The factors that determine activity on the Exchange are innumerable, with events, current or expected, often bearing no apparent relation to price variation. Beside the somewhat natural causes for variation come artificial causes: The Exchange reacts to itself, and the current trading is a function, not only of prior trading, but also of its relationship to the rest of the market. The determination of this activity depends on an infinite number of factors: It is thus impossible to hope for mathematical forecasting. Contradictory opinions about these variations are so evenly divided that at the same instant buyers expect a rise and sellers a fall.
The calculus of probability can doubles never be applied to market activity, and the dynamics of the Exchange will never be an exact science. But it is possible to study mathematically the state of the market at a given instant – that is to say, to establish the laws of probability for price variation that the market at that instant dictates. If the market, in effect, does not predict its fluctuations, it does assess them as being more or less likely, and this likelihood can be evaluated mathematically.
That was from Louis Bachelier, “Theorie de la Speculation”. Bachelier in 1900 created a stochastic model of Brownian motion that was later used for pricing stock options.
However, Bachelier recognized that any market exchange didn’t just depend on the historical data captured in prices. It depended on many other interactions happening in the rest of the market that could always generate new behavior whose range of outcomes cannot be predicted from the data.
When he said “The Exchange reacts to itself,” Bachelier understood a lot about modern complexity theory — that market prices cannot be explained by an account of their historical trajectories alone. The market is one interconnected whole, meaning there will be non-linear feedback effects between prices. The trajectory of one price affects the conditions of another price. And the state of the market as a whole creates downward causation on the individual prices. So observations of prices are not identically or independently distributed.
Of course, Bachelier’s insights into stochastic processes applies to weapon system analysis as well. You might know what historical costs of systems are, and even if we assume away marked technical differences between classes of systems, that doesn’t mean you can have an understanding of the risk involved in a future program. All the various input prices, company organization, contract terms, and various other matters besides, can create novel outcomes that affect price, schedule, and technical attributes.
Unfortunately, weapon systems analysis went the way of finance after WWII, assuming that simplistic mathematical models that have elements of probability are actually representative of the real world. Rather than looking at the specifics of the investment and its management, you focus on crunching the numbers. They all still assume that, even if the outcome of an individual observation cannot be predicted exactly, that the distribution in which it will fall is known with 100% precision. And clearly that is wrong. Finance got the message in 2008. Defense management might never learn the lesson.
Now, in weapon systems analysis, where there are orders of magnitude fewer observations, such models move from bad to dangerous. No matter what you do to torture the data, we only have maybe 6 fighter jets produced in the last 50 years (F-14, F-15, F-16, F-18, F-22, F-35, and perhaps F-111, but that made its first flight in 1964). Bombers, tanks, ships, subs, and satellites are all similar. One may forgive financial institutions for pretending that they have perfect knowledge of price distributions when they have decades of daily — up to the minute — price movements. Such pretensions in defense are dangerous.
I think of defense acquisition as a problem of Exchange, not resource allocation. Such financial and systems analysis models focus on optimized allocation subject to given constraints. Exchange, however, properly makes you think about people — about deal-making under uncertainty, and relationships, management techniques, specific technologies, organizational design, and so forth.
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