Fortune's Formula (41 page)

Resorts International deal: Tobias 1984, 69–70.

Committed 150 percent to arbitrage: Thorp 1971.

“Sleep at night” test: Thorp, interview.

“No one who’s been with me for five years”: Bruck 1988, 83.

“Michael is the most important individual”: Bruck 1988, 84.

“Someone like Mike comes along once every five hundred years”: Bruck 1988, 84.

Saw Milken behind a pane of glass: Thorp, interview.

“What are you talking about?” Bruck 1994, 216.

Milken told friend he liked Ross, thought they were similar: Bruck 1994, 215.

Equity for bond buyers went to Milken: See Stewart 1991; also Bruck 1994, 216.

Contracted pupils in poker games: Lowenstein 2000, 29.

“For a while”: Dunbar 2000, 40.

“Although our trading didn’t turn out very well”: Dunbar 2000, 40–41.

Tested Black’s formulas on HP computer: Thorp, interview and e-mail.

“a masterpiece”: Thorp, e-mail.

“I never thought about credit, actually”: Thorp, interview.

Changed fund name in 1974: Kurson 2003.

Returns: Thorp, e-mail. $20 million: Laing 1974.

“Playing the Odds”: Laing 1974.

“In some cases, the funds’ trading is dictated”: Laing 1974.

“an incipient but growing switch”: Laing 1974.

“just one of many tools”: Laing 1974.

“The whole computer-model bit is ridiculous”: Laing 1974.

“The better one was one of those crazy funds”: Laing 1974.

Lost $107,000 on U.S. Financial: Laing 1974.

Phoned attorneys: Laing 1974.

Asked money managers if they beat the market: Bernstein 1992, 75; Thorp, interview.

Capital Asset Pricing Model: Sharpe 1964.

AMC convertible bond deal: Kurson 1999a, 42–44.

“Situations that simple”: Kurson 1999a, 44.

Sharpe on “active” and “passive” investors: Thorp, interview; see also Sharpe 1991.

The Sting
inspired by delayed wire service con: Cooney 1982, 76. I am all but certain that the alias “Kelly,” adopted by Robert Redford’s character, is a coincidence. But screenwriter David Ward was well versed in the history of the wire services and associated confidence games. One character makes a reference to tapping into “Moe Annenberg’s wire.”

“Why aren’t you out there doing it?”: Liversidge 1988, 74.

Thorp made $6 million: Thorp, interview; see also
Financial World
, July 14, 1987, 109, which estimates Thorp’s 1986 earnings as “a hefty $8 million to $9 million.”

Newman concerned about tax-related trades, government scrutiny: Thorp, interview.

“I’ve estimated for myself”: Thorp, interview.

Dorchester, Belvedere partnership: Bruck 1988, 81–82.

Capital about $60 million: Ziemba 2003, 151.

Profit in AT&T deal: Spanier 1988, 35–36. Kurson 2003 says the deal “enriched Thorp’s investors by $2. 5 million.”

S&P futures trading: Tobias 1984, 68–72.

Return figures: Thorp, e-mail.

“Taking candy from a baby”: Baldwin 1986.

“near the rumors, information and opportunities”: Wiles and Hum 1986.

Quit teaching job in 1982: Baldwin 1986.

Mod shirts and sandals: Laing 1974.

Bomb shelter: Liversidge 1988, 70.

IV. ST. PETERSBURG WAGER

“Peter tosses a coin”: Bernoulli 1954.

Ducat worth $40: See Bernstein 1996, 106n.

“Although the standard calculation”: Bernoulli 1954.

Keynes’s book: Keynes 1921.

Mentioned by von Neumann and Morgenstern; other economic thinkers: See list of references in Bernoulli 1954, 35.

“The
value
of an item must not be based on its
price
”: Bernoulli 1954, 24.

“In the absence of the unusual”: Bernoulli 1954, 25.

“As the quantity of any commodity”: Jevons 1986.

“prototype for Everyman’s utility function”: Savage 1954, 94. Savage adds, however, that “it cannot be taken seriously over extreme ranges.”

“hold any terrors for the economist”: Samuelson 1969, 243.

“bliss level”: Stephen Ross mentions the term in a passage quoted in Goldman 1974, 98.

“if a speculator is in the habit of risking his capital”: Williams 1936, 453–54.

“Nature’s admonition to avoid the dice altogether”: Bernoulli 1954, 29.

“It may be reasonable for some individuals”: Bernoulli 1954, 29.

“Since all of our propositions harmonize”: Bernoulli 1954, 31.

Last man hired before Depression: Bibb Latané, e-mail.

February 17, 1956: McEnally 1986, 29.

Presented geometric mean principle at 1956 Cowles seminar; Markowitz present: Latané 1978, 395.

