a single word Curiously, my son had the same experience. He didn’t say anything until he was about the same age. His sister, about a year and a half older, was his interpreter. They would go around as a little pair and when he indicated with body language and facial expressions what he wanted, she would get it done.
complete sentences Henriette Anne Klauser, in Writing on Both Sides of the Brain, Harper, San Francisco, 1997, pp. 36–38, tells a similar story of a first grader who wouldn’t write no matter how she prompted him until, suddenly after seven months, he released a torrent of fluency.
Great Flu Pandemic More people died from the Great Flu Pandemic of 1918–19 than from any other plague in history, and more than from World War I itself.
the US version In the US and the UK, a million is one followed by six zeros. US usage adds three zeros for each step up, so a billion has nine zeros, a trillion twelve zeros, and so on. Practice in the UK adds six zeros at each stage so a billion has twelve zeros, etc.
one standard deviation Standard deviation indicates the size of a typical fluctuation around an average value.
to the news See Nassim Taleb’s readable and insightful book Fooled by Randomness.
quick mental estimate By the rule of 72, discussed later, a 24 percent annual growth rate doubles money in about 72/24=3 years. After nine years we have three doublings, to two, then four, and finally eight times the starting value. But it actually takes about 3.22 years because the rule of 72 underestimates the doubling time more and more as rates increase beyond 8 percent.
of the Alamo The story of this epic battle and the subsequent ordeals of those held captive by the Japanese is told by Eric Morris in Corregidor: The American Alamo of World War II, Stein and Day, New York, 1981, reprinted paperback, Cooper Square Press, New York, 2000.
surgical facilities The horrors of life in such camps is eloquently rendered in Three Came Home: A Woman’s Ordeal in a Japanese Prison Camp, by Agnes Keith, 1949, paperback 1985, Eland Books, London and Hippocrene Books, New York.
was still running Edmund Scientific’s Scientifics 2000 Catalog for Science and Engineering Enthusiasts, page 31.
several thousand feet See The Darwin Awards, Evolution in Action, “Lawnchair Larry,” pp. 280–81, by Wendy Northcutt, Plume (Penguin), New York, 2002.
of these flares String soaked in potassium nitrate solution and dried.
recipe and procedure About fifty years later, while listening to Ken Follett’s novel The Man From St. Petersburg, I noted that the terrorist antihero’s recipe and procedure for making nitroglycerine were consistent with how I made it as a boy in my mother’s refrigerator.
depth of 5 feet digitalcollections.lmu.edu/cdm/ref/collection/chgface/id/294.
a man’s hand As in 1 Kings 18:44.
dimensional analysis I was familiar with the book Dimensional Analysis by Percy W. Bridgeman, Yale University Press, New Haven, CT, 1922.
joined the rest In 2015, my granddaughter Claire Goul was one of three hundred semifinalists in the same contest. It was now the Intel Science Talent Search and had become more competitive, with three top prizes of $150,000 each, compared to one top prize of $10,000 back in 1949.
standard American wheel European wheels had only one green number and further improvements in the odds, such as the player betting on red or black only losing half his stake if that number came up.
systems must fail One of the most well-known examples is the Pythagorean theorem from plane geometry. It says that for a right triangle, the sum of the squares of the sides equals the square of the hypotenuse. For instance, the triangle with sides 3, 4, and 5 is a right triangle and 32+42=52. Also 122+52=132 for another right triangle. There are infinitely many and we could check them one at a time, but never finish. The theorem does it all at once.
a rubber ring Feynman put the rubber ring, which was made from the same material as that used on the Challenger, in the ice water and showed that, when it became cold like it did during the launch of the Challenger, it became so brittle it was likely to fail. Feynman tells the story in Classic Feynman, edited by Ralph Leighton, Norton, New York, 2006.
wealthy older student T. T. Thornton
for every frame You can see the film at www.edwardothorp.com.
a new strategy Baldwin, et al (1956).
and even awe For the rules of blackjack and my original report of this experience, see Thorp, Beat The Dealer, 1962, rev. ed. 1966.
mathematics course The course was measure theory, basic to probability and statistics.
partially played decks For one fifty-two-card deck we can choose a subset by selecting 0, 1, 2, 3, or 4 Aces in five ways, similarly selecting the number of cards for values Two through Nine in each of five ways, and selecting between 0 and 16 Ten-value cards in seventeen ways for a grand total of 5×5×…5×17−1 (there are nine 5s, one each for Ace, Two,…Nine) or a little over 33 million different total partial decks. (We subtract one to delete the case where zero cards of each value are chosen, leading to a subset with no cards in it.) For the eight-deck game the corresponding figures is 33×…×33×129−1, or about 6 quadrillion (6 followed by 15 zeros) partial decks.
to a gigantic For people who like to compute, suppose that each of these strategy tables was written on a separate piece of paper the size of a dollar bill. I estimate the volume of a dollar bill at 1.08 cubic centimeters so the strategy tables would occupy 37 cubic meters or 1300 cubic feet. For eight decks they would fill a space of 6.5 cubic kilometers or 1.6 cubic miles.
0.21 percent The Baldwin group said later that their figure of 0.62 percent for the casino’s edge should have been 0.32 percent. An arithmetic error caused the incorrect figure.
the blackjack rules Casino blackjack rules have varied over time and among casinos. The rules I used for the calculations were then typical.
(half the deck) The chance that the last twenty-six cards contain all four Aces is about 5.5 percent.
type from the deck Later exact calculations give numbers which are a bit more favorable to the player. These results also are affected by the many variations in casino rules. For details see Thorp (1962, 1966), Griffin (1999), Wong (1994).
$200 bankroll This book spans more than eighty years, during which the value of money has changed dramatically. For an accurate perspective the reader can convert money to current dollars using Appendix A.
my mathematical work The discovery was an example in functional analysis, in which both Taylor and the mathematician were specialists.
Shannon at noon Our meeting was on September 29, 1960, and I memorialized the details in a letter I wrote that same evening to a friend, mathematician Berthold Schweizer.
to the academy Thorp, Edward O., “A Favorable Strategy for Twenty-One,” Proceedings of the National Academy of Sciences, Vol. 47, No. 1, 1961, pp. 110–12.
the program booklet Thorp (1960). Fortune’s Formula also was the title of William Poundstone’s 2005 book covering some of this story about blackjack, roulette, the stock market, and the Kelly Criterion.
The Boston Globe “Can Beat Blackjack, Says Prof.,” by Richard H. Stewart, Boston Globe, January 24, 1961, page 1.
across the country For example, Columbus Dispatch (1961), Las Vegas Sun (1961), Miami News (1961), New York Herald Tribune (1961), New York World Telegram and Sun (1961), Washington Post and Times Herald (1961).
ran his story Thomas Wolfe, Washington Post, January 25, 1961, page A3.
offered a strand Paul O’Neil (Life magazine, 1964), in a generally accurate story, erroneously quotes me as saying of the string of pearls, “We had it appraised first thing in the morning. It was worth $16.” Neither statement is correct. This was repeated by Bruck (1994) even though I told her this part of the Life story was wrong. A good misquote is hard to kill.
the everyday gambler Schwartz, David G., Roll the Bones, Gotham Books, New York, 2006.
was a characteristic Feller (1957), (1968).
the investment worlds The greatest bond investor ever, William H. Gross, also learned this lesson in the casinos of Las Vegas. Motivated by Beat the Dealer, he went there in the summer of 1966, turning a $200 bankroll into $10,000. See Bill Gross on Investing, William H. Gross, Wiley, New York, 1997, 1998. He would later use the ideas in co-managing two trillion dollars for PIMCO.
with the house I realized later that I would have had an advantage if I had started each deal with big bets, maintaining them if the count was good and causing the dealer to shuffle when it wasn’t.
a serious loss Why might a bigger bankroll lead to more risk of losing it all? The reasons are partly technical, partly psychological. First the technical: To exploit the larger bankroll we would be likely to make maximum bets ($500 in those days) even in situations that were just slightly favorable. This would increase the size of the fluctuations in our stake and require a longer playing time than I had available to be fairly sure of coming out ahead.
