Financial Risk Management

CHAPTER 7Historical Approach to Risk

STEP‐BY‐STEP CALCULATION OF HISTORICAL VAR

This approach to risk measurement is grounded in historical simulation and therefore does not require any theoretical probability distribution to compute a risk measure such as Value‐at‐Risk (VaR) or Expected Shortfall (ES).

Within a historical framework, we will never start a risk calculation with the following statement: “we assume that the profit and loss of our portfolio follows a Gaussian distribution (or whatever else)”. There is no distributional assumption about the returns of assets in a portfolio. That is why the historical method is an empirical or nonparametric approach to risk measurement.

It is empirical because it only relies on historical data (observed in the past). It is nonparametric because it does not rely on a theoretical probability distribution specified from parameters such as, for example, the Gaussian distribution. This explains why historical methods are used extensively in financial institutions. As the risk measure is derived from historical returns, there is no bias generated by assuming something wrong about the profit and loss of the portfolio.

To illustrate the historical simulation method, we use a portfolio with two assets for the sake of clarity: Google and Amazon. These two companies belong to the so‐called GAFAM and operate in software and computer services, and general retailers, respectively. The historical method is of course extendable to a portfolio with ...