5.2 Volatility and Value at Risk (VaR)

Before discussing volatility and VaR we need to think about what financial risk measurement is. Financial risk is in some ways so simple, because it is all about money—profit and loss and the variability of P&L. Political risk is about the possibility of insurrection, expropriation—or the Republicans winning the next presidential election. Risk in flying an airplane is that an engine may flame out or that fog may obscure the landing strip. Risk is multifaceted and amorphous in so many areas. For a financial firm, the primary focus is whether tomorrow or next year will show a profit or a loss. Of course, other things matter, but for a financial firm those other things are dominated by the profit and loss—the P&L. What generates the P&L is multifaceted and possibly amorphous but the P&L itself is pretty concrete and simple. Money is something we can measure, something most of us can agree about, that more is better than less and a profit is good and a loss is bad.

From this, it follows that the distribution of P&L is what matters when discussing financial risk. Let's take an extremely simple financial business, betting on the outcome of a coin flip. We make $10 on heads and lose $10 on tails. We could graph the P&L distribution as in Panel A of Figure 5.1. The probability is one-half of losing $10 and one-half of making $10. This kind of distribution is fundamental to how we should think about financial risk. It shows us the possible outcomes ...

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