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.

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.