Realistic expectations: costs, time and risk of loss.

What it costs to trade

A strategy does not earn what its backtest says, but what is left after paying to trade it. Costs have five sources, and only the first one appears on the broker's fee schedule:

• Commissions: what the broker charges for each order. It is the most visible cost and, in liquid stocks, the smallest.
• Bid-ask spread: the difference between the price at which you can buy and the price at which you can sell. Each round-trip trade pays it once.
• Slippage: the difference between the signal price and the price actually executed. It grows with the size of the order and with the volatility of the moment.
• Financing: interest on leveraged positions, securities borrowing on short positions, rollover in forex and funding on crypto perpetuals.
• Taxes: in Spain, gains are taxed in the savings base of personal income tax (IRPF; level 7). They do not change the strategy, but they do change what is left at the end.

flowchart TB
  B[Gross return] --> C1[− commissions] --> C2[− spread and slippage] --> C3[− financing] --> C4[− taxes] --> N[Net return]

If the first four are grouped into a cost per round-trip trade (buy and sell) $c$, and the strategy makes $n$ round trips a year, the net return is approximately:

The formula is simple and its consequence harsh: the cost of each trade is multiplied by the turnover. In Python:

import pandas as pd

def rentabilidad_neta(bruta: float, operaciones: int,
                      coste: float) -> float:
    """Net annual return.

    `coste`: cost of one round-trip trade, as a fraction.
    """
    return bruta - operaciones * coste

operaciones = [1, 5, 10, 25, 50, 100]
costes = [0.001, 0.002, 0.005]
tabla = pd.DataFrame(
    {f"cost {c:.1%}": [rentabilidad_neta(0.08, n, c) for n in operaciones]
     for c in costes},
    index=pd.Index(operaciones, name="trades/year"),
)
tabla.round(3)

             cost 0.1%  cost 0.2%  cost 0.5%
trades/year
1                0.079      0.078      0.075
5                0.075      0.070      0.055
10               0.070      0.060      0.030
25               0.055      0.030     -0.045
50               0.030     -0.020     -0.170
100             -0.020     -0.120     -0.420

With 8% gross and 0.2% per trade, the strategy is still good at 10 trades a year and loses money from 40 on:

That is why high-turnover strategies need a much larger gross edge, and why a backtest without costs says nothing. From level 2 on, every backtest in the course includes costs.

Losses are not symmetric

If a €10,000 account loses 50%, €5,000 is left. Getting back to €10,000 does not take a 50% gain: you have to double what is left, a 100% gain. In general, after a loss $p$ the required gain is:

for perdida in (0.10, 0.20, 0.50, 0.75):
    subida = 1 / (1 - perdida) - 1
    print(f"After losing {perdida:.0%}, you need a gain of {subida:.1%}")

After losing 10%, you need a gain of 11.1%
After losing 20%, you need a gain of 25.0%
After losing 50%, you need a gain of 100.0%
After losing 75%, you need a gain of 300.0%

The figure at the top shows the full curve. Up to 20% the asymmetry is small; from 40% on, recovery requires returns that few strategies deliver in years. This is why risk management (level 4) matters more than looking for the rule that earns the most: a 60% drawdown is not fixed by a good streak.

Bad years with a good strategy

The Sharpe ratio measures the average return per unit of volatility: an annual Sharpe of 1 means that the average return of a year equals its standard deviation. If annual returns were normal, the probability of closing a year at a loss would be $\Phi(-\text{SR})$, where $\Phi$ is the cumulative distribution function of the standard normal:

from statistics import NormalDist

for sharpe in (0.5, 1.0, 1.5):
    p = NormalDist().cdf(-sharpe)
    print(f"Sharpe {sharpe}: {p:.1%} of years at a loss")

Sharpe 0.5: 30.9% of years at a loss
Sharpe 1.0: 15.9% of years at a loss
Sharpe 1.5: 6.7% of years at a loss

A Sharpe of 1 sustained for years is an excellent result for a systematic strategy, and even so one year in six closes negative. Real returns have fatter tails than the normal distribution (level 1), so the real figure is usually somewhat worse.

