Close the lesson.
Try the problem.
Show the calculation or reasoning before opening the answer. The point is not speed. It is noticing which assumptions you forgot.
A stop changes, so the size changes
An account has 12,000 units of currency. A hypothetical planned risk budget is 0.5%, the entry is 40, and the stop is 38.50. Round-trip cost is 0.10 per unit. What whole-unit size fits the budget? What if the stop moves to 37?
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The budget is 60. At a 1.50 price distance plus 0.10 cost, floor(60 / 1.60) = 37 units, with planned risk 59.20. At a 3.00 distance plus 0.10 cost, floor(60 / 3.10) = 19 units, with planned risk 58.90. Keeping 37 units after widening the stop raises the planned loss to 114.70. These are planning figures, not guaranteed loss limits.
Winning often is not the same as making money
A hypothetical process wins 70% of the time. Average gross wins are 40, average gross losses are 110, and average costs are 3 per trade. Calculate expectancy.
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Expectancy = 0.70 × 40 − 0.30 × 110 − 3 = −8 per trade. The high win rate does not overcome the larger losses and costs. The estimate also assumes that the sample is representative, which still needs to be tested.
Two percentage moves are not mirror images
A portfolio falls from 20,000 to 14,000. What is the drawdown, and what gain returns it to 20,000?
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The loss is 6,000 / 20,000 = 30%. Recovery needs 6,000 / 14,000 = 42.857%, not 30%. A 30% gain from 14,000 reaches only 18,200. Contributions would change the accounting and must be separated from investment return.
Translate the quote before sizing
For a hypothetical GBP/JPY exposure, one pip is 0.01 JPY per GBP. The position is 20,000 GBP and the account conversion is 0.0067 USD per JPY. What is the USD pip value?
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Pip value = 20,000 × 0.01 × 0.0067 = 1.34 USD per pip. A 40-pip move is about 53.60 USD before costs if the conversion rate is unchanged. The account conversion can change, and a contract may use a different multiplier.
A flat price is not necessarily break-even
Buy 100 units at 25, paying a 0.2% entry commission and a 0.2% exit commission. Ignore other costs. What sale price breaks even?
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The sale price must satisfy 100 × sale × 0.998 = 100 × 25 × 1.002. Sale = 25 × 1.002 / 0.998 ≈ 25.1002. The required rise is about 0.4008%. A return to the entry price still loses the commissions.
One shock, three labels
A 10,000 portfolio contains 4,000 in asset A, 3,000 in B, 1,000 in C and 2,000 cash. Simultaneous hypothetical shocks are −20%, −10% and −50%. What is the portfolio loss?
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Losses are 800, 300 and 500, totaling 1,600. Portfolio drawdown is 16%, with 8,400 remaining, assuming cash is unchanged and no leverage, fees or FX effects. Three asset labels do not prevent a common adverse outcome.
A split is not a free return
You hold 30 shares priced at 120 before a 3-for-1 split. With no other market move, how many shares and what reference price follow?
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You hold 90 shares at an adjusted reference price of 40, keeping the same 3,600 value. Real trading can move around that reference. A chart or backtest must account for the split rather than treating the nominal price change as a two-thirds loss.
A funding payment can reverse the apparent result
A hypothetical perpetual position has 15,000 notional and gains 45 in price P/L. It pays 0.02% funding three times at unchanged notional and incurs 12 in trading costs. What remains?
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Each funding payment is 15,000 × 0.0002 = 3; three cost 9. Net result is 45 − 9 − 12 = 24. This assumes the stated rate is per payment interval, not annual, and notional stays unchanged. Real funding rates and payment direction can change.
The sample is not the population
A strategy wins 11 of 20 hypothetical independent trials. Does the 55% observed win rate establish a durable edge?
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No. A 95% Wilson interval is approximately 34.2% to 74.2%, even before considering selection bias, dependence or a changing environment. Win probability also says nothing by itself about payoff sizes and costs. Run the uncertainty calculator and compare 55 wins out of 100.
Read the balance sheet through a currency move
A fictional company has a 1,000,000 foreign-currency payment due. The home-currency exchange cost rises from 0.80 to 0.88 per foreign unit. What changes before any hedge?
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The payment rises from 800,000 to 880,000 in home currency, an 80,000 increase. It is a change in the home-currency cost of the obligation, not necessarily the company’s total economic loss: revenues, other assets, hedges and timing may offset or alter the exposure.
A backtest knows something it should not
A historical simulation buys at the closing price after using the same day’s final closing price to decide whether to buy. What needs checking?
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The simulation may have an unavailable execution assumption. Determine when the closing value became known, when the order could be submitted and which execution was actually available. A closing auction can have submission deadlines before the final price is known. Move the decision or fill to a genuinely available time and include costs.
A limit order protects a price, not a plan
A sell stop-limit triggers at 48 with a limit of 47.50. The next tradable bid is 44 and stays below 47.50. Has the order protected a maximum loss at 47.50?
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No. The limit prevents execution below the specified price, but the order may remain unfilled. The exposure can continue losing value. A stop-market prioritizes execution after triggering but can fill well below the trigger. Neither order removes gap risk.
Check the method before checking the answer
Write the unit, time period and sign convention before calculating. Distinguish an amount from a rate, a per-payment charge from an annual rate, and a planned exit from an available execution. Keep intermediate values unrounded where possible; round the final position down only when the exercise requires whole units and the budget must not be exceeded.
After opening the answer, check it by another route. Multiply the chosen quantity back by the per-unit loss, reconcile starting and ending balances, or identify the omitted cash flow. Then state one condition that would invalidate the simplified answer. Mark an exercise understood only when you can explain both its calculation and its limitation without copying the displayed solution.