Leverage
Leverage magnifies gains and losses by the same factor while simultaneously shortening the path to a forced close-out. At 20x leverage, a five-percent price drop is enough for total loss.
With leverage, you move more money than you have. With a €1,000 stake and 10x leverage, you move €10,000. If the price rises one percent, you gain ten percent of your stake.
Everyone understands that part. Many overlook the other part: if the price falls one percent, you lose ten percent. And at a ten percent price drop, your entire stake is gone.
The formula for that is simple: a hundred divided by the leverage gives the price move that wipes you out entirely. Leverage 20 means five percent. Leverage 50 means two percent.
A two-percent daily move is completely normal in many markets. In crypto, ten percent in a day is nothing unusual. That's why high leverage there isn't a bold bet, it's a matter of hours.
Leverage scales the return on deployed equity by a factor L, while the underlying price move stays unchanged. The liquidation threshold sits approximately at a price move of 1/L, reduced further by financing costs and fees, which pull the actual threshold closer.
There's an added effect on geometric return. Since variance scales with L² but expected value only with L, the ratio worsens as leverage rises. From the approximation g ≈ L·μ − L²·σ²/2 follows a growth-optimal leverage of roughly μ/σ², above which expected growth rate falls despite a higher expected return, and eventually turns negative. High leverage is therefore not just riskier, but eventually loss-making even with a positive expected value.
For daily-reset leveraged products, path dependence adds a further layer. Since leverage is applied to each day's base, performance over multiple periods diverges from L times the underlying's performance. In sideways, choppy markets, this effect systematically erodes value, regardless of the underlying's direction.
Summary
- A hundred divided by the leverage gives the price drop that wipes out everything.
- Variance grows with the square of leverage, expected value only linearly.
- Daily-reset leveraged products lose value in sideways markets even without a directional error.
Did you get it?
At what price move is a 25x-leveraged stake wiped out?
Four percent, since 100 divided by 25 is 4.
Why does growth rate fall past a certain leverage?
Because variance grows with the square of leverage, while expected value only grows linearly.
What happens to daily leveraged products in sideways markets?
They systematically lose value through path dependence.
Related
- LiquidationStage 2
- When to stopStage 2
- Calculating position sizeStage 2