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on September 8, 2005
This is an excellent book about the discovery of the Kelly formula that is unknown outside gambling. This story has three protagonists. Two of them were scientists working at Bell Labs: Claude Shannon, a genius polymath who developed information theory; and John Kelly, a maverick genius, who is directly responsible for the development of Kelly's formula. The third one is a brilliant MIT mathematician, Ed Thorp.

Ed Thorp tested the Kelly formula in both gambling and investing. Also, he came up with an options formula before Fischer Black and Myron Scholes. His formula missed a risk-free rate component due to the structure of the market at the time. As a result, Ed Thorp remained in obscurity while Black and Scholes became famous.

Ed Thorp succeeded in deriving superior returns in both gambling and investing. But, it was not so much because of Kelly's formula. He developed other tools to achieve superior returns. In gambling, Ed Thorp succeeded at Black Jack by developing the card counting method. He just used intuitively Kelly's formula to increase his bets whenever the odds were in his favor. Later, he ran a hedge fund for 20 years until the late 80s and earned a rate of return of 14% handily beating the market's 8% during the period. Also, his hedge fund hardly lost any value on black Monday in October 1987, when the market crashed by 22%. The volatility of his returns was far lower than the market. He did this by exploiting market inefficiencies using warrants, options, and convertible bonds. The Kelly formula was for him a risk management discipline and not a direct source of excess return.

Ed Thorp's career as a hedge fund manager was temporarily cut short. This was due to his fund being involved in a tax-avoiding securities scheme with Drexel Burnham. Thorp was not guilty; but, the fund had to be liquidated. The author stated many of Milken wrongdoings. One included getting large equity positions attached to the junk bonds he issued. The companies thought they were issuing convertible bonds. However, the equity component went straight into Milken's pocket as he sold the bonds to investors as high yield debt with no equity attached.

Ed Thorp rebounded from this mishap and started a second hedge fund in 1994. Thorp continued reaping above market return. As the author states, Ed Thorp's genius consists in "...his continuous ability to discover new market inefficiencies ... as old ones played out." Ed Thorp closed this second fund in 2002. He is now independently exploring inefficiencies in gambling.

Claude Shannon amassed large wealth by recording one of the best investment records. His performance had little to do with Kelly's formula. Between 1966 and 1986, his record beat even Warren Buffet (28% to 27% respectively). Shannon strategy was similar to Buffet. Both their stock portfolios were concentrated, and held for the long term. Shannon achieved his record by holding mainly three stocks (Teledyne, Motorola, and HP). The difference between the two was that Shannon invested in technology because he understood it well, while Buffet did not.

John Kelly was a chain smoking, gun collecting brilliant physicist. He died young at 41 of an aneurysm. He worked closely with Shannon at Bell Labs. Besides being a charismatic character the author does not write much about his life compared to the other two (Shannon and Thorp).

The Kelly formula is Edge/Odds (as explained on page 72). In investment circles, this formula is not always useful because it is hard to quantify your Edge (value of proprietary information). However, Kelly's formula has intuitive practical implications. It entails you should focus on an investment internal rate of return (IRR) instead of its average yearly return. The IRR is always less. Another implication is that higher risk is not always compensated by higher return. There is an optimal risk level beyond which risk taking becomes destructive. The author mentions the Long Term Capital Management as a case in point.

I recommend other excellent similar books: "Fischer Black and the Revolutionary Idea of Finance" by Perry Mehrling, and "When Genius Failed. The Rise and Fall of Long Term Capital Management" by Roger Lowenstein. Both these books describe luminaries in finance and investment fields who were often in contact with Ed Thorp and Claude Shannon. Another excellent book is Sylvia Nasar's "A Beautiful Mind" about John Nash, the Game Theorist.
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"Fortune's Formula" tells the story of the Kelly Criterion -through the experiments, ideas, wins, and losses of those who have espoused it and who have derided it, at race tracks, black jack tables, sports books, and, finally, on Wall Street. The Kelly Criterion is a risk management formula published in 1956 by Bell Labs information theorist John Kelly, Jr. that dictates how much of your bankroll you should bet based on your edge divided by the odds so that you will have zero risk of ruin no matter how bad your luck is, while increasing wealth faster than any other betting system. It does not address what bets you should make, which is another matter entirely. Instead of writing a simple analysis of the Kelly Criterion, author William Poundstone brings this story alive by relating the histories of key figures who have used, promoted, or criticized the Kelly Criterion: information theorists, economists, traders, gamblers, and gangsters. Some readers may find this approach unfocused and unnecessary. But I think the personalities lend "Fortune's Formula" an epic quality and place the Kelly Criterion firmly in the context of real life, with real consequences, as opposed to the realm of abstruse theories that never leave the halls of academe.

