Fixed fraction position sizing

The code

The function at the top is the arithmetic on a single trade. The rest plays one fixed run of 200 coin flip trades at each of six fractions. The fractions are examples that show the shape of the effect. They are not suggestions.

Each trade also pays a small cost, as every real trade does, and the last line of the table is the comparison with doing nothing.

This script reads no file. Its inputs are made inside the script from a fixed seed.

The file that was run: fixed_fraction.py

# Fixed fraction position sizing: put the same share of the account at risk on every trade.
# There are no prices here at all. The trade outcomes are coin flips from a fixed seed: a win
# and a loss are equally likely and the same size, so the trades have no edge by construction.
# The point is what the size of the fraction alone does to the same run of trades.
import random


def position_size(balance, fraction, stop_distance):
    """How many units to trade so that being stopped out costs `fraction` of the balance."""
    if stop_distance <= 0:
        raise ValueError("stop distance must be greater than zero")
    return balance * fraction / stop_distance


# The arithmetic on one trade. Example figures only.
print("Units for 10,000 at risk of 1 percent with a stop 25 points away:", position_size(10_000, 0.01, 25))
print("The same with a stop 50 points away:", position_size(10_000, 0.01, 50))

# One fixed run of 200 trades: +1 means the trade made what it risked, -1 means it lost it.
rng = random.Random(7)
outcomes = [rng.choice([1, -1]) for _ in range(200)]
print("Trades:", len(outcomes), "of which wins:", outcomes.count(1), "and losses:", outcomes.count(-1))

COST = 0.05          # cost of each trade, as a share of the amount risked
START = 10_000.0


def play(fraction):
    """Run the same outcomes with one fraction. Return the final balance and the worst fall from a high."""
    balance = peak = START
    worst_fall = 0.0
    for outcome in outcomes:
        at_risk = balance * fraction             # sized from the balance as it is now
        balance += at_risk * (outcome - COST)
        peak = max(peak, balance)
        worst_fall = max(worst_fall, (peak - balance) / peak * 100)
    return balance, worst_fall


# Example fractions, to show the shape of the effect. They are not suggestions.
print("fraction   final balance   worst fall from a high")
for fraction in [0.005, 0.01, 0.02, 0.05, 0.10, 0.25]:
    balance, worst_fall = play(fraction)
    print(f"{fraction * 100:5.1f} %   {balance:13,.2f}   {worst_fall:5.1f} %")
print("Doing nothing leaves the balance at", f"{START:,.2f}")

# Why losses weigh more than gains: the gain needed to get back to where you started.
print("loss      gain needed to recover")
for loss in [10, 25, 50, 75]:
    print(f"{loss:3d} %     {100 / (100 - loss) * 100 - 100:6.1f} %")

What the run printed

Units for 10,000 at risk of 1 percent with a stop 25 points away: 4.0
The same with a stop 50 points away: 2.0
Trades: 200 of which wins: 102 and losses: 98
fraction   final balance   worst fall from a high
  0.5 %        9,680.20    10.8 %
  1.0 %        9,323.81    20.7 %
  2.0 %        8,520.61    37.7 %
  5.0 %        5,760.69    71.6 %
 10.0 %        1,990.20    94.7 %
 25.0 %            3.02   100.0 %
Doing nothing leaves the balance at 10,000.00
loss      gain needed to recover
 10 %       11.1 %
 25 %       33.3 %
 50 %      100.0 %
 75 %      300.0 %

Output of the run on 9 Oct 2026, copied as printed. Every input to this run was invented, so the result says nothing about any real market.

How to read it

Every row uses the same 200 outcomes, with slightly more wins than losses. Every row still ends below the starting balance, because trades with no edge that pay a cost lose the cost. Doing nothing ended higher than all of them.

What changes down the table is how much was lost and how deep the worst fall was. The same trades that cost a few percent at the smallest fraction left almost nothing at the largest. Nothing about the trades changed. Only the size did.

The second table is why. A loss of half the account needs a gain of 100 percent to recover, so large swings in both directions do not cancel out. They grind the balance down. These are coin flips, not a market, and the table says nothing about how any way of trading would do.