Against the Gods: The Remarkable Story of Risk (66 page)

14. This example is freely adapted from Groebner and Shannon, 1993,
Chapter 20.

15. The background material on Bayes is from Stigler, 1986, and Cone, 1952.

16. Groebner and Shannon, 1993, p. 1014.

17. Stigler, 1986, p. 123.

18. Cone, 1952, p. 50.

19. Ibid., p. 41.

20. Ibid., pp. 42-44.

21. Bayes, 1763.

22. Price's letter of transmittal and Bayes's essay are reprinted in Kendall and
Plackett, 1977, pp. 134-141.

23. An excellent description of this experiment may be found in Stigler,
1986, pp. 124-130.

24. Smith, 1984. This paper contains an excellent analysis of the Bayesian
approach.

25. David, 1962, p. 177.

CHAPTER 8

1. The biographical material on Gauss is primarily from Shaaf, 1964, and
from Bell, 1965.

2. Schaaf, 1964, p. 40.

3. Bell, 1965, p. 310.

4. The biographical background on Laplace is from Newman, 1988d, pp.
1291-1299.

5. Newman, 1988d, p. 1297.

6. Ibid., p. 1297.

7. Ibid., p. 1297.

8. Bell, 1965, p. 324.

9. Ibid., p. 307.

10. The following discussion and examples are from Schaaf, 1964, pp. 23-25.

11. Bell, 1965, p. 321.

12. Ibid., p. 331.

13. Quoted in Schaaf, 1964, p. 114.

14. Details on Roberts' experiment may be found in Bernstein, 1992, pp.
98-103.

CHAPTER 9

1. The biographical background on Galton is primarily from Forrest, 1974.

2. Newman, 1988e, p. 1142.

3. Ibid., p. 1143.

4. Kelves, 1985.

5. The details of these African anecdotes, including the quotations, are from
Forrest, 1974, pp. 38-57.

6. Forrest, 1974, p. 4.

7. Ibid., p. 12.

8. Ibid., p. 12.

9. Newman, 1988e.

10. Galton, 1869, p. 20. This citation was brought to my attention by Stigler
in personal correspondence.

11. The background material on Quetelet is from Keynes, 1921, pp.
334-335, and Stigler, 1986, pp. 161-182 and 206-268.

12. Stigler, 1986, p. 162.

13. Ibid., p. 169.

14. Ibid., p. 170.

15. Ibid., p. 171.

16. An excellent discussion of Cournot's views on probability may be found
in Stigler, 1986, pp. 195-201.

17. Stigler, 1986, p. 172.

18. A detailed description of Quetelet's experiment may be found in Galton,
1869, in Newman's abstract, p. 1157.

19. Stigler, 1986, p. 171.

20. Ibid., p. 203.

21. Forrest, 1974, p. 202.

22. Stigler, 1986, p. 268.

23. Forrest, 1974, p. 89.

24. Galton, 1883, p. 49. Also quoted in Stigler, 1986, p. 271.

25. Forrest, 1974, p. 92.

26. Ibid., p. 91.

27. Galton, 1869, from Newman's abstract, p. 1153.

28. Forrest, 1974, p. 201.

29. Galton, 1869, in Newman's abstract, p. 1162.

30. Forrest, 1974, p. 89.

31. Ibid., p. 217.

32. Ibid., p. 217.

33. Ibid., p. 101.

34. A detailed description of the Quincunx, including an illustration and photographs of Galton's original notes, may be found in Stigler, 1986, pp. 275-281.

35. Stigler, 1986, p. 281.

36. Forrest, 1974, p. 189.

37. Ibid., p. 189.

38. Ibid., p. 190.

39. This discussion, including the table that follows, are from Stigler, 1986,
pp. 283-290.

40. Stigler, 1986, p. 289.

41. Forrest, 1974, p. 199.

CHAPTER 10

1. Sanford C. Bernstein & Co., 1995.

2. DeBondt and Thaler, 1986.

3. Ibid.

4. See Dreman and Berry, 1995.

5. Morningstar Mutual Funds, April 1, 1994.
6. Reichenstein and Dorsett, 1995, pp. 46-47.

7. These conclusions are distilled from Reichenstein and Dorsett, 1995,
Table 11, p. 32.

8. Baumol, 1986. For an extended analysis of this process, see Baumol,
Nelson, and Wolff, 1994.

9. Baumol, 1986, p. 1077.
10. Ibid., p. 1077.

11. Ibid., p. 1084.

12. Keynes, 1924, p. 88.

13. Forrest, 1974, pp. 201-202.

14. Despite help from others, I have been unable to locate the source of this
quotation, which has long been in my files. A similar comment appears in Keynes,
1936, pp. 152-153.

CHAPTER 11

1. Bernoulli, 1738.

2. Jevons quotes these passages in The Theory of Political Economy. An
abstract appears in Newman, 1988a, pp. 1193-1212, and the quotation in question appears on p. 1197.