The men whom "Fortune's Formula" casts as protagonists are Claude Shannon, the MIT scholar who invented information science and who amassed a small fortune as a buy-and-hold investor, typically making 28% per year on a small portfolio, and Ed Thorpe, author of 1962's gambling classic "Beat the Dealer", 1967's "Beat the Market", co-founder of Princeton-Newport Partners fund (1969-1988) and founder of Ridgeline Partners (1994-2002) quant fund. Ed Thorpe's transformation from MIT egghead to black jack sharp to Wall Street wizard in an ongoing theme, as Thorpe is an immensely successful advocate of the Kelly Criterion -and he is still alive. There is unfortunately little information on John Kelly, because he died in 1965 at the age of 41. The key Kelly challenger is 1970 Nobel Laureate economist Paul Samuelson, who probably overstates his case in calling the Kelly Criterion a "complete swindle" when the point of disagreement seems to be the concept of "utility" in long-tern outcome. Whatever one thinks of Samuelson's outspoken arrogance, he is certainly entertaining. Mobster Manny Kimmel makes an appearance, as do traders Ivan Boesky, Michael Milken, and John Meriwether, as well as numerous information theorists.

William Poundstone obviously has a point of view. He is an advocate of the Kelly Criterion, believing that it produces better results than any other betting system over the long haul while withstanding even the most unlikely confluences of catastrophe that have a way of manifesting themselves periodically. He doesn't support efficient market hypothesis. He thinks people can, and have, made money consistently on the stock market. -But that you need a darned good method of managing risk to do it, a better method than Value at Risk reports. "Fortune's Formula"'s fascination is not only in its history of the Kelly Criterion, but in the realization that a risk management formula has so many seemingly disparate applications. As Poundstone says, "The idea pops up in the strangest places."
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on October 25, 2005
I found this to be a very exciting and informative book. Once I started, I was hooked: I couldn't put it down because I wanted to learn more -- not just about the formula but all the intellectual controversy surrounding it and the cast of characters involved. This book tells the story of the 'Kelly criterion' and how certain people used it to beat the casinos and earn consistently above-average returns in the stock market. The cast of characters extend from famous organized crime figures (Bugsy, Longy Zwillman, etc.) to Claude Shannon, father of information theory, to Milken, the junk bond king, and many more.

You can view this book as a study on the history of an idea, as a study of the financial markets, or as a social study of gambling and investing. There are many faces to it. I wouldn't say it is a book on finance, or a book on history, but a bit of everyhting really. It definitely is not a book on 'how to beat the market', don't look for that here. The book does give a good explanation of the Kelly formula, in my opinion, but the whole controversy surrounding it, as well as the story of Ed Thorpe, was much more interesting for me.

If you are interested in finance or financial history, math, or gambling, or how ideas evolve and why certain ideas are better known than others, you should read this book. I think that mathematically sophisticated readers can be a bit disappointed because there is no rigorous treatment of Kelly criterion. But the basic ideas of CAPM, efficient markets hypothesis, the essence of Kelly formula, and random walk, are explained quite succintly and clearly, in my opinion.

The only problem I had with the book was that the author went off in tangents quite a bit, which sometimes distracted from the main story. For instance, right after the description of Kelly formula, there is a discussion of Edgar Hoover's horseracing bets. It seems that the author had a lot of material, may be too much, that he did not want to cut, but also did not know where to put. That detracted from coherence somewhat, which is why I am giving this 4 stars. But at the end of the day, I am feeling better for having read the book -- I learned a lot, and it was an easy and interesting read. Definitely worth the money and time.
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on October 14, 2005
Let's consider the subtitle. "The Untold Story of the scientific betting system that beat the casinos and Wall Street."

Okay ... what's the system that beat the casinos? In two words: card counting. It's the "untold" system that was demonstrated in the movie "Rain Man." If you can keep track of the cards coming out of a particular deck, you recognize at some point that there are "lots of Queens in there. Definitely. Lots and lots of them." Such a realization moves the odds in your favor.

The problem with that system has little to do with science. It is, as those who've seen Rain Man will remember, that if you're obvious about it you get escorted out of the casino by intimidating beefy men. This book provides anecdotal evidence of the same phenomenon.

Moving on ... what is the "scientific system" that has beaten Wall Street? In a word, its arbitrage. Look for opportunities created by the inefficiencies of others, especially such inefficiencies as bifurcate markets, and exploit them, simultaneously selling in one market and buying in the other. This, like any particular card counting expedition, is (a) easier said than done and (b) tends to be self-terminating. One example in this book involves the S&P index. When S&P futures were first listed, some traders hadn't figured out how to value them. This inefficiency bifurcated the market. One could exploit it by selling the index futures contract, while buying the underlying stocks.

