# Simulation Methods

Empirical methods for risk management and wealth analysis

## Monte-Carlo Simulation

The most commonly used simulation method, Monte-Carlo simulation, is a multi-variate normal model to simulate asset returns using the specified return and risk estimation models.

While the number of possible future scenarios (paths) can be controlled by the user, typically the default value of 5,000 is sufficient to generate reasonably stable results without exhausting computer memory (RAM).

The returns of each asset are simulated for each period within the investment time horizon. Using the simulated asset returns, portfolio weights, and an annual rebalancing interval, we derive the portfolio return and level of portfolio wealth. We use this simulated set of empirical data to evaluate risk statistics and wealth analysis.

## Bootstrap Simulation

Bootstrapping is procedure by which new samples are generated from an original dataset by randomly selecting independent cross-sectional observations from the dataset. Bootstrap simulation offers the advantage of using actual empirical experience to simulate future scenarios capturing non-normal characteristics such as fat-tails. Whereas Monte-Carlo allows various specification of risk and return models, the Bootstrap method assumes that the historical risk model prevails.

## Block Bootstrap Simulation

Block Bootstrapping preserves the serial dependence properties of the data by sampling contiguous blocks of cross-sectional returns with replacement (as opposed to independent cross-sectional returns) from the empirical dataset.

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