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By leveraging one security, investors had potentially given up control of all of their others. This truth is extremely worthy of being remembered. The securities might seem unrelated, but since the same investors owned them, they were implicitly linked in times of stress. Apparently, it didn't occur to Rosenfeld that as Long-Term tended to buy the less liquid security in every market, its assets were not entirely independent of one another, unlike how one dice roll is independent of the next. Seen in these terms, Long-Term's letter represented a significant leap. While it wholeheartedly acknowledged risk, it eliminated uncertainty by assigning numerical odds to its likelihood of loss. However, Black-Scholes makes a very crucial assumption: that the volatility of a security is constant. To state that the value of an option to buy IBM depends on its volatility is meaningless unless there is an agreement on what its volatility is. There is a reason why financial markets reach extremes more frequently than coin flips. A key condition of random events is that each new flip is independent of the previous one. The coin doesn't remember that it landed on tails three times in a row; the odds on the fourth flip are still fifty-fifty. But markets have memories. If the Long-Term episode proved anything, it is that the systems of disclosure that have worked so well regarding traditional securities have not been able to perform the task effectively with respect to derivative contracts.