How long did that last? Four months! Then, says this book, "the market got the message .... The price anomalies vanished."

Poundstone tries to erect out of such exploitation of bifurcated markets a vast intellectual warfare between efficiency theorists and street-wise systems bettors who know better (no pun intended), a war between Samuelson and Thorpe. But it doesn't wash. Market efficiency theory is a default option, if you wil, a framework of ideas that underlies whatever particular anamolies suspend it from time to time. The fact that an anamoly can last a whole four months doesn't constitute an earth shattering discovery, and since the correction of any such inefficiency by definition moves the market closer to an efficiency model, one might say that Thorpe is helping bring Samuelson's theoretic point of view to completion. Good for him.

There's rebellion as a fact and there's rebellion as a style. Poundstone reminds me a little of a kid dressed rebelliously (baggy pants, untied shoelaces, the baseball cap turned backwards) who nonetheless, in everything important, thinks and acts along with dear old Dad. There is no rebellion against the "random walk cosa nostra" here. Just a baseball cap turned around.
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on January 19, 2007
Very interesting to read and very useful to know. The Kelly Criterion applies to all variants of investments (gambling, stock market, horse racing, etc). This book explains the history of the Kelly Criterion and academic misunderstanding of it.

The only problem with the book is that it did not explore the daily applications of the Kelly formula. Many readers would finish the book and ask: So how do I use this? The book also fail to explain how to adapt the Kelly concept to situations with multiple outcome states rather than only Win or Lose. Support for multiple outcome states is essential in real-life applications of Kelly Criterion [...]

Overall, the book is great as an introduction to money management.
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on July 19, 2007
Yes, perhaps the book's title is a bit misleading. Those who gave bad reviews to the book may have been looking for a get rich quick formula to beat the market or the casinos. The book focuses on the Kelly criterion and also gives quite a bit of attention to the efficient market hypothesis. The strength of the book is in its portrayals of the characters involved in the stories behind the Kelly Criterion and Efficient Market Theory.

Admittedly, at times it was a stretch to connect some of the players in this drama to the Kelly Criterion or the Efficient Market Hypothesis. Rudy Guiliani is one of several people in the book who are quite tangential to the main story line. However, I found this not to be a weakness of the book. Indeed, it enhanced my enjoyment of the story.

Those who are looking for a hard core mathematical examination of some of the topics of the book will be disappointed. As will those who are looking for a quick how-to in applying some of the theories. However, the vast majority of people will enjoy getting an inside look at some of the personalities involved in the development of these concepts and will love seeing how some of the theories held up in the "real world".
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on August 4, 2006
I found it very difficult to comment on this book. I can see different people with different expectations will have very different comments.

The name of the book should be accounted for some of the bad comments. The highlight of "Formula" and "Scientific" makes people expecting equations and theories inside. However, you can hardly find any formula, and even there're theories explained, just like most books targeting to all audiences, the explanation and equations are usually not "too accurate". The graphs are pretty good, though.

For me, I have a degree in Computer Science, and I have experiences and researches in gambling and investment, so by looking at the content of the book, I knew I was familiar witha t least 1/2 of the content (people and theories).

I found the Prologue is wasting my time. I started to get bored after a few chapters, especially the storytelling is not that attractive and different characters entering in a not very organized way...

However, I did find it interesting later when things are putting together... For example, if you learned Black-Scholes formula from economics studies, you probably don't know Ed. Thorp has derived essentially the same formula in a different form. Or if you learned Kelly criterion from science or gambling, you'll probably not know the geometric mean version in economics fields, and the difference between them.

So, as a conclusion, I'm not quite interested in the storytelling, but I'm quite impressed by the broad researches Poundstone has done. But maybe there're too many to be included in this book, it's hard to put everything together in a smooth way to make it interesting all the way to everyone.

What I think the book will mean to different readers are:

a) It's an excellent book for someone who have almost no knowledge (but have experience) in the theories of gambling and investment. This book will be a good eye-opening experience to you.

b) It's a good book for putting things together for people who learned some theories from different sources. It's also quite interesting to read how the people in different fields were doing similar things and coming with similar results.

c) For the real experts, this book should act as a review of the history, and I still believe there're at least some "untold stories" that even an investment expert will find it interesting.