Now the psychological: X and Y didn’t have my level of understanding of, and confidence in, the system. If, with a $100,000 bankroll they would in fact quit when we were down say $60,000, then I would be playing and sizing bets and taking risks as though I had a $100,000 bankroll when, unknown to anyone, I really only had a $60,000 bankroll. This subtle distinction between the ostensible bankroll and the real bankroll has contributed to the downfall of many gamblers and investors, as we shall see.
An additional psychological problem which I didn’t expect was Kimmel insisting playing his “pidgeon” version of my system, betting big, losing back much of the fruits of my labor, and then excitedly refusing to stop.
afternoon in Boston Ivi, her mother, and two sisters came to the US after World War II as refugees from Estonia.
great mathematics centers Segel, Joel, Recountings, A.K. Peters, Ltd. Wellesley, MA, 2009, tells the story of mathematics at MIT.
to stay on My family’s relationship with MIT continued two generations later. Three of my grandchildren, fraternal triplets, entered together as freshmen. See, e.g., “Triplets Celebrate After ALL are Accepted to Prestigious MIT…,” London Daily Mail, Saturday, July 25, 2015.
building the first one The MIT Media Lab timeline erroneously gives the year 1966 for our computer, probably because I first revealed its existence in the 1966 revised edition of Beat the Dealer. However, the correct year is 1961, when we completed and successfully tested it in Las Vegas, as explained in numerous subsequent publications, and verified in correspondence dated August 1961, between Shannon and me, now in the archives of the MIT Museum. The device itself also remains at the museum.
few early players Among them were Emmanuel Kimmel (Mr. X of Beat the Dealer), Jesse Marcum (the “little dark haired guy from Southern California” in Beat the Dealer), Russell Gutting (“Junior”), Benjamin F. (“System Smitty”) Smith, and Mr. F. (who I was told was Joe Bernstein, the “silver fox” in columnist Herb Caen’s book Don’t Call It Frisco). Marcum seems to have been the only one who consistently adhered to the method.
fairly thorough shuffles Of course, seven is not a magic number. The actual number of shuffles needed varies, depending how close to “random” is specified, the type of shuffle, and how “random” is measured.
in private games Danger in the Cards has been out of print for many years.
William F. Rickenbacker For more on this trip see the letters from Thorp and Barnhart in Blackjack Forum, Vol. XVII #1, Spring 1997, pp. 102–104, XX #1, Spring 2000, pp. 9–30, and XX #2, Summer 2000, pp. 105–107.
working for the board He wrote about our experience in a syndicated column titled “Even ‘Honest’ Vegas House Cheats.”
bits of publicity E.g., Time, “Games: ‘Beating the Dealer,’ ” January 25, 1963, p. 70.
“It's Bye! Bye! Blackjack” appeared Scherman, 1964.
a nine-page story O’Neil, Paul. “The Professor Who Breaks the Bank,” Life, March 27, 1964, pp. 80–91.
a heart attack In April of 1966.
thwart these card counters Vic Vickery, “Counting on Blackjack,” Las Vegas Style magazine, May 1993, pp. 61, 67.
Players Too Smart Carson City (UPI): New York Journal-American, April 3, 1964.
High–Low System I called this the Complete Point Count in Beat the Dealer.
pooling their bankrolls For the optimal trade-off between risk and return, the bet size in a given situation is proportional to bankroll. To the extent the players on a team are unsure about the current size of the group’s bankroll, they will tend to reduce their bets slightly.
Pacific Stock Exchange Google the Blackjack Hall of Fame write-ups for more on Francesco, Hyland, Uston, and others in this chapter.
the blackjack community As the popularity of the game surged, a blackjack community evolved. Special newsletters for counters were circulated and, later, websites appeared. Stanford Wong’s newsletters and websites provided cutting edge information on how and where to play for best advantage. Arnold Snyder’s quarterly Blackjack Forum had articles from leading players and theorists over its twenty years or so of publication and gave a good informal history of the war with the casinos. Anthony Curtis’s Las Vegas Advisor was a monthly guide to events, and to best deals on food, accommodations, and playing conditions. The Gambler’s Book Store, managed by Howard Schwartz, continued to offer the latest books and systems. Richard Reid’s website www.bjmath.com was a treasury of articles, workshops and discussions. The network that arose accelerated the development of new methods for advantageous play.
The second line Later more exact calculations changed these numbers somewhat. They also vary slightly with the number of decks.
nearest whole number Thirteen was chosen because it gave a good fit.
count was to use The strengths of various card counting systems are thoroughly discussed in The Theory of Blackjack by Peter Griffin, 6th Edition, Huntington Press, 1999.
in the discard tray An easy way to do this is by estimating how many half decks are left, as described in Professional Blackjack by Stanford Wong (pseud.), Pi Yee Press, 1994.
the point count If you divide the ultimate strategy values in table 1 by eight and round off to the nearest whole number, you get the values of 0 or 1 that make up the complete point count. However the values for sevens and nines are about as close to 1 and −1, respectively, as they are to zero. Choosing them thusly gives the alternative point count I was using in Puerto Rico.
“what I’ve got.” The quote is from Thorp (1966), pp. 84–85.
1970s, several people Notably, Keith Taft.
a powerful advantage I explained the idea in Thorp, Edward O., “Non-random Shuffling With Applications to the Game of Faro,” Journal of the American Statistical Association, pp. 842–47, December 1973. A much expanded version appears in Gambling and Society, edited by W. Eadington, Charles C. Thomas, Springfield, IL, 1975, as: “Probabilities and Strategies for the Game of Faro,” pp. 531–60.
cheating, the statutes N.R.S. 465.015.
success much more difficult Legends of Blackjack by Kevin Blackwood and Larry Barker, Kindle eBook, April 5, 2009, tells the stories of some of the leading professionals.
the Blackjack Ball “The Smartest Guy in the Room,” by R.M. Schneiderman, Newsweek, February 20, 2012, pp. 56–57.
in the movie 21 Inspired by the Ben Mezrich book Bringing Down the House.
rate the games Stanford Wong’s monthly newsletter is thorough.
exploitable patterns Pearson, Karl, The chances of death and other studies in evolution, London, New York, E. Arnold, 1897.
sailed the Caribbean Los Angeles Times, February 27, 2003, page B12, obituary of Albert Hibbs. See also Wilson (1965, 1970).
