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Simulation provides a complete picture when backtesting because it accounts for the dynamic nature of financial markets, which carry extreme downside and upside risk. The basic types of simulation are historical simulation and Monte Carlo simulation.

**Historical simulation** involves the construction of random results from different historical periods devoid of time continuum sequencing. Therefore, historical simulation is a non-deterministic rolling window backtest. Banks often use this method for market risk analysis. The problem with historical time series data is that it assumes that the past only happened in one way and that data is static. For financial variables, such assumptions are not true.

**Monte Carlo simulation** overcomes the flaws of historical simulation cited in the foregoing paragraph. In Monte Carlo simulation, observations are drawn randomly from a distribution where each key variable is assigned a statistical significance. It is a popular approach because it allows the use of several different distributions across a variety of key variables. The disadvantage of Monte Carlo simulation is that it is complex and involves intensive computation.

It is important to note that the main objective of the simulation is to account for randomness when investment performance is obtained using backtesting. A simulation is implemented in eight steps:

- Determine the target variable: What do we want to understand? This is often the return on an investment strategy or portfolio.
- Specify key decision variables.
- Specify the number of trials (
*N*) to be run. - Define the distributional properties of the key decision variables.
- Use a random number generator to draw
*N*random numbers for each key decision variable. - Compute the value of the target variable for each set of simulated key decision variables.
- Repeat steps 5 and 6 until the desired number of trials (
*N)*is complete. - We now have a set of
*N*values of the target variable.

## Question

Which of the following is most likely an advantage of Monte Carlo simulation?

Monte Carlo simulation:

- Is highly flexible.
- Is very complex.
- Involves intensive computation.
## Solution

The correct answer is A.Monte Carlo simulation is popular because it affords analysts more flexibility.

B and C are incorrect.These are disadvantages of Monte Carlo simulation.

Reading 43: Backtesting and Simulation

*LOS 43 (f) Contrast Monte Carlo and historical simulation approaches.*