“To suppose that safety-first consists in having a small gamble”: Letter, John Maynard Keynes to F. C. Scott, dated Feb. 6, 1942, in Keynes 1983, 12:81–83.

1959 article: Latané 1959.

Latané had not heard of Kelly at time of Cowles seminar: See footnote 6 on page 147 of Latané 1959, which cites Kelly and Shannon.

Markowitz learned of Latané’s work via Tobin, 1955–56: personal letter, October 25, 2004. Markowitz said he didn’t remember hearing Latané speak in 1956.

Chapter in
Portfolio Selection
: “Return in the Long Run,” Markowitz 1959, 116–25.

“Kelly[-Breiman-Bernoulli-Latané or capital growth] criterion”: Thorp 1971.

“the idea that we should pick the investment”: McEnally 1986, 22.

“the Kelly criterion should replace the Markowitz criterion”: Thorp 1969, 292.

Samuelson attended regular meetings on investing organized by Shannon: Betty Shannon and Thomas Cover, interviews; Paul Samuelson, personal letter, June 28, 2004. Cover was under the impression (from speaking with Claude) that these meetings were at the Shannon home. Betty said they were at MIT; it was a series of meetings on juggling that were held at their home.

1971 MIT talk: No one today is sure about the year. In Liversidge 1987 Shannon says the talk was “some twenty years ago.” Hershber n.d. [1986] puts it “fully 17 years ago,” apparently based on Claude and Betty’s recollections at that time. Though undated, the Hershberg article was almost certainly written in 1986, as it is mentioned in letters from Hershberg to the Shannons, dated June 23 and August 28, 1986, in the LOC.

Description of rebalancing in MIT talk: see David Forney in chnm.gmu.edu/tools/surveys/responses/80/; also Liversidge 1987.

“being whose facilities are so sharpened”: Maxwell 1871.

Bennett’s explanation of Maxwell’s demon: Bennett 1982.

“is in effect possessed of a ‘Maxwell’s Demon’”: Samuelson 1974, 19.

“Naw. The commissions would kill you”: David Forney in http://chnm.gmu.edu/tools/surveys/responses/80/.

Constant-proportion rebalanced portfolios discussed by economists: Rubinstein 1991 and Booth and Fama 1992.

“As pointed out to me by Professor L. J. Savage”: Latané 1959.

“Our analysis enables us to dispel a fallacy”: Samuelson 1969, 245–46.

“somewhat mystifying…Professor Savage has informed me”: Samuelson 1969, 245.

“provides an effective counter example”: Samuelson 1969, 246.

Shannon unaware of Samuelson’s article, reaction: Cover, interview; letter, Thomas Cover to Claude Shannon, dated July 5, 1985, Shannon’s papers, LOC.

Rubinstein endorsed, then recanted: See Rubinstein 1975 and Rubinstein 1987.

“From this indisputable fact”: Samuelson 1971, 898.

“The Kelly view, that maximizing investment growth of value”: Hunt 2000, 3.

“automatically built in”: Hakansson 1971, 555.

Auto accident analogy: Wilcox, interview. The 1996 U.S. death rate from auto accidents was 16. 2 per 100,000. Were this the only cause of death, the average life span would be about 6,170 years.

Kelly system maximizes median wealth: See Hakansson 1971.

“As Gertrude Stein never said: Epsilon ain’t zero”: Samuelson, 1963, 6. The literary reference is unclear. I was unable to find any Stein comment that sounds like it could have been the basis for Samuelson’s “Epsilon ain’t zero.” One quote attributed to Stein (it could describe the Kelly criterion controversy) is: “There ain’t no answer. There ain’t gonna be any answer. There never has been an answer. That’s the answer.”

“Again the geometric mean strategy proves to be fallacious”: Merton and Samuelson 1974, 76.

“Given the qualifications”: Latané 1978, 397.

“spare the dead”: Samuelson 1979, 306.

“It is surprising to note”: Ophir 1978, 103.

“We heartily agree that the corollary is false”: Thorp 1971.

“has nothing to do with the value function”: Kelly 1956, 925–26.

“My position as to the usefulness of
G
…I have never considered
G
”: Latané 1978, 310.

“We are not interested in utility theory”: Bell and Cover 1980, 162.

“it is difficult to identify the underlying utilities”: Latané 1978, 310.

Markowitz articles: Markowitz 1972 and 1976.

“What about the argument that expected average compound return”: Merton and Samuelson 1974.

“most people I talk to say ‘Yeah, sounds great to me’”: Thorp, interview.

“a private institutional investor”: Thorp 1971, reprinted and revised in Ziemba and Vickson 1975, 612.

“Institutional investor” was Convertible Hedge Associates: Thorp, e-mail.

Fund’s cumulative gain: Thorp 1971.

“Proponents of efficient market theory”: Thorp 1971.