Hibbs later wrote Caltech obituary for Hibbs at http://pr.caltech.edu/periodicals.
a thing of the past Decades later, professional gambler Billy Walters found and exploited effective roulette wheels, as reported in Beating the Wheel, by Russell T. Barnhart, Carol Publishing, New York, 1992. Walters is interviewed in Gambling Wizards, by Richard W. Munchkin, Huntington Press, Las Vegas, Nevada, 2002, pp. 16–18. With a plastic playing card and a few minutes at a roulette wheel, I can tell you whether any of the dividers, or frets, separating the pockets on the rotor, are high or low, loose or tight, and which numbers will be affected. For good measure I would also check to see if the wheel was level and that the rotor hung true on its spindle.
odds in his…favor Thanks to Richard Cohen for supplying this.
a 1956 paper Kelly, J. L., “A New Interpretation of Information Rate,” Bell System Technical Journal, Vol. 35, 1956, pp. 917–26.
and the stock market Thorp, Edward O., “Optimal Gambling Systems for Favorable Games,” Review of the International Statistical Institute, Vol. 37, 1969, pp. 273–93; Thorp, Edward O., “The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market,” Handbook of Asset and Liability Management, Vol. 1, S.A. Zenios and W.T. Ziemba, editors. Elsevier, New York, 2006.
called wearable computers “A Brief History of Wearable Computing” timeline—MIT Media Lab, www.media.mit.edu/wearables/lizzy/timeline.html.
only one person O’Neil, Paul, “The Professor Who Breaks the Bank,” Life, March 27, 1964, pp. 80–91.
our roulette system Thorp, Edward O., Beat The Dealer, 2nd Edition, Vintage, New York, 1966.
the details later Thorp, Edward O., “Systems for Roulette I,” Gambling Times, January/February 1979; Thorp, Edward O., “Physical Prediction of Roulette I, II, III, IV,” Gambling Times, May, July, August, October 1979; Thorp, Edward O., The Mathematics of Gambling, Lyle Stuart, Secaucus, New Jersey, 1984.
by hardware problems Bass, Thomas A., The Endaemonic Pie, Houghton Mifflin, New York, 1985.
May 30, 1985 One of the uninformed people writing for Wikipedia claimed our computer was used to “cheat” at roulette. This is false. We and the many others who subsequently used roulette and blackjack computers could not be prosecuted under the strong anti-(player) cheating statutes already in place in Nevada. That’s why the Nevada state legislature had to pass a law specifically outlawing “devices.”
thermonuclear weapons Ulam, S. M., Adventures of a Mathematician, Scribner’s, New York, 1976.
to a set of rules These rules are designed to make the casino’s edge roughly the same on the two bets.
for the two bets Thorp and Walden (1966).
Walden and I proved Thorp and Walden (1973).
is in blackjack Griffin (1995), Thorp (1984), Vancura (1996).
so the effect Griffin (1995), Thorp (1984), Vancura (1996).
as many tables Vancura (1996).
can be ruinous The Kelly Criterion highlights the perils of overbetting even when you have the edge.
waiting fifteen years The NASDAQ Composite finally exceeded its March 2000 peak in April of 2015. However, investors were still behind more than 20 percent after adjusting for inflation.
weren’t available yet Bogle on Mutual Funds, pp. 169–70 says “The indexing concept was…introduced…to the mutual fund industry in 1976.” and in fact by the author himself, John C. Bogle.
or the stock market According to a Fidelity Research Institute Report dated February 2007 stocks averaged about 10 percent a year, beating residential real estate by more than 4 percent a year for 1963–2005 and by more than 5.5 percent annualized over 1835–2005. Bonds also did better than residential real estate.
to Mr. Market See The Warren Buffett Way, by Robert G. Hagstrom, Jr., Wiley, New York, 1994, pp. 50–51, and The Warren Buffett Portfolio, by Roberg G. Hagstrom, Jr., Wiley, New York, 1999, pp. 143–44.
thesis on the subject Kassouf, Sheen T., Evaluation of Convertible Securities, Analytical Publishers Co., 602 Vanderbilt Street, Brooklyn, New York 11218, 1962. A brief summary of hedging with warrants and convertible bonds.
Beat the Market You can read more about our theories and investments in Beat the Market at www.edwardothorp.com.
researcher and biologist You can read about his remarkable scientific aptitude and career on The National Academics Press website, www.nap.edu/books, in Biographical Memoirs v.53 (1982), National Academy of Sciences. In 1974 Gerard, who became one of my first investors using money paid out to him by Buffett, passed away. His wife, Frosty, survived him for several years. When she died, part of their Princeton Newport investment went to support the University of California, Irvine.
analysis of common stocks The classic 1940 second edition was reissued by McGraw-Hill in 2002.
was his contribution Some biographies of Buffett say $105,000. My figure, which I recall from conversations with Warren, is confirmed in the definitive biography of Buffett, The Snowball, by Alice Schroeder, Random House, New York, 2008.
a manic 150 percent Returns on equities are from Ibbotson Associates (2007).
Peter Minuit Minuit, Peter (1580–1638), Dutch colonial governor in America, helped establish New Amsterdam, the settlement that became New York City. He joined the Dutch West India Company and set out for the company’s settlement in America. He reached Manhattan Island in 1626 and became the first director general of the colony. Minuit purchased the island from one of the Algonquian-speaking tribes with trinkets valued at 60 Dutch guilders, a sum later calculated at $24.
with all the improvements From 1626 to 1968 is 342 years. Twenty-four dollars compounding at 8 percent would become $6.47 trillion, 1⁄8 or more of the net worth of the USA at that time. By 2013 this grows at 8 percent to $206 trillion, enough to buy half the world: estimating US 2013 net worth as $100 trillion ($77 billion for households plus $23 billion for government) and assuming the US has about 25 percent of the globe’s total net worth gives an estimate of $400 trillion for the market value of the world.
Discover magazine article “May the Best Man Lose,” Discover, Nov. 2000, pp. 85–91. For more on voting paradoxes, see Poundstone, William, Gaming the Vote: Why Elections Aren’t Fair (and What We Can Do About It), Hill and Wang, New York, 2008, and Saari, Donald G, “A Chaotic Exploration of Aggregation Paradoxes,” SIAM Review, Vol. 37, pp. 37–52, March 1995, and A Mathematician Looks at Voting, American Mathematical Society, 2001.
are typically stumped For more on nontransitive dice see Gardner, Martin, The Colossal Book of Mathematics, Norton, New York, 2001, and Finkelstein, Mark and Thorp, Edward, “Nontransitive Dice with Equal Means, in Optimal Play: Mathematical Studies of Games and Gambling, Stewart N. Ethier and William R. Eadington, editors, University of Nevada, Reno, 2007.
early as 1936 See Schroeder, loc. cit.
the last ten years Loomis, Carol, “The Jones Nobody Keeps Up With,” Personal Investing, Fortune, April 1966.
few existing hedge funds The hedge fund world at the start of 1968 was tiny, almost insignificant. The combined capital in dollars was less than one one-thousandth of what it was in 2016. Back in 1968, the top twenty funds ranged in size from $80 million down to $12 million.
Altogether, there were about 150 funds, with aggregate capital of a billion or two. This grew to more than two trillion dollars a half a century later. Since the dollar value of GNP was about a tenth of what it was forty-eight years later, hedge funds compared to GNP grew more than a hundred times from 1968 to 2016.
and were closing down The decline is catalogued in Robertson, Wyndham and Haines, Angela, “The Hedge Funds’ Dubious Prospects, A Report on Twenty-Eight Funds,” Personal Investing, Fortune, October 1970. The group consisted of the largest hedge funds as of December 31, 1968. The big winner was Buffett Partnership, Ltd., which was closing after a spectacular twelve years because stock prices were too high compared with the underlying value of the companies. The only other fund whose assets had increased was Steinhardt, Fine, Berkowitz & Co.
