Projecting Trading P&L and Drawdowns with Simulations

Summary

The document considers how to project future profit and loss and drawdowns for trading strategies and portfolios. It raises several possible approaches: extrapolating a backtest, resampling its empirical returns, forecasting time-varying variance with GARCH before Monte Carlo simulation, and modeling portfolio dependence with a copula or correlated shocks. It also considers using a trader’s historical Sharpe ratio or gain rate, while recognizing that drawdowns are harder to infer from such assumptions.

The response cautions that a single historical backtest is not a sound estimate of future outcomes and says its estimation uncertainty is not well defined. It favors making explicit distributional assumptions and running extensive Monte Carlo simulations. Such projections are meaningful only conditional on those assumptions and may be informative when reality differs modestly from them. They remain work models rather than guarantees: markets need not follow the chosen distributions, and simulations generally omit the market impact of the strategy’s own orders, which can be material for large trades. The document gives no empirical comparison or detailed implementation guidance.

Key ideas

• A single historical backtest realization does not by itself provide a reliable projection of future P&L.
• Monte Carlo simulation can estimate outcomes under explicit assumptions about return distributions.
• GARCH forecasts can represent changing volatility in simulated future paths.
• Portfolio simulations can model dependence between assets using correlated shocks or copulas.
• Simulations are conditional on their assumptions and may omit the market impact of orders.

Tags

# How to projectP&L or drawdowns on pair trading , trading and portfolios?


# How to projectP&L or drawdowns on pair trading , trading and portfolios?












This is for planning and risk management. I am stuck on the following thoughts -

- Back-test the trading strategy for a period similar to the one you expect and then project.

- Do the above using empirical distribution of the back-test period, similar to FHS.

- For portfolio, GARCH estimate variance into the future time steps, run MC using empirical distribution. This is like to except time varying volatility, also, you are doing it at each asset level. May use copula and draw correlated noise.

- Assume regardless of the market condition that trader or manager will find suitable trades and use his Sharpe ratio or %gain. Here draw-down will be difficult to handle. May be assume he will stick within his risk limits.

Please provide references with your answers.

## Answer by Pam (score 2)

https://quant.stackexchange.com/a/12987

Backtesting on a past realization does not provide any meaningful "estimate", as the variance of the "estimate" would be undefined.

More meaningful would be to make distributional assumptions and get estimates through extensive Monte Carlo simulations.

Clearly, the estimates that you get would be "meaningful" under your specific distributional assumption, and, in practice, under mild deviations from these assumptions.

(It remains understood that the mkt has no obligation whatsoever to "follow" your assumptions and distributions, and that is just a work model for you to get some indication. In addition, keep in mind that a simulated environment does not include the effect of your orders, which may and, with significant orders, actually is not negligible).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.