Published on March 24, 2017

The team of six, three men and three women, pretended not to know each other and made their way to the baccarat tables at the Dunes casino in Las Vegas.  It was the spring of 1963 and Las Vegas was still controlled by shady characters connected to the mafia.  It was the fourth night at the tables and the pit boss and casino management had taken note of the lead player’s wins and were not happy.  However, on this night, the pit boss was smiling and offered the player coffee with cream and sugar “just the way you like it”.  Shortly into the first round, the player sips his coffee and suddenly couldn’t think! He had been drugged.  A few days later, as the team of six left Las Vegas, their car’s accelerator suddenly stuck as they traveled down a mountain road.  A terrible “accident” was narrowly averted through use of the emergency brakes.

As Nassim Nicholas Taleb points out in the forward to A Man For All MarketsEdward Thorp has written a book that, at times, reads more like a James Bond thriller than the memoir of a mathematician who ventured outside his academic field to beat casinos, both in Las Vegas and on Wall Street.  Conventional wisdom in the 1950s held that it is impossible for players to gain a consistent edge in games such as blackjack, baccarat and roulette.  Driven by an innate sense of curiosity and powered by raw intellect, combined with some help from early computer technology, Ed Thorp demonstrated that players could gain an edge in blackjack through straight forward card counting methods.  After proving the theory through hands-on testing at the casino tables in Reno, Mr. Thorp published his findings in academic journals as well as in Beat the Dealera book that made card counting accessible to the non-technical reader and remains relevant to gamblers today.

While the methods for gaining an edge in baccarat were similar to those used in blackjack and could be pursued through human intellect alone, the challenge facing the roulette player was far more complicated.  The nature of roulette implies a built-in advantage for the casino and casts doubt on the wisdom of participating at all since the expected value of a large number of bets will be negative for the gambler.  However, the fact that many roulette wheels are not perfectly aligned and maintained implies that a gambler could gain an edge by waiting until the wheel and ball is in motion and betting based on minor flaws in the wheel.  Of course, the human eye is not sensitive enough to detect imprecision in the wheel without the aid of technology.  Mr. Thorp, in collaboration with Claude Shannon, developed the first wearable computer which was intended to provide the gambler with an edge in roulette.  The computer was first conceived in 1955 and was tested in Las Vegas in 1961.  It provided the gambler with an expected gain of 44 percent but minor hardware problems prevented serious betting and the technology was unveiled to the public in 1966.

From Casinos to Wall Street

Perhaps the stock market was a natural and inevitable next step for Mr. Thorp after achieving success in casino gambling.  The problem with Mr. Thorp’s methods for beating the dealer is that it attracted attention from unsavory characters associated with the casino industry, as the adventures of 1963 at the baccarat tables of Las Vegas demonstrated.  Surely, the life expectancy of someone gambling in the greatest casino of them all — the stock market — would be far greater than someone confining himself to the smoky casino halls of the 1960s.

In the idealistic view of economics, the stock market is a venue for providers of capital to invest in promising businesses that have the ability to generate attractive returns on capital.  Of course, there is an element of truth in this sentiment since capital is indeed provided to business via the stock market.  However, the volume of trading in the stock market makes it clear that the majority of activity has little to do with providing capital to business or allocating capital to its best and highest use.  Instead, in the short run, the stock market more closely resembles a casino with players who are interested in making quick gains.  The debate over whether the stock market is “efficient” has been raging for decades with academic theorists insisting that there are no systematic ways to outperform market averages without assuming proportionally more “risk”, as defined by the volatility of an individual stock relative to the overall market.

Mr. Thorp naturally was attracted to this giant casino which lacked the shady characters and dangers of Las Vegas, imposed no “table limits” that constrained the capital he could deploy, and had rules that did not change suddenly in the middle of play just as the player was on a winning streak.  Lacking any background related to investing, Mr. Thorp spent the summer of 1964 educating himself, as he had on many other subjects earlier in life.  He included Graham and Dodd’s Security Analysis in his reading but also went further into scores of other books including the study of technical analysis.  Early forays into investing in the silver market produced unsatisfactory results but Mr. Thorp’s self education continued, eventually reaching the subject of common stock warrants.

Warrants and Arbitrage

The value of a warrant on a common stock is derived based the difference between the current stock price and the exercise price of the warrant as well as the amount of time before the warrant expires.  A warrant will always have a positive value prior to expiration even if it cannot be exercised immediately at a profit because the possibility exists that it will become profitable to exercise prior to expiration.  Mr. Thorp came up with the idea of developing mathematical models to determine whether warrants are mispriced relative to the price of the common stock.  By purchasing the relatively underpriced security and shorting the overpriced security, one can exploit the market’s mistake without necessarily expressing an opinion on the merits of investing or shorting the underlying business.