Wall Street Letter The Wall Street Letter, Myron Kandel, Editor, Nov. 17, 1969.
never before tried The year before, Arbitrage Management Company was set up to exploit the hedging ideas in Beat the Market. Among others it involved Harry Markowitz, who later won a Nobel Prize in Economics, and John Shelton, a leading finance professor and warrant theorist. Though profitable, the gains were not enough to keep it from disappearing from the scene after three years.
would transform physics For a full account see the inspiring Annus Mirabilis: 1905, Albert Einstein and the Theory of Relativity, by John and Mary Gribbin, Penguin, New York, 2005.
of stock price changes See the article by Case M. Sprenkle in The Random Character of Stock Market Prices, Paul H. Cootner, editor, MIT Press, Cambridge, MA, 1964.
riskless interest rate Academic economists and financial theorists have long assumed, as in the Black-Scholes formula, that US Treasury bonds and their short-term version, bills, are riskless. The argument goes that the government can always print the money it needs in order to pay the interest and to redeem them at maturity. Congressional battles over whether to raise the debt ceiling, such as the clash in 2013, exposed the fallacy. The US can pay its debts but it may choose not to. Default is possible. Since investors generally demand to be paid a higher rate of interest to purchase risky debt, this dispute over the debt ceiling has led to higher borrowing costs for the US. Thus, those opposing an increase in the debt ceiling have made the debt itself larger.
warrant expiration date For an account of what I did, see my articles in Wilmott magazine, Sept. 2002, Dec. 2002, and Jan. 2003. They are also available on my website at www.edwardothorp.com. For an introduction to the methods of plausible reasoning see Mathematics and Plausible Reasoning, Vols. I and II, by George Polya, Princeton University Press, 1954, and his more elementary How to Solve It, 2nd Edition, Doubleday, 1957.
I began using it For a background discussion, see Derivatives: Models on Models, by Haug, Espen Gaarder, Wiley, New York, 2007, pp. 27–44.
Beat the Market They acknowledge this in their famous paper, Black, F. and Scholes, M., “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, May–June 1973, pp. 637–54.
the identical formula The fact that their formula was identical to the one I was using verified that my plausible reasoning led to the correct result.
down when he had Buffet: The Making of an American Capitalist, by Roger Lowenstein, Random House, New York, 1995, page 156.
customers high fees In a massive replay, hundreds of trillions of dollars’ worth of derivatives contracts now trade Over-the-Counter (OTC). Again, the banks and brokers love the high fees and are resistant to standardizing the contracts. The OTC contracts are under-collateralized and could easily precipitate a financial collapse similar to what we saw in 2008–09. Exchange-traded standardized contracts could eliminate this threat.
from the formula Years later I heard that one trader had consulted Black and also was using formula prices when trading began at the CBOE.
The Wall Street Journal “Computer Formulas Are One Man’s Secret to Success in Market,” by Jonathan R. Laing, Wall Street Journal, September 23, 1974, page 1.
running my hedge fund Fortune’s Formula, page 172, incorrectly reports that I was making as much then as Paul Newman was.
One of my stories Beat the Dealer, 1966 edition, pp. 167ff.
where I was speaking “Extensions of the Black-Scholes Option Model,” Thorp, Edward O., Contributed Papers 39th Session of the International Statistical Institute, Vienna, Austria, August 1973, pp. 1029–36.
model for stock prices This is the so-called lognormal model for stock price changes. A different but important situation which it fails to cover for option valuation is the bimodal, or two-peaked, payoff distribution which arises when one company makes a tender offer for another.
and applied finance Fischer Black and the Revolutionary Idea of Finance by Mehrling, Perry, Wiley, New York, 2005.
were eventually published See “Option Pricing: The American Put,” by Parkinson, Michael, Journal of Business 1977, v50(1), pp. 21–36, and “The Valuation of American Put Options,” by Brennan, Michael J. and Schwartz, Eduardo, Journal of Finance 1977, v32(2), pp. 449–62.
than $1 million Andrew Tobias used my account of this trade and several others we did in his book Money Angles, Simon and Schuster, New York, 1984, pp. 68–72.
is a general rule If you make 20 percent in year one and 30 percent in year two the wealth and relatives are 1.20 and 1.30. Multiplying gives 1.56, which is the wealth relative for the two successive years, the amount a dollar grows to if reinvested. Thus the two-year gain is 56 percent, not 20 percent+30 percent or 50 percent. If you simply add the numbers in the table you get +11.7 percent for the market, which isn’t nearly as bad. But to find out what a dollar invested at the start of 1973 grows to, or diminishes to, you need to multiply together the results for successive periods, which produces the –0.5 percent figure. The result from investing $1 for one period is called the “wealth relative” (wealth at the end of the period). For instance, if you make 12 percent during the year, the wealth relative for that twelve months is 1.12. When we add the numbers for the returns for PNP limited partners the result is 42.1 percent, significantly less, in this case, than the actual 48.9 percent figure obtained by multiplying successive wealth relatives.
only month-end values Month-end figures for the S&P 500 are from Ibbotson. Because the Great Depression was, on average, deflationary, the results based on inflation adjusted or “real” returns are less extreme.
quality and maturity More precisely, “duration,” which is the discounted weighted average time for the payment stream.
hundred billion dollars During the early stages of the run-up in interest rates, S&Ls were raising money by selling puts at bargain prices on Government National Mortgage Association (GNMA) bonds. Bonds usually trade in thousand-dollar denominations or “par” amount and are quoted as a percent of par, so these bonds—quoted at 98—were currently selling at $980 each. The puts we bought from the S&L which issued them gave us the right to sell the bonds to that S&L at this price for the life of the put, which in our case ranged from twelve to eighteen months. If the bonds fell, we could buy the bonds below 98 and “put them” to the bank, which was required to pay us 98 under the terms of the contract. If the bonds rose instead, the puts would expire worthless. As the price of a put tends to move in a direction opposite to that of the underlying security, we hedged the risk of loss on the put by buying GNMA (“Ginnie Mae”) futures, i.e., contracts to buy GNMA bonds at a certain price and time in the future. In futures markets, contracts require daily settlement of gains and losses. If the bonds fell in price we would have temporarily to lay out cash for our losses in the futures markets, even though we would ultimately get the money back when we cashed in our puts. Since our cash and borrowing power was finite, this limited how big a hedge we could safely carry to completion. To estimate the maximum safe size for our hedge we needed to consider the lowest price anyone imagined GNMA bonds could drop to during the next eighteen months. The number was 85, a fall of 13 points. I said, let’s be super-cautious and double our margin of safety to cover a collapse of 26 points, or a price of 72. This prudence was rewarded when the unexpected happened and the bonds fell as low as 68 during the duration of our trade.
at UC, Irvine It was then the Graduate School of Management.
were earnings yield Earnings yield is E/P, Where E is annual earnings (either trailing twelve months or predicted next twelve months—you choose). This is the inverse of P/E, the famous price/earnings ratio, but E/P is better because of problems in the interpretation of P/E when E is zero or negative.
several billion dollars Market Neutral Strategies, Bruce I. Jacobs and Kenneth N. Levy editors, Wiley, New Jersey, 2005.
