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Notes
- 1.
Vol. 81, 3, pp. 637–654.
- 2.
4/Spring, pp. 141–182.
- 3.
Merton, op. cit., p. 141.
- 4.
ML p. 145.
- 5.
ML p. 168.
- 6.
Random House, New York, 2000. This will be referred to as “ Genius. ”
- 7.
This autobiography as well as the one written by Scholes can be found on the website www. nobel.se/economics/laureates/1997.
- 8.
Genius, p. 13.
- 9.
That this liquidity crunch could cause a disaster should have been predictable since a very similar thing occurred in the fall of 1987. At this time so-called “ portfolio insurance” was rather widespread. The idea was to insure against falls in the stock market. The device for doing this was a so-called “ put. ” A put is a contract taken out when the stock is at its present price. It allows one to sell the stock at some specified future time at the price that prevailed when one bought the put. If the stock falls one can sell it for more than its current value. If the stock rises one does not exercise the put and is only out its cost. For various reasons, actual put contracts were not convenient for this activity. Instead one used the Black-Scholes-Merton mathematics to replicate the put with a mixture of bonds and stocks. The mathematics tells one how to continually re-adjust the mixture. The stocks are sold “ short. ” This means that you borrow the shares, sell them at the prevailing price, and then if the shares fall you can repurchase them at the lower price to return to the lender. The mathematics tells you that as the stocks in the portfolio fall you must buy larger and larger quantities of the hedging shorts to cover them. It was assumed erroneously that selling these shorted stocks would somehow have no effect on the market. In fact it simply increased the market decline which meant more and more shorts had to be sold, accelerating the decline. This was the source of the disaster. Incidentally, Professor Zvi Bodie of Boston University proposed a nice application of these ideas. Mutual funds and other purveyors of stock often tell us that if we hold onto a stock long enough this will mitigate the risks. Professor Bodie asked what would happen if we insured such a stock with a put. If the mutual funds were right the cost of the insurance should diminish in time. We can analyze this with the Black-Scholes mathematics if we replicate the put by a call option. What happens is that the cost of the insurance increases monotonically until it reaches the cost of the stock itself, showing that holding risky stocks makes them more risky over time.
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(2008). The Rise and Fall of the Quants. In: Physicists on Wall Street and Other Essays on Science and Society. Springer, New York, NY. https://doi.org/10.1007/978-0-387-76506-8_3
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