Quantitative Risk Management: A Practical Guide to Financial Risk, + Website

8.3 Methods for Estimating the P&L Distribution

So far we have been talking about the P&L distribution as if we already knew the distribution, as if somebody gave it to us. This is clearly not the case. We have to estimate the P&L distribution, and that is never easy. The process is usually complex, dependent on the particular circumstances, and subject to the details of the actual portfolio. The basic idea, however, is simple: we want to trace out an estimate of the P&L distribution, or enough of the distribution to allow calculation of the appropriate summary measures, usually the volatility or the VaR.

Our first inclination for estimating the portfolio P&L might be to simply measure the price history of our past portfolio. If our portfolio is just a single asset, say the 10-year U.S. Treasury bond introduced in Chapter 1, and we haven't changed that portfolio for a long time, then maybe this would be feasible. Real-world portfolios, however, include multiple trades and instruments that change over time. The history on the past portfolio usually will not represent how the current portfolio might behave. The behavior and interaction of many instruments, many not in the portfolio in the past, needs to be incorporated.

It is generally useful to think of the P&L as resulting from two components:

1. External market risk factors.

2. Positions—that is, the firm's holdings and the security characteristics that determine the sensitivity to risk factors.

The exposure to risk factors ...