In our previous article we discussed the importance of stop losses. We will expand on that topic and display mathematically why losses become harder to recover the larger they become. The main reason is the capital available to be invested decreases and hence a higher percentage gain is needed just to break even.
Here’s a mathematical example which shows why large losses are so damaging and hard to recover from.
Example: Loss vs Recovery Percentage
Assume you start with $100,000 in your trading account.
Case 1: Small Loss (10%)
- Loss = 10% of $100,000 = $10,000
- Remaining capital = $90,000
To recover back to $100,000:
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- Required gain = $10,000
- Percentage gain needed = 10,000/90,000 *100 = 11.11%
- A gain of 11.11% is realistic and achievable.
Case 2: Medium Loss (25%)
- Loss = 25% of $100,000 = $25,000
- Remaining capital = $75,000
To recover:
- Required gain = $25,000
- Percentage gain needed =25,000/75,000*100 = 33.33%
Already much harder than the original 25% loss.
Case 3: Large Loss (50%)
- Loss = 50% of $100,000 = $50,000
- Remaining capital = $50,000
To recover:
- Required gain = $50,000
- Percentage gain needed = 50,000/50,000*100 =100%
You must double your money just to break even.
Case 4: Very Large Loss (70%)
- Loss = 70% of $100,000 = $70,000
- Remaining capital = $30,000
To recover:
- Required gain = $70,000
- Percentage gain needed =70,000/30,000*100 = 233.33%
Nearly impossible for most traders.
Summary Table
Loss% Capital Left Gain Needed to Recover
10% $90,000 11.11%
25% $75,000 33.33%
50% $50,000 100%
70% $30,000 233.33%
Losses and gains are not symmetrical.
As losses increase, the required recovery gain grows exponentially, not linearly.
Why stop losses matter:
Small, controlled losses are easy to recover but large losses can destroy accounts.
Capital preservation is more important than chasing profits.
The psychological pain of realising a loss is greater than the joy of realising a gain which causes investors to hold on to losses for too long. We can see in the examples above how challenging it becomes to break even as the losses magnify.
Lauren Hua is a private client adviser at Fairmont Equities.
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