Through collaboration with a colleague in U.C. Irvine’s economics department, Mr. Thorp came up with a system for capitalizing on mispriced warrants and published the results in Beat the Market which was released in 1967.  One might ask why Mr. Thorp was willing to share his discoveries with the public, first with his technique for winning in blackjack and again with warrant mispricing.  Obviously, the more people who are employing a strategy, the less likely it will continue working as envisioned.  The casinos would become aware of card counting and take countermeasures to deal with it, some of which proved to be physically dangerous.  Stock market participants wouldn’t break your legs but would exploit a published strategy.  As underpriced securities are purchased, they become less inexpensive and as overpriced securities are sold, they become less overpriced.  Why give away the secrets?

Mr. Thorp’s ambition early in life was to excel in academia and he appears to have embraced the ethos of viewing scientific research as a public good.  He was also confident that he would have more ideas that could be exploited for monetary gain.  Shortly after publishing Beat the Market, Mr. Thorp independently came up with the formula that would later become known as the Black-Scholes pricing model for options.  Academics Fischer Black and Myron Scholes, who were partly motivated by Beat the Market, came up with their famous formula and published the findings in 1972 and 1973.  It appears that the formula should be known as Thorp-Black-Scholes, if not attributed entirely to Mr. Thorp.

Meeting Warren Buffett

The story takes a very interesting turn when Mr. Thorp is invited to meet Warren Buffett in 1969.  Mr. Thorp had started to manage accounts for clients, one of whom was the dean of the graduate school at U.C. Irvine, Ralph Waldo Gerard.  Mr. Gerard had been a limited partner in the famous Buffett Partnership which was in the process of winding down at the time.  Investors in the Buffett Partnership would be receiving cash plus the option to receive shares in Diversified Retailing and Berkshire Hathaway.  In retrospect, we can say that people who took cash rather than shares were crazy but virtually no one at the time thought that Berkshire would become Mr. Buffett’s investment vehicle for the next half century.

Mr. Gerard was planning to take cash and wanted Mr. Buffett’s opinion regarding Mr. Thorp.  Both men had employed warrant hedging and merger arbitrage strategies and spoke about it during a lunch arranged by Mr. Gerard.  Although Mr. Buffett’s style of investing extended far beyond Mr. Thorp’s activities, he apparently had a positive overall assessment since Mr. Gerard ended up investing additional funds with Mr. Thorp.

Princeton Newport Partners

At the time, Mr. Thorp was managing about $400,000 and the accounts were grossing about 25 percent a year, with 20 percent of profits payable to the general partner.  Mr. Thorp’s $20,000 income from the partnership was equivalent to his salary as a professor and would only accelerate in the coming years as Princeton Newport Partners attracted additional assets and enjoyed steady success.  Mr. Thorp retained his professorship for several years before finally dedicating all of his time toward investing in the early 1980s.

Princeton Newport employed a true “hedge fund” strategy, meaning that it was designed to be market neutral and profitable regardless of the movement in the overall stock market.  Today, what we call “hedge funds” are usually not market neutral funds of the type Mr. Thorp ran but are instead usually net long or net short, meaning that managers are taking a directional view of their holdings or the market as a whole.  Mr. Thorp focused on identifying opportunities that could be hedged in a way that did not depend on the movements of the overall market.  This resulted in a nearly twenty year track record in which the fund never posted a loss over a single calendar quarter.  From November 1, 1969 through the end of 1988, Princeton Newport Partners posted an annual compound return of 19.1 percent before fees, and 15.1 percent after fees.  This compared favorably to the S&P 500 annual return of 10.2 percent, but more importantly, it was accomplished with a small fraction of the volatility of the overall market.

Princeton Newport ran into trouble in late 1987 when the IRS and FBI raided the firm’s Princeton headquarters which housed the trading operations.  Rudolph Giuliani, who was then a politically ambitious U.S. Attorney, was on a campaign to prosecute suspected Wall Street criminals and was looking for information to bolster his case against Michael Milken at Drexel Burnham and Robert Freeman at Goldman Sachs.  Several employees of the Princeton office ended up facing charges but no one in the Newport office, run by Mr. Thorp, were ever implicated.  However, the damage had been done.  Returns in 1988 were only 4 percent as the firm was distracted by the investigation and Mr. Thorp decided to leave at the end of 1988, after which point the partnership eventually wound down.

