GARCH Monte Carlo for Risk Assessment

A backtest gives you one historical realization of how a strategy performed. GARCH Monte Carlo gives you thousands of plausible alternative realizations, all consistent with the volatility dynamics of the data. The result is a much richer view of how the strategy might behave — especially in the tails.

The Method

Given an estimated GARCH model on the strategy's return series:

1. Sample standardized residuals (the standardized innovations from the historical fit).
2. Use the GARCH parameters and yesterday's state to simulate the next return: r(t+1) = σ(t+1) × z(t+1), where σ(t+1) is computed from the GARCH recursion and z is the sampled innovation.
3. Update σ(t+1) and repeat for the desired horizon (e.g., 252 days = one year forward).
4. Repeat the entire simulation N times (typically 1,000 to 10,000) to build a distribution of paths.

The result: a forward-looking distribution of equity curves, drawdowns, ending values, etc. — all consistent with the volatility clustering observed historically.

What GARCH MC Tells You

• Distribution of future Sharpe. The realized Sharpe over the next year is a random variable. GARCH MC gives you its full distribution — point estimate plus 5th/95th percentiles.
• Distribution of max drawdown. The historical max DD is a single sample. GARCH MC simulates many futures and shows you the 95th-percentile DD — a much more honest worst-case for risk planning.
• Probability of ruin. The fraction of simulated paths that breach a given drawdown threshold (e.g., -50%). Useful for sizing.
• Probability of recovery. Given a drawdown of X, the conditional distribution of time to new high. Matters for psychological tradability.
• Per-strategy risk budget. If you allocate capital across strategies, the GARCH-MC distribution of each strategy's P&L gives you a coherent input to a portfolio-level optimization.

Practical Use Cases

Stress-Testing a New Strategy

Before deploying a strategy, run GARCH MC on its backtest returns. Look at the 5th-percentile equity curve over the next year. Is the worst-plausible-year still acceptable? If the 5th-percentile path is a 40% drawdown, you should know that going in — even if the historical max DD was only 20%.

Portfolio Construction

For a portfolio of strategies, run GARCH MC on each leg, then combine. The joint distribution gives you correlation-aware tail risk that historical max-DD numbers cannot.

Capital Sufficiency

If you trade with a fixed capital base, GARCH MC tells you the probability of running out of capital before reaching new highs. A strategy with positive expected return and 20% probability of -50% DD before recovery may still ruin you if your capital can't survive that path.

Limits and Caveats

• GARCH is itself a model. If the true return-generating process has features GARCH misses (jumps, regime changes), the simulation will under-represent those risks.
• Innovations matter. Using Gaussian innovations under-states tail risk because real returns have fat tails. Use empirical (bootstrapped from standardized residuals) or Student-t innovations.
• Historical regime bias. The GARCH parameters reflect the historical period. If the future has a regime not seen in the fitting sample, the simulation under-represents that regime.
• Parameter uncertainty. GARCH parameters themselves are estimates with uncertainty. A more rigorous approach samples from the parameter posterior in addition to sampling innovations.

How QuanterLab Implements It

RA001RGAX (the Risk Assessment module) and SC001STCB both expose GARCH MC as a post-backtest analysis. Inputs: the strategy return series, simulation horizon, number of paths, innovation distribution. Outputs: percentile bands on the equity curve, distribution of ending wealth, distribution of max DD, and a verdict on whether the strategy's historical drawdown is tame relative to its forward-looking distribution.

The Bottom Line

A backtest is one observation; GARCH MC turns it into a distribution. For risk planning, this is the difference between "the strategy lost 20% in 2018, so my max DD is 20%" and "the 95th-percentile forward DD is 38%." The latter is the number you should plan around.