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Red-Blooded Risk: The Secret History of Wall Street by Aaron Brown

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Quantitative Tulip Modeling

Using our example, suppose the increase in market size causes tulip flower prices to depreciate at 18 percent per year instead of 20 percent. The exponential nature of tulips means that the 2 percent change in depreciation rate will increase the value of our $205,000 brand-new star bulb by 66 percent to $339,000. However, an older bulb whose price had fallen to $1.15, barely over the $1.00 value of an ordinary bulb, will surge 568 percent to $7.70. Again, these numbers are not to be taken seriously as valuations, just as illustrations of the basic mathematics of an exponential commodity. Slight changes in assumptions can make huge differences in valuations, and the cheaper the commodity, the greater the potential for increases. These facts have been observed time and again whenever people are paying for exponential growth—real or imagined.

The legitimate improvement in fundamental tulip market prospects cannot be the full story of tulipomania, however. The observed peak prices of the cheaper bulbs are difficult to justify under any set of reasonable assumptions, and no one has ever suggested remotely plausible news that could reverse the three-year bull market on one midwinter day. At some point in the process, not necessarily in 1634 but perhaps much later, the rational exponential increase turned into a bubble. People bought because prices were going up; prices went up because people bought. The minute prices stopped rising, people started to take ...

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