when it opened Hours for the N.Y.S.E. were from 10 A.M. to 4 P.M. Monday through Friday, from October 1, 1974, until September 30, 1985, when the opening time changed to 9:30 A.M.
of which we pioneered Among them were the interest rate swap (the object here was to hedge away interest rate risk in our positions), the bond cash and carry, the commodity cash and carry, capturing a profit when closed-end funds could be purchased below their liquidation value, and special deals.
historical stock price data I learned only recently, while reading the interview of Harry Markowitz in Masters of Finance, IMCA, Greenwood Village, CO, 2014, page 109, that Markowitz and Usmen got the same answer for daily S&P 500 Index price changes as we did for a much larger data set of two hundred individual stocks. Their work, done sometime before 1987, and submitted before he won the Nobel Prize for Economics in 1990, was initially rejected for publication (!), appearing elsewhere only in 1996.
of the impact Market impact refers to the fact that “market orders” to buy are, on average, filled at or above the last previous price and “market orders” to sell tend to be filled at or below the last previous price.
gained 9 percent The accounting period with an odd length of five months arose here for PNP because the fiscal year end for PNP changed in 1987 from October 31 to December 31.
statistics confirmed Common metrics include the Sharpe ratio, the Sortino ratio, the distribution of drawdowns, and the MAR ratio (annual return divided by maximum drawdown). See, for instance, the three-part series by William Ziemba in Wilmott magazine: “The Great Investors,” March, May and July 2006.
or losing quarters For comparison, the S&P 500 was down in eleven of the thirty-two full quarters and small company stocks lost in thirteen.
associates, and clients Den of Thieves by James B. Stewart, Simon and Schuster, New York, 1991.
Ken Griffin The Quants by Scott Patterson, Crown, New York, 2010.
first limited partner Conversation with Citadel’s Scott Rafferty.
$5.6 billion The Forbes 400 list likely misses people that should be on it, the numbers are estimates, and wealth fluctuates, so the rankings are not exact. For example, Warren Buffett qualified when the list was started in 1982 but they didn’t discover him until 1985! Also missing from the Forbes list are “The $13 Billion Mystery Angels,” of the article by Zachary Mider, Bloomberg Businessweek, May 8, 2014. Mider reveals that a group of former PNP employees made at least $13 billion in the twenty-five years after starting their own firm in 1989, with the aid of our quantitative methods and computer algorithms.
Malibu, California For some of his thoughts, see J. Paul Getty, How to Be Rich: The Success of a Billionaire Businessman, Playboy Press, New York, 1965.
Corporation, said Los Angeles Times Magazine, January 23, 2000, pp. 10ff and page 35.
D. E. Shaw When D. E. Shaw hired one of our key employees the first thing they reportedly did was debrief him for six hours to find out everything he could tell them about PNP.
convertible bonds The program had methods for incorporating quality deterioration and credit default risk which were, I believe, unique at the time.
I’ve got enough The New Yorker, May 16, 2005.
buyers and sellers We chose a sample of ten option trades from the forty which we had not already proven to be fakes.
a legal mess For the classic story of a legal mess, see Jarndyce versus Jarndyce in Bleak House by Charles Dickens.
his best investment If Madoff is really gaining 20 percent a year and their best alternatives give, say, 16 percent a year, then they’re only out 4 percent a year.
to destroy documents Rothfeld, Michael and Strasburg, Jenny, “SEC Accused of Destroying Files,” Wall Street Journal, August 18, 2011, page C2.
the headline article Arvedlund, Erin E., “Don’t Ask, Don’t Tell,” Barron’s, May 7, 2001.
in the early 1990s “Bernard Madoff Gets 150 Years in Jail for Epic Fraud (Update 7), Bloomberg.com, June 29, 2009.
$65 billion News Release, “Bernard L. Madoff Charged in Eleven-Count Criminal Information,” U.S. Attorney for the Southern District of New York, March 10, 2009.
One individual reportedly One Jeffry M. Picower, according to The New York Times, Sunday, July 5, 2009, page B2. According to a later report in The New York Times by Diana B. Henriques, October 2, 2009, page B5, the trustee liquidating the Madoff assets, Irving H. Picard, “reported that one Picower account had been overdrawn by $6 billion when Mr. Madoff was arrested.”
the individual guesses If half of the crowd’s guesses are on each side of the average it is a mathematical fact that the average will be closer to the correct value than at least half of the individual estimates. What is interesting is that the crowd consensus is often much better yet.
hedging Japanese warrants “The Money Man: A Three-time Winner,” Forbes, November 25, 1991, pp. 96–97.
so-called secretary or marriage problem Today one might retitle it as “The Significant Other Problem.”
to gain a profit A couple of weeks after the EMLX hoax, the Los Angeles Times reported that the SEC, in a “web fraud sweep,” accused thirty-three companies and individuals of illegally using the Internet to make more than $10 million in profits by driving up the prices of more than seventy small thinly traded stocks, hyping them on chat rooms, websites, and in email messages.
before the Internet Two readable and entertaining accounts are the famous Extraordinary Popular Delusions and the Madness of Crowds, by Charles MacKay, and its more current sequel, Ponzi Schemes, Invaders from Mars and Other Extraordinary Popular Delusions, by Joseph Bulgatz.
Hell on one’s feet See page 71 of Haugen, The New Finance: The Case Against Efficient Markets, Second Edition (1999).
Recent reports “Toxic Equity Trading Order Flow on Wall Street,” by Arnuk, Sal and Saluzzi, Joseph, A Themis Trading LLC White Paper, www.themistrading.com, and “Algo Traders Take $21bn in Annual Profits,” by Tom Fairless of Financial News, quoting the research firm Tabb group.
for the A shares Reported as of 1:22 P.M. New York time on July 24, 2009.
one of the mechanisms “Traders Profit With Computers Set at High Speed,” by Charles Duhigg, New York Times, Friday, July 24, 2009, Page A1, and “SEC Starts Crackdown on ‘Flash’ Trading Techniques,” by Charles Duhigg, New York Times, Wednesday, August 5, 2009, Page B1. See also: (1) Patterson, Scott, and Geoffrey Rogow, “What’s Behind High-Frequency Trading,” Wall Street Journal, Saturday/Sunday, August 1–2, 2009, page B1. (2) Wilmott, Paul, “Hurrying Into the Next Panic?”, New York Times, Wednesday, July 29, 2009, page A19.
Krugman disagrees sharply Krugman, Paul, “Rewarding Bad Actors,” New York Times, Monday, August 3, 2009, page A19. See also O’Brien, Matthew, “High Speed Trading Isn’t About Efficiency—It’s About Cheating.” The Atlantic, February 2014.
cut a trading rate The dollar value of all trades in U.S. equities varies from year to year, as does the portion created by the high-frequency traders.
Business Day headline New York Times, September 28, 2000.
billion shares annually The Medallion Fund, a hedge fund closed to new investors, run by mathematician James Simons, includes a similar and far larger trading operation than ours with a higher rate of turnover and a vast annual trading volume. Now an investment vehicle for Simons and his associates in his firm Renaissance Technologies Corporation, it is probably the most successful hedge fund in history.
of our researchers David Gelbaum.
Gerry Bamberger For this and much more, see A Demon of Our Design, by Richard Bookstaber, Wiley, New York, 2008.
in the securities industry See the book The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It, by Scott Patterson, Crown, New York, 2010.
and more powerful It was based on the statistical notion of “principal components”; We called it ETS, for “Equity Trading System.”