My final advice... feel free to skip some of the stories, especially the description of some characters you're not interested in. Focus on what interests you. That will make you give 1 more star to the rating.
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on March 6, 2006
If you have ever heard of the Kelly Criteria for position-sizing, or wondered if Optimal F is a good way to manage risk, this book is for you. In a narrative, story-telling style that is much easier reading than a mathematical, economic, or statistical textbook, the author covers a whole range of interesting and informative theories that are relevant to trading and investing.

Knowing that a trader who uses the Kelly Formula to maximize return always has a 50% chance of losing 50% (or X% chance of losing (100-X)% generally) of their capital may be an eye-opener for many traders. Although this book will not tell you how to make money trading, it will generate more than a handful of useful areas of research, and get you thinking about risk management rather than entry signals.

Covering a multitude of financial, economic, and mathematical geniuses, this book has many interesting side-stories and anecdotes that are amusing, interesting and thought-provoking. The majority of this book is not strictly about trading, but all of the ideas have some application to trading and investing if you think hard and long enough.
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on June 25, 2008
This book is a concise look at the evolution of formal investment theory, with continual contextual references to its ties to gambling and to organized crime. It also is a hilarious and insightful history of gambling from the Bernoulli's in the 1700s through the hedge fund traders of the late 1990's.

The author devotes over 50 pages to notes and the index. This was appreciated since I wanted to look up more about so many of the anecdotes he included.

Mr. Poundstone poignantly describes the downfall of high-flying firms such as LTCM, where the investment wizards went from the darlings of Wall Street to the dredges of the investment community in large part because they were so clever; and they started to believe they were infallible.

One LTCM road-show presentation was held at the insurance company Conseco in Indianapolis. Andrew Chow, a Conseco derivatives trader, interrupted Scholes. "There aren't that many opportunities," Chow objected. "You can't make that kind of money in Treasury markets."
Scholes snapped: "You're the reason - because of fools like you we can." (Page 281)

Warren Buffett marveled at how "ten or 15 guys with an average IQ of maybe 170" could get themselves "into a position where they can lose all their money." That was much the sentiment of Daniel Bernoulli, way back in 1738, when he wrote: "A man who risks his entire fortune acts like a simpleton, however great may be the possible gain." (Page 291)

He also points out the real world flaws in some theoretically appealing scams. The St. Petersburg Wager seems mathematically correct; yet it overlooks a vitally important constraint (pages 182-184). Another is the unfounded weight we unconsciously give to historical returns, as evidenced by his retelling of another Warren Buffett story:
In a 1984 speech, Buffett asked his listeners to imagine that all 215 million Americans pair off and bet a dollar on the outcome of a coin toss. The one who calls the toss incorrectly is eliminated and pays his dollar to the one who was correct.
The next day, the winners pair off and play the same game with each other, each now betting $2. Losers are eliminated and that day's winners end up with $4. The game continues with a new toss at doubled stakes each day. After twenty tosses, 215 people will be left in the game. Each will have over a million dollars.
According to Buffett, some of these people will write books on their methods: "How I Turned a Dollar into a Million in Twenty Days Working Thirty Seconds a Morning." Some will badger ivory-tower economists who say it can't be done: "If it can't be done, why are there 215 us?" "Then some business school professor will probably be rude enough to bring up the fact that if 215 million orangutans had engaged in a similar exercise, the result would be the same - 215 egotistical orangutans with 20 straight winning flips." (Page 314)

The author follows the lives of a few major contributors to investment theory, information theory, and betting theory: Claude Shannon, who invented Information Theory and paved the way for the digital computer age; John Kelly, who developed the formula for gains with no possibility of ruin; and Edward Thorpe, who built upon these findings and beat the roulette wheels, the blackjack tables and the investment fund managers.
It's a fast read - only 329 pages before the notes and index. I highly recommend it!
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on June 10, 2007
James pragma's review below is so bad that i felt the need to write my own review. let me clarify some of what James gets wrong, and also clarify what the book is actually about.

James obviously misunderstood the book (and that is not the writer's fault in this case). Poundstone clarifies the Kelly betting system which was originally applied to card-counting but has uses beyond it. the central example and climax of the book is how the kelly betting system and the controversy surrounding it in light of efficient markets theory can help us explain the tragic blow up of a powerhouse hedge fund. the book is about risk, how to manage risk and avoid ruin. that has nothing to do with card counting as a system to get an advantage over the house (Which everybody knows about), the point is that Kelly invented a way to maximize long-term reward and minimize risk. but did he? that's the question.

James Pragma's review is nonsense. he failed to understand the book. in addition to what i say about, Poundstone gives us the history of math, information theory and gambling as it relates to the core story i mention above. it was a fun, informative book.
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