DHULFIKAR FINANCIAL EDUCATION — TRADING — Study 2: Losses, Costs and the Mathematics of Risk

DHULFIKAR FINANCIAL EDUCATION — TRADING — FUNDAMENTALS, PART 2 OF 4

Loss, costs and the mathematics of risk

Learning objective: After this lesson, you will be able to perform percentage loss and recovery calculations, distinguish costs from gross return, explain concentration risk, and state the limits of historical figures.

Evidential status: Original public learning text; not investment advice, not an accredited course, no measured learning gain. The examples use fictitious amounts and persons.

Explanation at three levels of understanding

Simple: If you buy something for €100 and it becomes €50, you have lost half of it. To reach €100 again, the value must then double.

Secondary: Returns are percentage changes relative to current value. Loss recovery is therefore asymmetrical.

Advanced: Analyze loss, recovery return, transaction costs, correlations, and model uncertainty separately, without presenting any statistic as a guarantee of return.

1. Calculating without return fairy tales

Start with €100. A 20% drop brings the amount to €80. A 20% increase on €80 subsequently brings the amount to €96, not back to €100. The same percentage refers to a different base after the drop. Investors who add percentages as if the base never changes underestimate potential damage.

With a loss fraction L between 0 and 1, the necessary recovery yield is L / (1 − L). For a 50% loss, this is 0.5 / 0.5 = 100%; for an 80% loss, this is 0.8 / 0.2 = 400%. This is pure arithmetic, not an expectation regarding future markets.

2. Costs are not the same as price movement

Various costs may arise: trading commission, bid-ask difference, currency exchange, management fee, financing interest, and taxes, depending on the situation. A strategy with +5% gross and 2% total costs leaves approximately +3% before any tax, in a simple approximation without compounded effects.

Many social trading overviews report historical growth without showing the actual costs incurred for each follower. Therefore, the follower and the signal provider should not simply be attributed the same net result. The source and calculation method of every return figure must be traceable.

3. Portfolio concentration and coherence

Three different stocks do not automatically constitute a safely diversified portfolio. If they depend on the same sector, interest rate developments, or currency, they can fall sharply at the same time. Diversification can reduce some risks, but it cannot magically eliminate market-wide risks.

The number of positions says little without their size and cohesion. A portfolio with 90% in one company and ten mini-positions remains highly concentrated. A useful control question is therefore: what happens if the largest exposure drops sharply all at once?

4. Leverage: same price difference, greater power effect

Leverage makes it possible to have exposure to a larger market position than the directly invested equity. With 5× exposure, a market movement of -10% roughly means a -50% effect on equity before costs, margin rules, and liquidation. Losses can accumulate particularly rapidly with certain products.

This is not an encouragement to use leveraged products. Margin calls, slippage, interest, and product terms make actual outcomes more complex. For a beginner's course, the main message should be: first learn to understand the concept and the risks, without placing real money in a leveraged position.

5. Simulation versus reality

A backtest uses historical data and past choices. A paper trading environment uses hypothetical orders. Neither proves how a real order will execute: liquidity, price jumps, waiting time, commissions, taxes, and human behavior can differ. A backtest that selects the best-performing strategy from thousands after the fact can give a misleading picture.

For each chart, ask yourself: which time period, which market conditions, how many variants tested, what are the costs, where are the failed strategies, and what data was actually available at the time? Without that data, a spectacular profit chart is not full proof.

6. Practice case: comparing based on net result

Two hypothetical strategies both start with €1,000. Strategy A ends at €1,100 before costs and has €80 in costs: net €1,020. Strategy B ends at €1,070 before costs and has €10 in costs: net €1,060. In this example, a higher gross trading result does not automatically mean higher net ending capital.

That does not make B 'the best investment' yet: risk, volatility, liquidity, potential major losses, and duration are not given. This case primarily teaches that missing data should limit your judgment, rather than supplementing the outcome with a false sense of certainty.

Five knowledge checks — self-test, no diploma

Try to answer yourself first. Then open the answer. The page does not track personal results and does not grant any authority to act.

After this lesson

Can you explain the case in your own words? Can you identify an assumption that you still need to verify? Can you justify why inaction can be a valid outcome? If necessary, note down any remaining questions for the next lesson; the site does not collect personal financial information.

Back to the full study program · Next lesson