Japanese warrant hedging See Forbes, November 25, 1991, pp. 96–99, “A Three Time Winner,” and the article by Shaw, Thorp and Ziemba, “Risk Arbitrage in the Nikkei Put Warrant Market of 1989–1990,” App. Math. Fin. 2, 243–71 (1995).
trend is greater The graph makes returns in the second epoch appear even more variable relative to the first than they really were. The proper display for comparing variability and growth rates is a so-called lognormal graph. For that graph of XYZ’s performance, see Thorp, Edward O., “Statistical Arbitrage, Part VI,” Wilmott, July 2005, pp. 34–36.
had ever experienced Reportedly, Simons’s secretive Renaissance Partners had a similar experience in August of 2008, losing 8 percent or so in a few days, then rebounding to make more than 100 percent for the year.
employees, only six Since the six people in my office also had other responsibilities, we had only 3.5 “full-time equivalents” on the project.
in statistical arbitrage Firms doing statistical arbitrage, such as the hedge fund group Citadel, already had in place most of the technology, talent, and expertise needed later to create and implement high frequency trading (HFT). For an account of HFT, see the book Flash Boys by Michael Lewis; In 2005, three years after we went out of the statistical arbitrage business, Steve and I worked with Jerry Baesel, who was then at Morgan Stanley Asset Management, to see if it was worth restarting. We concluded it was marginal because simulation showed a recent unlevered return of 10 percent or so, not attractive enough when compared to other investment opportunities then available to us. Meanwhile, we put the “shrink-wrapped” software on our shelf with a tag saying “add people and data to reactivate.” Had we been running the program during the 2008–09 economic crisis, I suspect that we would have had a rerun of our “miraculous” 1998–99 results.
or ten thousand shares The number of shares for which a depositor can apply varies from one offering to another, but between ¼ percent and 1 percent of the issue is common.
deals aren’t as good If, for example, the business value in the MW deal were $5 instead of $10, management helped themselves to $3 of the final enterprise value, and selling costs were $1, buyers of the IPO would get a value of $5+$10−$3−$1=$11 for their $10. The market won’t recognize this value right away, so the stock will start trading below $11 a share. Meanwhile, market prices for the group of S&Ls as a whole could drop, taking the new stock’s price down, too. Or, if the market sees management as greedy—$3 is a lot to take out for themselves—or not competent to put the new capital to work, the stock will decline.
so-called opportunity cost Opportunity cost refers to the cost of the opportunity that was given up. In addition to the cost of redirecting our capital from other investments, it includes the value of whatever didn’t get done because we redirected our personal time to the S&L project.
never did, either After BPL closed, Buffett accumulated Berkshire stock whenever he could, often from his friends, associates, and former partners. According to Schroeder, The Snowball, pp. 341–42, the stock was unregistered then so it had to be traded privately.
As Forbes Forbes 400, October 22, 1990, page 122.
growth, decided Quietly.
made my first purchase Buffett was so uninformative about his plans that his own children sold their stock fairly early. I started buying about the time his daughter Susie sold off the last of hers.
$74,000 a share “Ordinary” investors tend to switch their money from securities that drop in price to those that have gone up, a strategy sometimes described as chasing returns. An academic study of all domestic US equity mutual funds covering 1991 through 2004 showed that this behavior by the fund investors reduced their annual returns by an average of 1.6 percent; Friesen, Geoffrey C. and Sapp, Travis R.A., “Mutual Fund Flows and Investor Returns: An Empirical Examination of Fund Investor Timing Ability,” Journal of Banking and Finance, September 2007. Summarized in “Buying High and Selling Low,” Mark Hulbert, New York Times, July 12, 2009, Mutual Fund Report, page 18.
a famous interchange Paul Marx told me this story.
principles of security analysis As practiced by Graham, Dodd, Buffett, Munger, Fisher and others.
Three Successive Periods I chose the dates for the first three periods because the price graphs suggested that they were natural divisions. The fourth and last period covers the aftermath of the Great Recession.
fund in the country The woes of Harvard’s endowment fund are chronicled in “Rich Harvard, Poor Harvard,” by Nina Munk, Vanity Fair, August 2009, pp. 106ff.
average 18 percent This loss figure of 18 percent is commonly cited by the industry and I use it throughout the book. However, it substantially understates the drop because some funds did not fully discount their toxic assets, others with illiquid assets reported too late to be counted, reports are voluntary so losers are less likely to respond, and the impact of funds which disappeared during the year may not have been included.
billion in 2007 New York Times, March 25, 2009, page B1.
Management fees Incentive fees in 2015 averaged 17.7 percent of any profit, compared to 19.3 percent in 2008, according to The Wall Street Journal, September 10, 2015. Management fees had declined to an average of 1.54 percent.
hedge fund returns The studies encountered difficulties obtaining clean long-term data and in correcting for survivorship bias: funds that died early and may not be in the database are expected to have performed more poorly. Omitting them and studying only the survivors overstates the results.
Later analyses Dichev, Ilia D. and Yu, Gwen, “Higher risk, lower returns: What hedge fund investors really earn,” Journal of Financial Economics, 100 (2011) 248–63; Lack, Simon, The Hedge Fund Mirage, Wiley, New York, 2012.
One study Bloomberg Businessweek, “Buzzkill Profs: Hedge Funds Do Half as Well as You Think,” August 17, 2015, reports on a study by Getmansky, Lo, and Lee. Using data from 1996 through 2014, they conclude that a reported average return of 12.6 percent was really 6.3 percent when the losers, who tend not to report, are included.
As Shakespeare Julius Caesar, Act I, Scene II, lines 140–41.
in an article International Fund Investment, April 2000, page 64.
managers that year New York Times, March 25, 2009, page B1.
playing this game New York Times, September 9, 1999, National Edition, page C10.
tend to fade Consider the statistical phenomenon of regression toward the mean.
of their stake Numerous books and articles give accounts of what happened, including Roger Lowenstein, When Genius Failed, Random House, New York (2001), “Failed Wizards of Wall Street,” Business Week, September 21, 1998, pp. 114–20, and “Hedge Fund’s Star Power Lulled Big Financiers Into Complacency,” by Timothy L. O’Brien and Laura M. Holson, New York Times, October 23, 1998. For some of my comments, see Tim O’Brien’s story “When Economic Bombs Drop, Risk Models Fail” in the New York Times, October 4, 1998. A sensational Nova program on LTCM that aired in February 2000, asserted that the total LTCM contracts outstanding amounted to a trillion dollars.
good to him Perhaps too good. He later stole millions from his firm and fled to Brazil.
following classification Forbes, October 11, 1999, page 60.
$83 trillion Orange County Register, March 7, 2014, Business, page 3.
is not available How big is the underground economy? What’s the value of privately held non-traded businesses? How much of the national wealth consisting of patents, copyrights, and innovation is being counted? Most household labor is not monetized, hence is not customarily counted in national income.
$1.36 million Source: Money magazine report on a University of Michigan study, the lead author being Fabian T. Pfeffer. Much of the increase in inequality comes from the fact that housing prices were about the same in 2014 as they were in 2003, whereas US stocks, as represented by the S&P 500, doubled. The rich have a higher proportion of their wealth in stocks and less in housing than poorer people.
for large stocks Ibbotson Associates yearbook.
saves $6 each day He saves more each day in later years assuming the price of cigarettes increases along with inflation.
