Historical Simulation is a non-parametric method used to estimate Value at Risk (VaR). It involves sorting historical returns in ascending order and identifying the loss threshold corresponding to a desired confidence level. The underlying assumption is that the future will resemble the past, and the distribution of historical returns will repeat in the future.
Here are the steps involved in calculating VaR using Historical Simulation:
a. Collect historical data: Gather the historical prices or returns data for the portfolio or assets over a specific time period.
b. Calculate portfolio returns: Based on the assigned weights for each asset and the historical data, calculate the portfolio returns.
c. Order the returns: Sort the historical returns from worst to best, creating a ranked distribution.
d. Determine the VaR level: Choose the desired confidence level (e.g., 95%, 99%) to establish the VaR level.
e. Estimate VaR: Estimate VaR by selecting the nth worst return from the ranked distribution, where n is determined by the confidence level and the number of observations.
Advantages of Historical Simulation:
a. Simple and fast calculation method.
b. No assumptions are needed about the distribution of returns.
c. Robust against outliers in the data.
Disadvantages of Historical Simulation:
a. Sensitive to changes in market conditions.
b. May not be suitable for portfolios with significant changes in risk over time.
c. Cannot accommodate changes in the market structure.
