Risk Management in Turbulent Times

By Gilles Bénéplanc; Jean-Charles Rochet | Go to book overview

4
The Basic Tools of Risk Modeling

In this book, we adopt the point of view of a corporation seeking to quantify random events that can impact its future profits and losses. A crucial element is quantifiability. In his treatise, “Risk, Uncertainty and Profit” (published in 1921), Knight distinguishes “risk” (events to which the decision maker can assess probability distributions) from “uncertainty” (events that cannot be expressed in terms of such probabilities). Pure uncertainty corresponds to cases where it is not possible to build a quantitative approach of the severity and the frequency of the risk. Keynes (in his famous article of 1937, “The General Theory of Employment,” in the Quarterly Journal of Economics) gives examples, such as: “The prospect of an European war (indeed!),…, or the price of copper and the rate of interest twenty years hence…” True risk modeling is only possible for those random events that can be quantified both in terms of frequency and severity. Note again that risk does not always have a negative connotation—for example, exchange rate fluctuations can generate profits as well as losses.

There are basically two methods for quantifying risks: the frequentist approach, which can be applied in stationary environments when enough past observations are available, or the subjective approach, which has to be applied when there are not enough such observations. We show below how these methods can be combined. We also suggest a way to take care of Knightian uncertainty by the use of “worst-case scenarios.” The chapter concludes by a discussion of the dangers of the stationarity assumption: what if the future differs from the past?

4.1 ASSESSING PROBABILITIES: THE FREQUENTIST AND
SUBJECTIVE APPROACHES

The frequentist approach relies on the law of large numbers (see Chapter 5 for more detail). This law states that in large samples, the frequency of occurrence of independent and identical events is approximately equal to a constant, which is called the probability of the event.

For example, the sentence “The probability of drawing heads when throwing a coin is 1/2” just means that if the coin is thrown many times, the frequency of occurrence of heads is very likely to be close to 1/2. This notion of probability is justified by the fact that in a stationary1 environment, the future frequency of such events can be predicted from that of past events, at least if the samples involved are large. This method has been employed for a long time in the insurance industry.

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