Against the Gods: The Remarkable Story of Risk (65 page)

Finally, the science of risk management sometimes creates new risks even as it brings old risks under control. Our faith in risk management encourages us to take risks we would not otherwise take. On most counts, that is beneficial, but we must be wary of adding to the amount of risk in the system. Research reveals that seatbelts encourage drivers to drive more aggressively. Consequently, the number of accidents rises even though the seriousness of injury in any one accident declines.*
Derivative financial instruments designed as hedges have tempted investors to transform them into speculative vehicles with sleigh-rides for payoffs and involving risks that no corporate risk manager should contemplate. The introduction of portfolio insurance in the late 1970s
encouraged a higher level of equity exposure than had prevailed before.
In the same fashion, conservative institutional investors tend to use
broad diversification to justify higher exposure to risk in untested
areas-but diversification is not a guarantee against loss, only against
losing everything at once.

Nothing is more soothing or more persuasive than the computer
screen, with its imposing arrays of numbers, glowing colors, and elegantly structured graphs. As we stare at the passing show, we become
so absorbed that we tend to forget that the computer only answers
questions; it does not ask them. Whenever we ignore that truth, the
computer supports us in our conceptual errors. Those who live only by
the numbers may find that the computer has simply replaced the oracles to whom people resorted in ancient times for guidance in risk
management and decision-making.

At the same time, we must avoid rejecting numbers when they
show more promise of accuracy than intuition and hunch, where, as
Kahneman and Tversky have demonstrated, inconsistency and myopia
so often prevail. G.B. Airy, one of many brilliant mathematicians who
have served as director of Britain's Royal Observatory, wrote in 1849,
"I am a devoted admirer of theory, hypothesis, formula, and every other
emanation of pure intellect which keeps erring man straight among the
stumbling-blocks and quagmires of matter-of-fact observations."9

The central theme of this whole story is that the quantitative
achievements of the heroes we have met shaped the trajectory of
progress over the past 450 years. In engineering, medicine, science,
finance, business, and even in government, decisions that touch everyone's life are now made in accordance with disciplined procedures that
far outperform the seat-of-the-pants methods of the past. Many catastrophic errors of judgment are thus either avoided, or else their consequences are muted.

Cardano the Renaissance gambler, followed by Pascal the geometer and Fermat the lawyer, the monks of Port-Royal and the ministers
of Newington, the notions man and the man with the sprained brain,
Daniel Bernoulli and his uncle Jacob, secretive Gauss and voluble Quetelet, von Neumann the playful and Morgenstern the ponderous,
the religious de Moivre and the agnostic Knight, pithy Black and
loquacious Scholes, Kenneth Arrow and Harry Markowitz-all of
them have transformed the perception of risk from chance of loss into
opportunity for gain, from FATE and ORIGINAL DESIGN to sophisticated, probability-based forecasts of the future, and from helplessness
to choice.

Opposed though he was to mechanical applications of the laws of
probability and the quantification of uncertainty, Keynes recognized
that this body of thought had profound implications for humanity:

The importance of probability can only be derived from the judgment that it is rational to be guided by it in action; and a practical
dependence on it can only be justified by a judgment that in action
we ought to act to take some account of it.

It is for this reason that probability is to us the "guide of life,"
since to us, as Locke says, "in the greatest part of our concernment,
God has afforded only the Twilight, as I may so say, of Probability,
suitable, I presume, to that state of Mediocrity and Probationership
He has been pleased to place us in here."10

