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

9.2 Calculating P&L Distribution

In Chapter 8, we discussed volatility and VaR, using as an example a normal distribution with volatility $130,800. This is actually the P&L distribution for the U.S. Treasury bond position (treated on its own) estimated using the parametric or delta-normal approach. I will try to use this as an example to illustrate how we calculate the P&L distribution and from that the VaR and volatility.

We will follow the four steps outlined in Section 8.3 “Methods for Estimating the P&L Distribution”:

1. Asset to Risk Factor Mapping—Translate from assets held into market risk factors.

2. Risk Factor Distributions—Estimate the range of possibilities for the market risk factors.

3. Generate the Portfolio P&L Distribution—Generate risk factor P&L and sum to produce the overall portfolio P&L distribution.

4. VaR, Volatility, and so on—Estimate the VaR, volatility, or other desired characteristics of the P&L distribution.

We will estimate the P&L distribution (and the VaR and so on) using the parametric, historic, and Monte Carlo approaches.

Calculating Volatility and VaR for Single Bond Position

The U.S. Treasury position is long $20 million notional of the 10-year U.S. Treasury bond (the 3.75 percent of November 15, 2018). Given just this information, it is hard to have a firm idea of the risk for this position. After we estimate the P&L distribution, however, we will end up with a good idea of the risk under normal trading conditions.

The portfolio is evaluated ...