Risk may be a four-letter word, but it's one we can't avoid. Every day we make decisions that involve financial and economic risk. How much car insurance should we buy? Should we refinance the mortgage now or a year from now? Should we save more for retirement, or spend the extra money on a new car? Making any decision that has more than one possible outcome is similar to gambling: We put the money on the roulette table and take our chances.
Interestingly enough, the tools we use today to measure and analyze risk were first developed to help players analyze games of chance like roulette and blackjack. For thousands of years, people have played games based on a throw of the dice, but they had little understanding of how those games actually worked. In ancient times, dice of various sorts were used to consult the gods, so any effort to analyze the odds was thought improper. But even those who ignored religious concerns could not correctly analyze a single throw of a die because they did not understand the concept of zero. That meant that the complex computations necessary to develop a theory of probability were impossible.1
By the mid-17th century, the power of religion had waned and mathematical tools had developed to the point that people could begin to make sense out of cards, dice, and other games.2 Since the invention of probability theory, we have come to realize that many everyday events, including those in economics, finance, and even weather forecasting, are best thought of as analogous to the flip of a coin or the throw of a die. For better or worse, we no longer treat these random events as if they were divinely ordained.
Still, while experts can make educated guesses about the future path of interest rates, inflation, or the stock market, their predictions are really only that—guesses. And while meteorologists are fairly good at forecasting the weather a day or two ahead, economists, financial advisors, and business gurus have dismal records.3 So understanding the possibility of various occurrences should allow everyone to make better choices. While risk cannot be eliminated, it can often be managed effectively.
Finally, while most people view risk as a curse to be avoided whenever possible, risk also creates opportunities. The payoff from a winning bet on one hand of cards can often erase the losses on a losing hand. Thus the importance of probability theory to the development of modern financial markets is hard to overemphasize. People require compensation for taking risks. Without the capacity to measure risk, we could not calculate a fair price for transferring risk from one person to another, nor could we price stocks and bonds, much less sell insurance. The market for options didn't exist until economists learned how to compute the price of an option using probability theory.
In this chapter, we will learn how to measure risk and assess whether it will increase or decrease. We will also come to understand why changes in risk lead to changes in the demand for particular financial instruments and to corresponding changes in the price of those instruments.
1For further details on this history, see F.N. David, Games, Gods and Gambling: The Origins and History of Probability and Statistical Ideas from the Earliest Times to the Newtonian Era, (New York, Hafner Publishing Co.,1962); P.L. Bernstein, Against the Gods: The Remarkable Story of Risk, (New York, John Wiley & Sons, 1998); and I. Hacking, The Emergence of Probability: A Philosophical Study of Early Ideas about Probability, Induction and Statistical Inference, (London, Cambridge University Press, 1975).
2Blaise Pascal's invention of probability theory in the mid-17th century is described in some detail in the supplementary material on the website http://www.mhhe.com/economics/cecchetti1e. This includes a description of the problem he tackled in developing probability theory and an analysis of the problem using the tools presented here.
3William A. Sherden's book The Fortune Sellers, (New York, NY: John Wiley & Sons, 1998) suggests that meteorologists are the only people who can legitimately claim to predict anything.