Bernie Madoff

Mr. Thorp was already a very wealthy man as Princeton Newport liquidated.  Rather than immediately starting another large fund, he stepped back for a while but still provided consulting services related to hedge fund selection.  It was in this context that he encountered the Bernie Madoff fraud seventeen years before it ultimately collapsed.  The first warning sign was the evasive behavior of Peter Madoff who was filling in for Bernie during Mr. Thorp’s planned office visit.  Peter made it clear that Mr. Thorp would not even be allowed through the front door.

Mr. Thorp was not deterred and went on to examine the accounting records that the Madoff firm had provided to his client.  These records conclusively proved that the Madoff operation was a scam:

“After analyzing about 160 individual options trades, we found that for half of them no trades occurred on the exchange where Madoff said that they supposedly took place.  For many of the remaining half that did trade, the quantity reported by Madoff just for my client’s two accounts exceeded the entire volume reported for everyone.  To check the minority of remaining trades, those that did not conflict with the prices and volumes reported by the exchanges, I asked an official at Bear Stearns to find out in confidence who all the buyers and sellers of the options were.  We could not connect any of them to Madoff’s firm.”

The result of Mr. Thorp’s investigation saved his client from continued participation in the fraud.  The client closed his accounts.  Mr. Thorp made it known within his network that the Madoff operation was a Ponzi scheme.  The establishment at the time would not have believed that Bernie Madoff could be a fraud.  He was a major figure in the securities industry and other attempts to unmask his operation were ignored as well.  It is amazing that the Securities and Exchange Commission never uncovered this fraud.  At the end, Bernie Madoff turned himself in when it became obvious that the game was over in December 2008.

Personal Finance 101

The last few chapters of the book delve into a number of personal finance topics that, while perhaps unexpected in a memoir, provide many good insights for both beginning and experienced investors.  Mr. Thorp goes through the facts and figures associated with wealth in the United States, explains the power of compound growth, examines whether one can beat the market today, looks as indexing strategies as a potential passive approach, and then considers how investors should allocate their wealth between asset classes.

The fact that Mr. Thorp dedicates this much space in his memoir to personal finance indicates that he believes lack of education in this area is a serious impediment to the well being of the public.  He believes that personal finance should be taught in elementary and secondary schools, noting that most people seem to not understand basic probability and statistics.  Clearly, if more Americans understood the power of compound growth when leaving high school, there would be far fewer cases of misery caused by mistaken accumulation of debt and lack of savings.

Although not the focus of the book, many readers will find Mr. Thorp’s treatment of personal finance worthwhile.  The question of whether to attempt to beat the market or not is ultimately a personal decision.  Those who wish to make the attempt must choose between finding managers who can hopefully outperform the market after taking into consideration their fees or must do the work required to personally manage the account.  Indexing seems to be the right choice for the vast majority of people.


Mr. Thorp concludes with a compelling account of the causes and aftermath of the financial crisis.  The follies described may be familiar to most readers but will be an eye opener for some.  Although it would be comforting to believe that a similar crisis will not occur in the future due to wise regulatory changes, Mr. Thorp seems rather pessimistic regarding the efficacy of the reforms put in place after the crisis.  Perhaps his strongest indictment involves the corrupt corporate governance that insulated management at the expense of shareholders and continues to this day.  The incentive structures prevalent in corporate America today are largely unchanged and destined to cause trouble in the future.

Warren Buffett reappears toward the end of the book as Mr. Thorp notes his use of Berkshire Hathaway shares to endow a chair in mathematics at U.C. Irvine.  In a move similar to Warren Buffett’s gift to the Bill and Melinda Gates Foundation (but predating it), Mr. Thorp donated Class A Berkshire stock to the university and directed that shares should be converted to Class B stock and sold slowly in order to fund the endowment.  Like Mr. Buffett’s instructions to the Gates Foundation, Mr. Thorp insisted that his gift would result in funding for additional research that would not otherwise have been funded through existing financial resources of the university.  Unlike Mr. Buffett’s intention for his gift to the Gates Foundation, Mr. Thorp would like his gift to continue to provide funding for the chair in perpetuity.  As such, he limited the annual draw from the endowment to only 2 percent. Since 2003, size of the endowment has more than doubled after accounting for yearly spending.

Mr. Thorp’s memoir is likely to be appreciated by more than one type of reader.  Gamblers and investors will naturally be fascinated by the detail he provides, but those focused on public policy will find his views on the financial crisis compelling and readers less familiar with personal finance will have the bonus of a brief lesson and some actionable advice.  Perhaps the most important lesson to take away from this book is that intellectual curiosity combined with a refusal to blindly accept conventional wisdom is almost always required to advance human knowledge and, in some cases, achieve great wealth.

Book Review: A Man For All Markets
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