Suppose there is an asset portfolio, and wi is used to represent the weight of asset I in the portfolio. Among them, assets can be either a single security or a benchmark asset exposure obtained through mapping. In fact, the latter is often more common in practice. The simulation results do not reflect the past returns of the portfolio, because the weights of different assets in the portfolio were constantly changing in the past. However, the asset-weighted portfolio return should remain unchanged.

In this way, by determining the target percentile of portfolio income distribution, the maximum potential loss corresponding to the required confidence level can be directly calculated. According to the example in the introduction of this chapter, if the risk manager uses the sample data of 200 historical rates of return, he can choose the third lowest rate of return among the 200 sample data to measure the VaR at 99% confidence level.

So the basic assumption behind the historical simulation method is that the joint income distribution of assets can be reasonably similar to the historical joint income distribution ~