A simulation makes it more concrete. Ten thousand ten-year paths of a strategy with a Sharpe of 0.5 (a 5% average return and 10% volatility), with independent, normal years:

import numpy as np

rng = np.random.default_rng(42)
anos = rng.normal(loc=0.05, scale=0.10, size=(10_000, 10))
en_perdidas = anos < 0
tres_seguidos = (
    en_perdidas[:, :-2] & en_perdidas[:, 1:-1] & en_perdidas[:, 2:]
).any(axis=1)
capital_final = np.prod(1 + anos, axis=1)

print(f"At least one losing year: {en_perdidas.any(axis=1).mean():.1%}")
print(f"Three losing years in a row: {tres_seguidos.mean():.1%}")
print(f"Lose money over ten years: {(capital_final < 1).mean():.1%}")

At least one losing year: 97.5%
Three losing years in a row: 16.8%
Lose money over ten years: 7.8%

The strategy has a real edge by construction, and even so almost every path has losing years, and a non-negligible share has streaks of three losing years in a row. Whoever abandons a strategy after a bad year is, most of the time, abandoning a strategy that works.

Time: how much data you need

The other side of the problem: if bad years are normal, how many good years does it take to believe a backtest? A useful approximation relates the annual Sharpe to the t-statistic of the average return after $T$ years of data:

A t-statistic of 2 is the usual threshold for saying that a mean differs from zero with 95% confidence. Solving for $T$:

for sharpe in (0.5, 0.75, 1.0):
    anos_necesarios = (2 / sharpe) ** 2
    print(f"Sharpe {sharpe}: {anos_necesarios:.0f} years of data")

Sharpe 0.5: 16 years of data
Sharpe 0.75: 7 years of data
Sharpe 1.0: 4 years of data

With a Sharpe of 0.5 (a good strategy at low frequency), you need about 16 years of data for the result not to be compatible with chance. And that is for one strategy: if you test a hundred variants and pick the best, the threshold rises (level 2, multiple testing). This calculation explains two ideas of the course: backtests of two or three years prove nothing, and parameters are chosen from hypotheses, not by searching for the maximum.

Learning time counts too. The full syllabus is about 750–850 hours: at 10–15 hours a week, between 12 and 18 months. Skipping levels 0 to 2 does not shorten that path; it only makes it more expensive.

Risk of loss and leverage

Leverage multiplies exposure and, with it, losses. With 10-to-1 leverage, a 10% fall in the asset wipes out 100% of the capital. Leveraged retail products (CFDs, options, futures, crypto perpetuals) make it possible to lose the entire deposit in a very short time.

The course does not recommend trading with real money until level 4, and always after weeks of paper trading (simulated trading with real prices) and with automatic risk limits.

Exercises

1. A strategy makes 12% gross per year, makes 40 round-trip trades and each one costs 0.3%. What is its net return? At most, how many trades a year could it make without losing money?

2. A fund falls 35% in a crisis. What gain does it need to recover? If it then makes 8% a year, how many years does it take?

import math

subida = 1 / (1 - 0.35) - 1
anos_recuperacion = math.log(1 / (1 - 0.35)) / math.log(1.08)
print(f"Required gain: {subida:.1%}")
print(f"Years at 8% a year: {anos_recuperacion:.1f}")

Required gain: 53.8%
Years at 8% a year: 5.6

3. A strategy has an annual Sharpe of 0.8. What fraction of years closes at a loss, if annual returns are normal? How many years of data are needed for a t-statistic of 2?

from statistics import NormalDist

sharpe = 0.8
print(f"Losing years: {NormalDist().cdf(-sharpe):.1%}")
print(f"Years of data: {(2 / sharpe) ** 2:.2f}")

Losing years: 21.2%
Years of data: 6.25