3. Quoted in Skidelsky, 1983, p. 47.

4. All the following quotations are from Jevons, 1970.

5. Kendall, 1972, p. 43.

6. Keynes, 1931, p. vii.

CHAPTER 12

1. Laplace, 1814, p. 1301.

2. Ibid., p. 1302.

3. Ibid., p. 1307.

4. Ibid., p. 1308.

5. Newman, 1988b, p. 1353.

6. The story about Louis Bachelier is recounted in more detail in Bernstein,
1992, pp. 19-20

7. Poincare in Newman, 1988a, p. 1359.

8. Ibid., pp. 1362-1363.

9. Ibid., p. 1359.

10. Ibid., p. 1360.

11. Ibid., p. 1361.

12. Ibid., p. 1362.

13. Keynes, 1921, p.3.

14. Personal correspondence.

15. Arrow, 1992, p. 46.

16. Ibid., p. 47.

17. Keynes, 1937, p. 213.

18. Arrow and Hahn, 1971.

19. Arrow, 1992, p. 45.

20. The data for the two charts that follow are from Morningstar Mutual
Funds, a bi-weekly publication.

21. This particular stress test is derived from Rubinstein, 1991. Mark Kritzman
assisted me in developing this application.

22. EPA, 1992.

23. Ibid., p. 1-1.

24. Ibid., p. 1-8.

25. Ibid., Table 5-2.

26. Ibid., 1994, p. 3.

27. Ibid., 1992, p. 1-1.

CHAPTER 13

1. Knight, 1921, p. 209.

2. Keynes, 1933, in Moggridge, 1972, Vol. X, p. 262.

3. Keynes, 1936, p. 161.

4. Dixon, 1986, p. 587.

5. Most of the background material on Knight was generously supplied to
me by Donald Dewey and is drawn from Dewey, 1987; Dewey, 1990; and personal correspondence.

6. Quoted by Herbert Stein in Wall Street Journal, November 1, 1995, p. A14.

7. Knight, 1921, p. 205.

8. Arrow, 1951.

9. Knight, 1921, p. 197.

10. Ibid., p. 226.

11. Ibid., p. 223.

12. Ibid., p. 227.

13. Donald Dewey provided me with the text of this letter.

14. Quoted in Newman, 1988c, p. 1336, which cites the Times Literary
Supplement, February 23, 1951, p. 111.

15. Keynes, 1971, p. 98.

16. Keynes, 1936, p. 176n.

17. Skidelsky, 1986, p. 1.

18. See Blaug, 1994, p. 1209, for citations on Keynes's personal financial affairs.
19. This quotation appears in Moggridge, Vol. X, p. 440. See also Keynes,
1921, p. 408.

20. Keynes, 1971, p. 88.

21. Keynes, 1933, in Keynes, 1972, pp. 338-339.

22. Keynes, 1921, p. 51.

23. Ibid., pp. 3-4.

24. Ibid., pp. 22-26

25. Ibid., pp. 407.

26. Ibid., pp. 206-209.

27. Bateman, 1987, p. 101.

28. Keynes, 1921, pp. 3-4.

29. Ibid., p. 5.

30. Knight, 1921, p. 237.

31. Keynes, 1936, p. 171.

32. Ibid., p. 33.

33. Ibid., p. 33.

34. Ibid., p. 3.

35. Keynes, 1937.

36. Laplace, 1814, p. 1301.

CHAPTER 14

1. Most of the background material and much of the detail about von
Neumann is from Macrae, 1992.

2. Ibid., p. 20.

3. Ibid., p. 87.

4. Quoted in Leonard, 1995, p. 7.

5. Re Morgenstern's anti-Semitism, see Leonard, 1995, Section III.1.

6. Ibid., p. 16.

7. Ibid.

8. Leonard, 1994, footnote 3.

9. Ibid., footnote 4.

10. This and the subsequent quotations in this paragraph are from Mirowski,
1991, p. 239.

11. Leonard, 1995, p. 22n.

12. Ibid., p. 22.

13. von Neumann, 1944, p. 3.

14. Ibid., p. 9.

15. Ibid., p. 20.

16. This example is adapted from von Neumann, 1944, Chapter I, Section
3.3, pp. 17-20.

17. Blinder, 1982, esp. pp. 22-24.

18. For an interesting biography of Nash and his contribution to game theory, see Nasar, 1994.

19. von Neumann, 1944, p. 33.

20. Mirowski, 1991, p. 234.

21. Ibid., p. 229.

22. Ibid., pp. 231 and 237.

CHAPTER 15

1. From an address on February 7, 1995, on the subject of investing worldwide.

2. The full text of "The Prudent Man Decision" may be found in The
Journal of Portfolio Management, Fall 1976, pp. 67-71.

3. A full biographical sketch of Markowitz and a detailed analysis of his
1952 paper appears in Bernstein, 1992, Chapter 2.