“We consider almost surely having more wealth”: Thorp 1971.

“a person accepting Latané’s [line of reasoning] has to forgo”: Ophir 1979, 303.

Leverage justified with stocks: Rubinstein 1991; Rotando and Thorp 1992; and especially Thorp 1998. The latter shows that optimal leverage is acutely sensitive to the interest rate charged.

“What I think he was trying to say”: Thorp, interview.

“Why then do some still think they should want”: Samuelson 1979, 305.

“No need to say more”: Samuelson 1979, 306.

“Reviewers who are best placed to understand an author’s work”: Begley 2004.

1/
n
rule an approximation for blackjack, exact for continuous betting: See Thorp 1997 (revised 1998), 10.

“All serious gamblers use something close to the Kelly criterion”: http://may.casinocitytimes.com/articles/1131.html.

“a certain John L Kelly”: “The Kelly Criterion Defended” on Predict-A-Win for UK Football, http://www.predict-a-win.co.uk/ba_tkcd.php.

“The next time some tout in a bad suit advises you”: http://www.professionalgambler.com/behind.html.

“according to expert researcher Dr. Nigel E. Turner, Ph.D., Scientist”: http://www.professionalgambler.com/binomial.html.

“We have no evidence that Buffett”: Hagstrom 2000, 128.

“My experience has been that most cautious gamblers or investors”: Thorp 1997 (revised 1998), 10.

“bright clear line”: “Gambling, Investment, and the Kelly Criterion,” http://www.friendlymachine.com/2003/11/gambling_invest.html.

“Those individuals or institutions who are long term compounders”: Thorp 1997 (revised 1998), 38. On reading the present work, Thorp spotted a minor typo in the 1997 article, which has been corrected here (“a lesser fraction” rather than “a lesser function”).

Market caps on position sizes; use of Kelly criterion as conceptual guide: Thorp, interview and e-mail; see also Thorp 1971.

Lost $2 million and made $2 million; October about even: Thorp, e-mail; Liversidge 1988.

34 percent: Ziemba 2003, 151.

“So improbable is such an event”: Rubinstein 1988.

“If I did use
some
”: Letter, Paul A. Samuelson to Thomas M. Cover, dated September 7, 1988 (supplied by Cover).

“complete swindle…mathematicians who ignore remainders”: Letter, Paul A. Samuelson to Thomas M. Cover, dated Nov. 2, 1988 (supplied by Cover).

“If I like your ways”: Letter, Paul A. Samuelson to Thomas M. Cover, dated May 16, 1991 (supplied by Cover).

V. RICO

Boesky said father ran delicatessens, actually ran topless bars: Stewart 1991, 41.

Claimed he worked for U.S. Information Agency but no record: Stewart 1991, 42.

Boesky bio: Stewart 1991, 42–43.

Unlisted phone number: Hicks 1982.

“Ivan, you little pig”: Stewart 1991, 45.

Nickname “Piggy”: See Kinkead 1984, 102.

“The maximum permitted by law”: Kinkead 1984, 105.

“Not at all”: Kinkead 1984, 104.

“You are insinuating improprieties”: Kinkead 1984, 105.

Boesky’s payment to Siegel: Stewart 1991, 113.

Boesky told Siegel he was a CIA agent in Iran: Stewart 1991, 42.

Siegel suspected assassination: Stewart 1991, 177.

“What’s the matter, Marty?”: Stewart 1991, 178.

“Boesky’s competitors whisper darkly”: Kinkead 1984.

Criminal connections of Harold Giuliani, Leo D’Avanzo: See Barrett 2000, 13–66.

Picture of Nixon as dartboard: Barrett 2000, 53.

RICO named for
Little Caesar
character: The law’s author, G. Robert Blakey of Notre Dame Law School, refused to confirm or deny this story. See http://www.snopes.com/language/acronyms/rico.htm.

Supreme Court ruling on scope of RICO:
U.S. v. Turkette
, 452 U.S. 576 (1981).

“I dreamed up the tactic”: Giuliani 2002, 214.

“Rudy decided that RICO would be his Excalibur”: Barrett 2000, 147.

Friends suspected Ross bought the chips: Bruck 1994, 97.

Ross a card-counter: Bruck 1994, 39.

“I felt at the end of the year that I had netted out”: Bruck 1994, 160.

Solomon Weiss prosecution: Bruck 1994, 108–63. Nickname of Charles Kimmel: Bruck 1994, 146.

Caesar Kimmel’s failed restaurant venture, retirement: Bruck 1994, 207–10.

Flat Fleet Feet: See http://www.arlingtonpark.com/bet_the_races/understanding/horses.html.

Ross’s interview and Giuliani’s statement: Bruck 1994, 159–60.

FBI tapes, wealthiest gangster: See Bruck 1994, 239.