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

5.7 Conclusion

This chapter has aimed to explain some of the basic tools used in quantitative risk measurement—volatility and VaR to measure the size of risk, and marginal contribution and best hedges to understand the composition of risk. These tools are important but they are not the only tools, and I have only outlined the intuition and have not laid out the technical foundations. The focus has been on how to use and think about these tools, with little or no attention directed toward how to estimate or calculate them.

Later chapters cover the details, the formulae, and the calculations necessary to produce the numbers. Chapter 8 concentrates on the formulae and technicalities behind volatility and VaR, while Chapter 9 applies these to a simple portfolio to make the concepts and calculations concrete. Chapter 10 turns to the portfolio tools of marginal contribution, best hedges, and so on.

Notes

1. The rule that 32 percent of the probability falls outside of ±1σ is strictly true for the normal distribution. For most reasonable P&L distributions we run into in finance, it will be somewhere on the order of 20 percent to 30 percent. In other words, under standard trading conditions, P&L will be within ±1σ roughly one day out of three or four or five.

2. Take the simple example of owning $1 million versus $100 million of a U.S. Treasury bond. The scale of the distribution will be very different, but the shape of the distribution will not change. The tail behavior—for example, the ...