4. Darvan, 1994 (reprint).

5. Williams, 1938, p. 1.

6. Kaplan and Welles, 1969, p. 168.

7. All quotations from Markowitz are from Markowitz, 1952.

8. Baumol, 1966.

9. Wells Fargo-Nikko Investment Advisors, Global Currents, March 1995,
p. 1.

10. See Sorensen, 1995, p. 12.

11. Phillips, 1995.

12. Jeffrey, 1984.

13. Sharpe, 1990, p. 34.

14. Thaler, personal correspondence.

CHAPTER 16

1. A large literature is available on the theories and backgrounds of
Kahneman and Tversky, but McKean, 1985, is the most illuminating for lay
readers.

2. McKean, 1985, p. 24.

3. Ibid., p. 25

4. Kahneman and Tversky, 1979, p. 268.

5. McKean, 1985, p. 22; see also Kahneman and Tversky, 1984.

6. Tversky, 1990, p. 75. At greater length on this subject, see Kahneman
and Tversky, 1979.

7. I am grateful to Dr. Richard Geist of Harvard Medical School for bringing this point to my attention.

8. Tversky, 1990, p. 75.

9. Ibid., p. 75.

10. Ibid., pp. 58-60.

11. Miller, 1995.

12. Kahneman and Tversky, 1984.

13. McKean, 1985, p. 30.

14. Ibid., p. 29.

15. This anecdote appears in an unpublished Thaler paper titled "Mental
Accounting Matters."

16. McKean, 1985, p. 31.

17. Redelmeier and Shafir, 1995, pp. 302-305.

18. Tversky and Koehler, 1994, p. 548.

19. Redelmeier, Koehler, Lieberman, and Tversky, 1995.

20. Ellsberg, 1961.

21. Fox and Tversky, 1995.

22. Ibid., pp. 587-588.

23. Tversky and Kahneman, 1992.

24. Kahneman and Tversky, 1973.

25. Thaler, 1995.

26. Kagel and Roth, 1995, p. 4.

27. Von Neumann and Morgenstern, 1953, p. 5.

CHAPTER 17

1. Personal conversation.
2. Bell, 1983, p. 1160.

3. "The recent rally in long-term bonds is driven by short-term speculation," Roger Lowenstein, INTRINSIC VALUE, The Wall Street Journal, June 1,
1995, p. Cl.

4. Keynes, 1936, p. 158.

5. Personal correspondence.

6. The following anecdote is from Thaler, 1991, pp. xi-xii.

7. Ibid., p. xii.

8. Statman, 1982, p. 451.

9. Thaler and Shefrin, 1981.

10. Shefrin and Statman, 1984.

11. Miller, 1987, p. 15.

12. Bernstein, 1986, p. 805.

13. Lakonishok, Shleifer, and Vishny, 1993.

14. Kahneman, Knetsch, and Thaler, 1990, pp. 170-177.

15. French and Poterba, 1989.

16. Keynes, 1936, pp. 155-156.

17. Bernstein, 1992, p. 34.

18. Ibid., p. 143.

19. For a detailed examination of this question, and related literature, see
Shiller, 1989.

20. Vertin, 1974, p. 10.

CHAPTER 18

1. Quoted in "Unemployment and Mr. Keynes's Revolution in Economic
Thought," Canadian Journal of Economics and Political Science, Vol. 3 (1977), p. 113.

2. See Garber, 1989.

3. For details on this note, see Smithson and Smith, 1995, pp. 26-28 (which
contains an illustration), and Ball, 1991, pp. 74-79 and Appendix E.

4. For the full story on the evolution of the option valuation formula, see
Bernstein, 1992, Chapter 11. The narration here draws generously on that chapter. All quotations here are taken from that source.

5. For the full story on the evolution of portfolio insurance, see Bernstein,
1992, Chapter 14. The narration here draws generously on that chapter. All quotations here are taken from that source.

6. Source: Office of the Comptroller of the Currency, published in The
New York Times of June 15, 1995.

7. "Global Market for Derivatives," The Wall Street Journal, December 19,
1995, p. 1.

8. The primary source and all the quotations for this part of the story is
Loomis, 1995.

9. Unless otherwise specified, all quotations from here to the end of the
chapter are from Loomis, 1995.

10. Quoted in Grant's Interest Rate Observer, March 17, 1995.

11. Address to Garn Institute of Finance, University of Utah, November 30,
1994.

CHAPTER 19

1. Kendall, 1972, p. 42.

2. Quoted in Adams, 1995, p. 17.

3. Chesterton, 1909, pp. 149-150.

4. Chorafas, 1994, p. 15.

5. Ibid., p. 16.

6. See especially Hsieh, 1995, and Focardi, 1996.

7. For interesting and lucid descriptions of advances in these areas, see
Focardi, 1996, and Leinweber and Amott, 1995. The Journal of Investing, Winter
1995, has five excellent articles on the subject.

8. See "Can the Complexity Gurus Explain It All," Business Week, November 6, 1995, pp. 22-24; this article includes reviews of two books on this
subject.

9. Kruskal and Stigler, 1994, p. 7.

10. Keynes, 1921, p. 323.