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

5.5 Summary for Volatility and VaR

Volatility and VaR both measure spread or dispersion of the P&L distribution. It is the P&L distribution that matters—how likely we are to see losses versus gains. We use the volatility and VaR to summarize the spread of the distribution and to build intuition for risk, but it is actually the distribution, such as displayed in Figure 5.2, that matters.

For risk, the most important characteristic of the distribution is the spread or dispersion. Volatility and VaR are simply two different numbers that summarize the dispersion. (For a normal distribution. they are interchangeable, otherwise they show us slightly different views.) There is nothing magic about volatility and VaR. When you truly understand what they mean, you see that they are incredibly simple.

The importance of the numbers is what we do with them—“It's not the figures themselves, it's what you do with them that matters.” How do we use them to inform our decisions? How do we use them to get a gut feeling for the risk?

Table 5.1 provides a cheat sheet for volatility and VaR. What is really important is how we use volatility and VaR. We need to understand what they are trying to tell us.

Table 5.1 Some Suggestions for Using Volatility and VaR.

Measure	Probability	Intuition
Volatility, σ	Better or worse, 30%	There is roughly a 30% chance of profit better than +σ or loss worse than –σ, so we should expect bigger P&L roughly one day out of three. So if volatility is $100,000, the ...