INTRODUCTION

1. Quoted in Keynes, 1921, frontispiece to Chapter XXVIII.

2. Personal conversation.

3. Arrow, 1992, p. 46.

CHAPTER 1

1. Quoted in Ignatin and Smith, 1976, p. 80. The quotation is from Book
I, Chapter X, of The Wealth of Nations.

2. Keynes, 1936, p. 159.

3. Ibid., p. 150.

4. This entire paragraph is from Bolen, 1976.

5. Excellent background on all this may be found in David, 1962, pp. 2-21.

6. See David, 1962, p. 34.

7. Hayano, 1982.

8. Johnson, 1995.

9. See David, p. 2.

10. Sambursky, 1956, p. 36.

11. Ibid., p. 37.

12. Ibid., pp. 36-40.

13. Rabinovitch, 1969.

14. Frankfort, 1956; quoted in Heilbroner, 1995, p. 23. See also David,
1962, pp. 21-26.

15. See Eves, 1983, p. 136.

CHAPTER 2

1. Most of the background and biographical material on Fibonacci comes
from the Encyclopedia Brittanica; Eves, 1983, p. 161; Hogben, 1968, p. 250; and
Garland, 1987.

2. Two stimulating commentaries on the Fibonacci numbers are Garland,
1987, and Hoffer, 1975. The examples here are drawn from those two sources.

3. The background material presented here comes primarily from Hogben,
1968, Chapter I.

4. See Hogben, 1968, p. 35; also Eves, 1983, Chapter I.

5. See Hogben, 1968, p. 36 and pp. 246-250.

6. The background material on Diophantus is from Turnbull, 1951, p. 113.

7. Ibid., p. 110.

8. Ibid., p. 111.

9. See Hogben, 1968, pp. 244-246.

10. From Newman, 1988a, p. 433.

11. The background material on al-Khowarizmi is primarily from Muir,
1961, and Hogben, 1968.

12. Hogben, 1968, p. 243.

13. See Hogben, 1968, Chapter VI, for an extended and stimulating discussion of the development of algebra and the uses of zero.

14. The background material on Omar Khayyam is from Fitzgerald.

15. Hogben, 1968, p. 245.

CHAPTER 3

1. The background material on Paccioli comes primarily from David, 1962,
pp. 36-39, and Kemp, 1981, pp. 146-148.

2. The material on Paccioli and Leonardo is from Kemp, 1981, pp. 248-250.

3. David, 1962, p. 37.

4. Sambursky, 1956.

5. Ibid.

6. Ibid.

7. The background material on Cardano and the quotations are primarily
from Ore, 1953, and Morley, 1854, with some quotes from Cardan, 1930.

8. David, 1962, p. 61.

9. See Sarton, 1957, pp. 29-32; also Muir, 1961, pp. 35-38.

10. Hacking, 1975, p. 18. The complete discussion, which runs through
Chapter 3, "Opinion," is well worth careful study.

11. Hacking, 1975, p. 22.

12. Ibid., p. 26.

13. Ibid., p. 44.

14. David, 1962, p. 58.

15. Kogelman and Heller, 1986, pp. 164-165.

16. The background material on Galileo is primarily from David, 1962,
Chapter 7, pp. 61-69.

17. David, 1962, p. 65.

18. Ibid., p. 13.

19. Stigler, 1988.

CHAPTER 4

1. The background material on Pascal is from Muir, 1961, pp. 77-100;
David, 1962, pp. 34-79; and Hacking, 1975, pp. 55-70.

2. See David, 1962, p. 74.

3. Muir, 1961, p. 90.

4. Ibid., p. 93.

5. Ibid., p. 94.

6. Ibid., p. 95.

7. David, 1961, p. 69; see also Appendix 4.

8. See Huff, 1959, pp. 63-69.

9. See Hogben, 1968, p. 551; see also Hacking, 1975, pp. 58-59.

10. See David, 1962, pp. 71-75.

11. Turnbull, 1951, p. 130.

12. Ibid., p. 131.

13. See Hogben, 1968, pp. 277-279; see also David, 1962, p. 34.

14. Turnbull, 1951, p. 131; also Eves, 1984, p. 6.

15. I am grateful to Stanley Kogelman for helping me work out these
examples.

16. This point, and the quotation from Pascal that follows, are from Guilbaud,
1968; the translation is mine.

17. David, 1962, p. 252.

18. All the material that follows is from Hacking, 1975, Chapter 8, "The
Great Decision," pp. 63-70.

19. Hacking, p. 62.

20. The material about the Port-Royal monastery is from Hacking, 1975,
pp. 73-77.

21. Ibid., p. 25.

22. Ibid., p. 74.

23. Ibid., p. 77.

24. Ibid., p. 77.

25. Ibid., p. 77.

26. Ibid., p. 77.

CHAPTER 5

1. I am grateful to Stigler (1977) for this description and to Stephen Stigler
personally for drawing the Trial of the Pyx to my attention.