An article http://quickenloans.quicken.com/Articles/fthbc_afford_budget.asp.
$10,000 difference grows Mentally calculated by the rule of 240 in Appendix C.
The formula Assume the power law N = AW–B, where W is a high enough wealth level to exclude most people, and N is the number having wealth at least W, and A and B are unknowns. The two facts I used to find A and B were (1) when N = 400, W = $1.3 billion, and (2) the total wealth of the 400 was $1.2 trillion, giving an average value of three times the cutoff. The result is N = 400 [(1.3 billion)/W]4/3. The value 4/3 for B seems to be roughly the same from year to year, as the average wealth seems to be about three times the cutoff. So you can recalibrate the formula each year that this is true by simply replacing 1.3 billion by the current cutoff. Using 1999 data, in “How Rich Is Rich?—Part 1,” Wilmott magazine, July 2003, pp. 44–45, I found the slightly different value 1.43 instead of 4/3. Perhaps coincidentally, the 2009 Forbes 400 edition offers a calculator using this formula on page 20 at forbes.com/baldwin. Forbes, page 20, says the formula uses the exponent 0.7, which equals 1/B and, therefore, a value for B of 1.43. Their formula inverts mine and expresses W as a function of N. For an extended discussion of formulas for estimating wealth and income, including evidence for the Pareto equation, see Inhaber and Carroll (1992) and the many further references therein as well as Scafetta, Picozzi and West, “An out-of-equilibrium model of the distribution of wealth,” Quantitative Finance, Vol. 4 (2004) pp. 353–64.
billion dollars or more The Orange County Business Journal listed 36, with Lakers basketball star Kobe Bryant in 36th place at $250 million. Since I know of people they missed, the figure of 49 may be closer to the truth.
$81 billion The Gates household had as much wealth as 150 thousand average US households. In other words, one one-thousandth of all the private wealth in the United States.
large increases in wealth Carrying this a step further, you could guess someone’s future wealth, in current dollars, by estimating the present value of their future savings, plus their current net worth. This is similar to some methods used by analysts to calculate the value of a company in current dollars, and hence the fair price for its stock. Using an estimated future inflation rate you could then arrive at a value for their wealth on any future date.
$37 million each Bloomberg, August 17, 2009, citing UC–Berkeley economics professor Emmanuel Saez, noted for his continuing studies of, and statistics on, the distribution of income and wealth in America. Note that the average of $37 million, divided by the cutoff of $11.5 million, is 3.2, very close to the result of the same calculation for the wealth distribution of the Forbes 400, suggesting that 2007 superrich taxable income followed the same, or nearly the same, power law as that for wealth.
disputed origin The claimed sources include Benjamin Franklin, various Rothschilds, Albert Einstein, Bernard Baruch, and “unknown.”
$22 million result These figures do not include trading costs or income taxes. A buy-and-hold investor loses little to trading costs and is taxed only on dividends. Taxes, if any, vary with the investor.
less than the last So-called decreasing marginal utility.
as one day less Adults with the same chronological age vary widely in their fitness age. Qualifiers for the Senior Olympic Games have a functional and fitness age averaging twenty-five years less than their calendar age, as reported in “Older Athletes Have a Strikingly Young Fitness Age,” by Gretchen Reynolds, in the New York Times, July 1, 2015. Studies of identical twins give persuasive evidence of the longevity benefits of exercise. See, for instance, “One Twin Exercises, the Other Doesn’t,” Gretchen Reynolds, New York Times, March 4, 2015.
forty hours of commuting Assuming he works on average about twenty days a month.
a month to operate Costs include fuel, maintenance, insurance, license fees, and depreciation, plus the owner’s time spent taking care of these.
the US stocks The Vanguard Total Stock Market Index Admiral Shares, ticker symbol VTSAX, does this. Actually, it invests in each stock proportionally to the market value of the so-called float, which is the estimated fraction of freely trading shares, as opposed to shares being held which are not available for trading. The difference in performance between the two methods has been negligible.
it first appeared Justin Fox, The Myth of the Rational Market, page 119, reports that Ben Graham, in 1962, pointed out that investment funds as a whole shouldn’t expect to beat the market “because in a significant sense they…are the market.”
the clearest exposition Sharpe, William, “The Arithmetic of Active Management,” Financial Analyst’s Journal, Vol. 47, No. 1, pp. 7–9, January/February, 1991.
all areas of investing According to Lipper, Inc., Wall Street Journal, July 6, 2009, section R, the average equity mutual fund expense ratio alone was 1.22 percent in 2007, compared to 0.20 percent for Vanguard’s no-load equity index funds. As the expense ratio is only a part of the fees investors pay, the “helpers” collect substantially more than 1 percent per year and, with trading costs, active investors lag passives by well over 2 percent annually.
five and ten years Fund Track, by Sam Mamudi, Wall Street Journal, October 8, 2009, page C9.
corresponding economic loss These extra taxable gains or losses will be offset later if you liquidate your investment.
to catch up Taxes leave me with 70 percent of my sales price. To get back to $100, $70 has to increase by $30 or 42.6 percent.
beat the market This sounds nonsensical at first. What it means is that no one has any information whatsoever that has predictive value.
to the contrary They display the well-known characteristic known as cognitive dissonance.
and hundreds of books An excellent history of these meanderings is Justin Fox’s book The Myth of the Rational Market.
all the future earnings Interpreted as net value paid out or accumulated for the benefit of a sole owner.
on inside information As chronicled by James Stewart in Den of Thieves, Connie Bruck in The Predators’ Ball, and others.
this type profitably Tobias, Andrew, Money Angles, Simon and Schuster, New York, 1984, pp. 71–72. Often, management would offer to redeem shares at an intermediate price, thus cashing out the dissidents and retaining an asset base of unredeemed shares which they could continue to be paid to manage.
in a few months Buying SPACs was not without risk because the assets were not protected from creditors in bankruptcy. Jeff, who discovered the strategy, researched the risks in each case before investing.
or 82 percent I have omitted details such as how the actual cash required for the investment might vary from the $9,000 of the example because of the interaction of margin regulations with the investor’s preexisting portfolio, and also because of time-varying marks to the market on the short position.
The Wall Street Journal Wall Street Journal, March 3, 2000, page C19, “Palm Soars As 3Com Unit Makes Its Trading Debut.”
the EMH explained Malkiel, Burton G., A Random Walk Down Wall Street, Norton & Co., New York, 2007.
The New York Times New York Times, March 3, 2000, page A1, “Offspring Upstages Parent In Palm Inc.’s Initial Trading.”
academic literature documents It often takes weeks or months for the stock price to fully adjust after announcements of unexpected earnings, stock buybacks, and spin-offs.
already been counted Mutual fund management companies and hedge fund general partnership interests have a separate and often considerable market value but they have already been counted as part of the private equity subcategory.
between asset classes For a highly mathematical discussion of this effect, sometimes called “volatility pumping,” see The Kelly Capital Growth Investment Criterion: Theory and Practice, editors Leonard C. MacLean, Edward O. Thorp, and William T. Ziemba, World Scientific, 2010.
The results For a comprehensive history of returns for world stock markets, see Triumph of the Optimists, by Dimson [et al].
