a strategy comparison needs its own consistent sample.
Common mistake: Adding the full-position +1R and +2R outcomes without half-volume weights, changing the R denominator after an exit, or charging the full 7 USD commission to each half.
Model assumptions
- Synthetic linear contract, initial risk defined before costs, with no financing or additional price cost.
- The 7 USD figure is the total round-trip charge for the full original volume, not a separate fee for each exit.
https://forexmechanics.com/tools/decision-lab/#case=partial-exit
E10 / worked answer
Evaluating a frozen strategy on held-out trades
Decision: Report the held-out observations separately for the version frozen beforehand, with the small sample and training selection process visible. Once these outcomes guide retuning, they are no longer untouched evaluation data for the changed version.
Numeric target: -0.3 R per trade
Worked calculation
- Holdout total = 1 − 1 − 1 + 0.5 − 1 = −1.5R.
- Observed holdout mean = −1.5 / 5 = −0.30R per trade.
- The selected +0.40R training mean is a separate statistic from a different dataset.
Explain the result
Record every variation tried, the data split and the rules frozen before evaluation. This makes selection and later changes inspectable.
Bootstrap scenarios condition on the supplied sample. They do not repair selection bias, omitted costs or a nonrepresentative test period.
The illustrative holdout reports −0.30R per trade across five observations. That is the observed result of this sample, not a known population expectancy.
Five trades do not prove that the strategy has no edge or a stable negative edge. A changed rule set needs a new version and a genuinely fresh evaluation plan.
Common mistake: Treating the selected training mean as proven future expectancy, mixing it into the holdout average, or retuning on the holdout while continuing to call it untouched.
Model assumptions
- All training and holdout numbers are invented; no real strategy track record is claimed.
- The five holdout outcomes are already net and all are retained. Their mean is descriptive, not a forecast or proof of an edge.
https://forexmechanics.com/tools/decision-lab/#case=out-of-sample