2. The background material on Graunt is from Muir, 1961; David, 1962;
and Newman, 1988g. (Direct quotations from Natural and Political Obligations are
primarily from Newman.)

3. Newman, 1988g, p. 1394.

4. The background material on Petty is from Hacking, 1975, pp. 102-105.
5. The material about Wilkins and the Royal Society is from Hacking,
1975, pp. 169-171.

6. Graunt, p. 1401.

7. Ibid., p. 1401.

8. Hacking, 1975, p. 103.

9. I am grateful to Stephen Stigler for making this point clear to me.
10. See Hacking, 1975, pp. 103-105.

11. The illustration is from Stigler, 1996.

12. David, 1962, p. 107. An extended explanation of Graunt's calculations
and estimating procedure appears on pp. 107-109.

13. Hacking, 1975, p. 107.

14. Ibid., p. 110.

15. See discussion in Hacking, 1975, pp. 105-110.

16. The background material on Naumann and Halley and the quotations
from Halley are primarily from Newman, 1988g, pp. 1393-1396 and 1414-1432.

17. See discussion in Hacking, 1975, pp. 111-121.

18. The material that follows on the history of insurance in general and
Lloyd's in particular is from Flower and Jones, 1974; also Hodgson, 1984.

19. Macaulay, 1848, p. 494. For Macaulay's full and fascinating story of the
English national debt, see the entire chapter that runs from p. 487 to p. 498.

20. Flower and Jones, 1974.

21. American Academy of Actuaries, 1994, and Moorehead, 1989.

22. Interesting background material on the role of the Monte dei Paschi may
be found in Chichilnisky and Heal, 1993.

23. See, in particular, Townsend, 1995, and Besley, 1995.

24. Flower and Jones, 1974, p. 13.

CHAPTER 6

1. Bernoulli, Daniel, 1738.

2. The background material on the Bernoulli family is from Newman, 1988f.

3. Bell, 1965, p. 131.

4. Newman, 1988f, p. 759.

5. Ibid.

6. Ibid.

7. Ibid.

8. This story and the quotes are from David, 1962, pp. 133-135.
9. Stigler, 1993.

10. All Bernoulli quotations are from Bernoulli, 1738.

11. An extended and lucid example of expected utilities and risk may be
found in Bodie, Kane, and Marcus, 1992, Chapter 7, pp. 183-209. See also
Kritzman, 1995, Chapter 3, pp. 21-32.

12. Todhunter, 1949. See also Bassett, 1987, and the list of references therein.

13. Siegel, 1994, Chapter 8, pp. 95-104.

CHAPTER 7

1. Background material on Jacob Bernoulli is from Newman, 1988f.

2. Hacking, 1975, p. 166; see also Kendall, 1974.

3. Gesammelte Werke (ed. Pertz and Gerhardt), Halle 1855, vol. 3, pp. 71-97. I
am grateful to Marta Steele and Doris Bullard for the translation into English.
Chapter XXX of Keynes, 1921, has an illuminating discussion of this exchange
between Leibniz and Bernoulli.

4. An excellent analysis of Ars Conjectandi may be found in David, 1962, pp.
133-139 and in Stigler, 1986, pp. 63-78.

5. Bernoulli, Jacob, 1713, p. 1430.

6. Ibid., p. 1431.

7. Hacking, 1975, p. 145.

8. Ibid., p. 146.

9. Ibid., p. 163.

10. David, 1962, p. 137.

11. Stigler, 1986, p. 71. This book was an invaluable source of information
for this chapter.

12. The background material on de Moivre is from Stigler, 1986, Chapter 2,
and David, 1962, Chapter XV.

13. Stigler, 1986, p. 85.