1940–2004 period “Causes of the United States Housing Bubble,” from Wikipedia, 09/16/09 version; Ziemba, William, “What Signals Worked and What Did Not 1980–2009, Parts I, II, III, Wilmott magazine, May, July and Sept. 2009.
owning your home On average, significant money in excess of inflation is made in commercial real estate but not in residential real estate. Homeowners and would-be buyers often don’t understand the distinction. They also are misled by the stories of big winners at various times and in different localities. They share this error with stock market investors, which is no surprise as many are the same people. Behavioral finance theorists have analyzed this human tendency.
median large endowment “Princeton’s Endowment Declines 23 percent,” by John Hechinger, Wall Street Journal, September 30, 2009, page C3.
Fortune’s Formula The title, Fortune’s Formula, should sound familiar, as it was the title of the talk I gave on blackjack to the American Mathematical Society in 1961. Bill Poundstone considerately asked if he might use it as his title. In Beat the Dealer I called this, naturally enough, the Kelly Gambling System. Since 1966 I’ve called it the Kelly Criterion and the name has stuck.
larger the bet You can read about the details in articles I have written, most of which are available on my website at www.edwardothorp.com.
considerable controversy In addition to Poundstone’s history, mathematically trained readers can study some of the burgeoning modern developments in The Kelly Capital Growth Investment Criterion: Theory and Practice, editors Leonard C. MacLean, Edward O. Thorp, and William T. Ziemba, World Scientific, 2010.
As he told The Wall Street Journal “Old Pros Size Up the Game,” by Scott Patterson, Wall Street Journal, March 22, 2008, page A9. Gross left PIMCO in 2014 and went to Janus to manage money.
out in Wilmott magazine See “Understanding the Kelly Criterion,” by Edward O. Thorp, Wilmott, May 2008, pp. 57–59, and http://undergroundvalue.blogspot.com/2008/02/notes-from-buffett-meeting-2152008_23.html.
Computer simulations The simulations were done by mathematician Art Quaife.
stock index fund Why not continue to hold Berkshire? One reason is that I can’t foresee who will be managing the endowment in the distant future and believe it best to lock them into the well-understood mechanical approach of indexing. This avoids the waste that occurs from active investing.
H. W. Brands Fortune, August 11, 2003.
resilient than universities As quoted in Sample, Steven B. and Bermis, Warren, Los Angeles Times Book Review, July 13, 2003, page R9.
criteria for selection I thank Professor Ronald Stern for encouraging and facilitating the creation of the chair, Paul Marx of the University Foundation for legal help and for many insightful conversations, and my wife, Vivian, for her part in creating the conditions that made our contribution possible.
early card counters See The Bond King, by Timothy Middleton, Wiley, New Jersey, 2004, and Everything You’ve Heard About Investing is Wrong, by William H. Gross, Random House, New York, 1997, as well as the revised version Bill Gross on Investing, by William H. Gross, Wiley, New York, 1997, 1998.
past twenty-five years Gross, 1997, op. cit. page 90.
causes, so a group The idea of meeting with Bill Gross started with Professor Stern, then Dean of the School of Physical Sciences, and Greg Gissendanner, who was UCI’s University Advancement Officer at the School. My friend and attorney, Paul Marx, knew Bill and set up a lunch.
ahead of schedule Sue and Bill Gross later gave an additional $4 million to complete the fourth floor conference center and laboratories.
all-time closing high Source: www.finance.yahoo.com, daily closing prices, adjusted for splits and dividends. Figures are truncated from 1565.15 and 676.53.
$48.5 trillion The Federal Reserve, as reported in the Los Angeles Times, March 12, 2010.
$161 per share The successive 10 percent increases over the previous stock price compound, moving the stock from $100 to $110, then to $121, $133.10, etc., reaching $161.05 after the fifth increase.
more than ten times Month-end returns from the end of 1925 to the end of August 1929 show no decline in the index from a previous peak of 10 percent, suggesting that conditions were encouraging for borrowing as stock prices increased.
maintenance margin For a discussion of maintenance margin, see, for instance, Beat the Market, by Thorp, Edward O. and Kassouf, Sheen T., Random House, New York, 1967, Chapter 11.
impact of speculation Wikipedia.
Frontline Frontline: The Warning, October 20, 2009, pbs.org, available on DVD.
gross national product What would have been produced by workers who are unemployed never gets “made up.” Social waste included deteriorating empty untended houses and the impact on society of shattered lives.
Krugman pointed out Krugman, Paul, “How Did Economists Get It So Wrong?” New York Times Magazine, September 6, 2009, pp. 36–43.
in his book The Quants: How a Small Band of Math Wizards Took Over Wall Street and Nearly Destroyed It, by Scott Patterson, Crown, New York, 2010.
remain solvent He also said, on the same point, “In the long run we are all dead.”
anyone, later told Patterson, Scott, Wall Street Journal.
Krugman points out Krugman, Paul, “Good and Boring,” New York Times Op-Ed, February 1, 2010.
411 to 1 Hiltzik, Michael, “Echoes of Bell in CEO Salaries,” Los Angeles Times, page 31, October 3, 2010. Wall Street Journal (as reprinted in The Orange County Register, May 11, 2014, Business, page 3) says a study by the Economic Policy Institute found that for the 350 companies with the largest sales, CEOs received 18 times the pay of their workers in 1965 but were compensated 201 times as much, on average, in 2012.
as Moshe Adler Adler, Moshe, “Overthrowing the Overpaid,” Los Angeles Times Opinion, page A15, January 4, 2010.
Garrett Hardin Hardin, Garrett, “The Tragedy of the Commons,” Science, Vol. 162, No. 3859 December 13, 1968, pp. 1243–48.
protects my neighbors Vaccination is a positive externality as it protects others from contracting a disease from the recipient.
collection of insights Poor Charlie’s Almanack: The Wit and Wisdom of Charles T. Munger, Foreward by Warren Buffett, edited by Peter Kaufman. Expanded third edition, 2008.
much of their income Read the evolving discussion of the taxation of so-called carried interest in Wikipedia and elsewhere on the Internet. The 2012 Republican presidential candidate, Mitt Romney, was a substantial beneficiary.
of national income The top 1 percent have about a third of taxable income, the next 9 percent have another third, and the bottom 90 percent have the remaining third.
20 percent or so To get a simplistic feel for the numbers, government received $3.25 trillion in income in 2015 and GNP was $18 trillion. If we exempt $2 trillion for the very poorest citizens and tax the remaining $16 trillion of GNP at a single rate, the result is 3.25/16 or 20 percent.
a year by 2015 According to the UC Admissions Office, this is mitigated by the fact that more than half of undergraduates pay no tuition and more than two-thirds receive grants and scholarships averaging $16,300.
of them Chinese My grandson Edward, while a high school senior, was taking an advanced mathematics class (partial differential equations) at UCI. Thirty-one of the thirty-six students were Chinese. As they were unaware that Edward speaks Mandarin fluently, he overheard many candid conversations.
dollar has changed For an insightful discussion of why the inflation index from the 1970s may be much too low as a result of a series of government revisions in the method of calculation, and the consequences to investors and consumers, see “Fooling With Inflation” by Bill Gross (June 2008) at www.pimco.com.
For updated Consumer Price Index numbers and for month-by-month values, go to www.bls.gov/cpi or do the usual Google search.
$2 billion in cash Los Angeles Times, Thursday, September 7, 2000, page C5.