What does leverage do to all of this math?

Leverage doesn't introduce a new risk. It multiplies every risk in the previous three units — and it adds one genuinely new mechanism: somebody else can close your position for you.

The multiplier

With leverage L, a price move of x% becomes an equity move of L × x%. That's the whole idea and the whole problem.

Worked example. A hypothetical $25,000 of equity at 2:1 controls a $50,000 position, with $25,000 borrowed. The position falls 33% to $33,333.

• Equity = $33,333 − $25,000 = $8,333.
• That is a 67% loss of equity from a 33% price move. Exactly 2×, as advertised — in the direction nobody advertises.

The forced exit

Brokers require maintenance margin — commonly around 25% of position value for US equities. In the example above, equity stays above the line only while (V − $25,000) ÷ V ≥ 0.25, i.e. while V ≥ $33,333. Below that: a margin call. Add cash, or the broker liquidates — at their timing, not yours.

This is the part that has no unlevered equivalent. Unlevered, a position that goes against you leaves you holding a losing position and a choice. Levered, past a computable price, the choice is removed. Being right eventually is worth nothing if you were liquidated first.

The interactions

• With the recovery curve (Unit 3). That 66.7% equity drawdown needs +200% to recover (0.667 ÷ 0.333). Leverage doesn't merely deepen holes; it moves them into the steep part of a convex function.
• With gaps (Unit 2). Stops don't operate when the market isn't trading. A leveraged position through an overnight gap can lose more than the account holds. Some products and jurisdictions provide negative-balance protection; many do not, and that detail is worth knowing before rather than after.
• With costs (this unit). Borrowed money accrues interest every day the position is open. A levered position must clear that hurdle before it earns anything, which turns a marginal edge negative.
• With sizing (Unit 1). The formula still works — but the exposure cap that felt conservative unlevered becomes the binding constraint, and the "1%" you computed is 1% of equity, not 1% of a position now several times larger.

What the record shows

This is documented observation, stated plainly rather than as a warning label:

• European and UK regulators require providers of leveraged retail CFDs to publish the share of their own retail client accounts that lose money. When ESMA analysed samples of retail CFD accounts ahead of the 2018 product-intervention measures, it reported that between roughly 74% and 89% of retail accounts lost money, with average losses per client running from around €1,600 to €29,000 depending on the sample. Firms' own mandated disclosures, recalculated periodically, have since commonly displayed figures in a similar band — typically somewhere in the 70s or 80s percent — but they vary by firm, product mix and period, and individual firms publish figures well below it.
• Academic studies of day traders using complete brokerage records — the large Taiwanese and Brazilian samples are the best known — have found that only a very small minority were consistently profitable net of costs, and that simply persisting longer did not reliably convert traders into winners.

These describe populations, not individuals, and they are not a prediction about anyone. The useful reading is that the base rate is harsh, which is precisely why the arithmetic in this course is the difference between an informed activity and a countdown.

Nothing here says what leverage to use, or whether to use any at all. It says what the multiplier does to every formula you've learned.

Try it now

1. Take a hypothetical $20,000 account at 3:1. Compute the position size, then the equity impact of a −10% move in the position.
2. Compute the price level at which a 25% maintenance requirement would be breached, by solving (V − $40,000) ÷ V = 0.25. Express it as a percentage decline from the starting position value — then count how many times the year below has fallen that far inside a single week. The number is usually larger than people expect.

3. Compute the gain needed to recover the equity drawdown from step 1 using D ÷ (1 − D), then compute the same figure for the identical −10% move taken unlevered. The ratio between those two numbers is what leverage actually bought.