Backtesting

Backtesting

Purpose

Test a strategy honestly. The default outcome of a backtest is a beautiful equity curve that describes the past and predicts nothing — and every bias in the process pushes in that direction.

When to Use

• Testing a strategy before risking capital.
• Validating that an apparent edge is real.
• Diagnosing why a live strategy underperforms its backtest.
• Reviewing someone else's backtest.

Capabilities

• Bias elimination: survivorship, look-ahead, selection.
• Realistic cost modeling: commissions, spread, slippage, borrow.
• Walk-forward and out-of-sample validation.
• Statistical significance and multiple-testing correction.
• Robustness testing.

Inputs

• The strategy rules, stated precisely enough to be executed mechanically.
• Point-in-time historical data, including delisted instruments.
• Realistic assumptions about execution.

Outputs

• Performance metrics with costs included.
• Out-of-sample results, reported honestly.
• A judgment on whether the edge is real, with the evidence.

Workflow

1. Eliminate the biases before you run anything — Survivorship (delisted names must be in the universe), look-ahead (data must be used only when it was available), and selection (the strategy must be specified before it is tested).
2. Model the costs honestly — Commission, the bid-ask spread, slippage that scales with size and inversely with liquidity, and borrow costs on shorts. Most published edges are smaller than realistic costs.
3. Split the data before you look at it — In-sample for development, out-of-sample for validation, and a final hold-out you touch exactly once.
4. Walk forward — Re-fit on a rolling window and test on the period immediately after. A single in-sample fit tells you nothing about a strategy that will be run forward in time.
5. Correct for multiple testing — If you tested forty variants, the best one looks good by chance. A p-value that has not been adjusted for the number of things you tried is not a p-value.
6. Stress it — Perturb the parameters. A strategy that only works with a 14-day lookback and fails with 13 or 15 is fitted to noise.

Best Practices

• The most common backtesting error is look-ahead bias, and it is usually accidental: using a closing price to make a decision that would have been made during the day, or using a fundamental figure on the fiscal date rather than the filing date.
• Transaction costs kill more strategies than any other factor. A strategy trading daily with a 0.05% edge per trade is a losing strategy after a 0.10% round-trip cost, and it will have looked excellent before costs.
• A Sharpe ratio above 2 on a simple strategy in a liquid market is a bug, not a discovery. Look for the bias.
• Parameter sensitivity is the honesty test. If performance collapses when a parameter moves by one unit, the strategy has fitted noise. Plot the surface.
• The out-of-sample period must be genuinely untouched. If you look at it, adjust, and look again, it is now in-sample and you have no validation left.
• Report the strategy's worst period, not just its average. The maximum drawdown and its duration determine whether it is survivable in practice.

Examples

A backtest that does not lie to itself:

def backtest(strategy: Strategy, start: date, end: date) -> BacktestResult:
    equity, trades = [], []

    for day in trading_days(start, end):
        # Point-in-time universe: includes everything that was tradable THAT DAY,
        # including companies that were later delisted or went to zero.
        universe = universe_as_of(day)

        # Point-in-time fundamentals: as reported, on or before this date. Not
        # as later restated, and never before the filing date.
        data = fundamentals_as_of(day, universe)

        # Signals are computed on data available at the CLOSE of the prior day.
        # Trades execute at the NEXT day's open. Using today's close to decide
        # and today's close to fill is the classic look-ahead error.
        signals = strategy.signals(data.shift(1))

        for signal in signals:
            fill = next_open(signal.symbol, day)
            cost = transaction_cost(
                price=fill,
                shares=signal.shares,
                adv=data.loc[signal.symbol, "adv_20d"],
            )
            trades.append(Trade(day, signal.symbol, fill, cost))

        equity.append(mark_to_market(day))

    return BacktestResult(equity=equity, trades=trades)


def transaction_cost(price: float, shares: int, adv: float) -> float:
    """Commission + half the spread + slippage that scales with participation."""
    notional = price * shares
    commission = max(1.0, shares * 0.005)
    spread_cost = notional * 0.0005                       # half-spread, liquid names

    # Market impact grows with the fraction of daily volume you consume.
    participation = (shares * price) / max(adv, 1)
    impact = notional * 0.10 * math.sqrt(participation)   # square-root impact model

    return commission + spread_cost + impact

The result, reported honestly:

Strategy: momentum + quality, 25 names, monthly rebalance.

                        In-sample    Out-of-sample   Difference
                        2010-2018    2019-2024
CAGR (gross)              18.4%          11.2%
CAGR (net of costs)       14.1%           6.8%        <- costs take 4-5 points
Sharpe (net)               1.12           0.54        <- halved out of sample
Max drawdown             -22.4%         -31.7%
Longest drawdown          8 months      19 months     <- the number that matters

Multiple testing: 34 variants were tested. The reported result is the best of
34. Adjusting for that (Bonferroni), the out-of-sample Sharpe of 0.54 is not
distinguishable from zero at the 5% level.

Parameter sensitivity: performance is stable for lookbacks of 100-150 days
(Sharpe 0.48-0.57) and collapses below 80 days. That stability is mildly
reassuring; the multiple-testing problem is not.

Judgment: the edge, if it exists, is much smaller than the in-sample result
suggests and is not statistically established. A 19-month drawdown is longer
than most people can actually sit through. Not deployable at meaningful size
on this evidence.

Notes

• The gap between in-sample and out-of-sample performance in the example — a Sharpe of 1.12 falling to 0.54 — is entirely typical, and it is the reason out-of-sample testing is not optional.
• The square-root market-impact model is a standard approximation: impact scales with the square root of participation rate. It matters enormously for any strategy trading size, and it is usually omitted from backtests that look excellent.
• This is educational material about backtesting methodology, not financial advice, and no backtest result constitutes a recommendation.