Ed Thorp – The Innovator

Ed Thorp

Today’s post is a profile of Guru investor Ed Thorp, who appears in Jack Schwager’s book Hedge Fund Market Wizards. His chapter is called The Innovator.

This article is part of our ‘Guru’ series – investor profiles of those who have succeeded in the markets, with takeaways for the private investor in the UK.

You can find the rest of the series here.

Ed Thorp

Ed Thorp

Ed Thorp is not a typical trader.

  • He began in casino games, but later switched to the markets because nobody could kick him out of those.

He is famous for building (with Claude Shannon) the first wearable computer, which they used to predict where a roulette ball would end up.

  • He also invented card counting to improve the betting odds in blackjack, as described in his best-selling book Beat the Dealer.
  • After the book, the casinos switched to 6-deck shoes to make card-counting more difficult.

He then invented (with Sheen Kassouf) a way to trade convertibles (bond, options and warrants) using hedging with stocks.

  • This was described in the book Beat the Market, and involved an equivalent to the Black-Scholes option model years before the latter was discovered.

He started the first market neutral fund and the first quant hedge fund.

  • He was also the first to “prove” that Bernie Madoff was a fraud.

Thorp appears in Jack Schwager’s book Hedge Fund Market Wizards.

  • His chapter is called The Innovator.

Since his interview with Schwager, Thorp has written a form of autobiography, called A Man for All Markets:


According to the efficient market hypothesis (EMH) – which assumes that the markets immediately discount all known information – you can only beat the markets through luck.

  • The many traders with exceptional track records that we have covered in this series of articles are similar to the infinite number of monkeys with typewriters who must eventually produce Shakespeare.
  • Given enough traders, some must show exceptional track records.

But if you need more traders than there are atoms in the universe, what then?


Thorp’s first hedge fund, Princeton Newport Partners (PNP) was open from 1969 to 1988, and produced average annual compounded returns of 19.1% (15.1% after fees).

  • It had 227 winning months and 3 losing months – all under 1%
  • That’s a 98.7% winning percentage

Even discounting the fact that the winning months were much more profitable than the losing months were unprofitable, this is a 1 in 10 to the power of 63 record.

  • If there were a billion traders on earth, that would still be ridiculously unlikely (( 1 in 10 to the power 62 according the Schwager, though I make it 10 to the power 57 ))
  • Schwager says that “the odds of randomly selecting a specific atom in the earth would be about a trillion times better”. (( There are 10 to the power 50 atoms in the earth ))

So you can beat the market, but it is hard.

  • Schwager says that the fact that most people don’t is what makes the EMH look plausible.

In 1992, Thorp Ridgeline Partners, using an actively traded statistical arbitrage strategy.

  • He averaged 21% annual compound return with 7% annual volatility over the next 10 years.

He then moved to allocating his capital amongst other hedge funds, and later traded a trend-following system (2007 to 2010).

Early life and education

Thorp’s father was a soldier in World War 1, and then a security guard during the depression, which made him careful with money and distrusting of business.

Everything needed to be repaired and re-used.

  • Thorp learned to always look for the downside and make sure it was covered.

Thorp was interested in science as a child, but went to a bad high school and had to teach himself.

  • He built a lab at home and bought chemicals with his paper round money.

He won a science contest aged 16 and expected to become a science professor.

He went to UCLA where he got a degree and masters in physics.

  • Near the end of his PhD he ran into maths issues and took some more classes.
  • He ended up switching the PhD to maths, and became a maths professor at UCLA and then MIT.
Casino games

In high school, a teacher mentioned a trip to Vegas, and how it was “impossible to beat those guys”.

  • That got Thorp thinking about roulette.

Years later, as a maths professor, he read an article about how to reduce the house edge in blackjack.

  • He went to Vegas, and lost 8 of his 10 dollars.

But back at UCLA, he realised he could improve the strategy to better than even by looking at what cards had already been played.

He contacted the authors of the article, got hold of their data, and started re-running the experiment with certain cards removed from the deck.

  • But using just a desk calculator, progress was slow.
  • Thorp realised it would take “several thousand years” to complete the job.

This was 1959, and his job at MIT gave him access to an IBM 704 computer, which used punch card programmes. (( I was still using them 25 years later, first at college and then in my first proper job ))

Within a year Thorp has worked out that with four extra aces, the odds were 2.5% positive.

  • You can’t have eight aces in a pack, but if half the deck has gone with no aces showing, the ratios are the same.

You can picture the blackjack probability problem as a 10-dimensional space, with the fraction of each card varying along a single axis. Any deck is a point in that space. (( The space is 10-rather than 13-dimensional for blackjack because all the face cards count 10, as does the 10 itself ))

When I first wrote a paper, I described a fives strategy, because it was simple. If all the fives are out, you have a 3.3 percent edge, so make really big bets 10 percent of the time when all the fives are out.


To get his paper published, Thorp needed a sponsor, which is how he met Claude Shannon.

  • Shannon asked what else Thorp was working on, and they began to collaborate on a way to beat roulette.
  • They set up a second-hand wheel in a basement and monitored the movement of the ball with a strobe light, practicing the correct amount of anticipation needed to accurately position the ball.

After a few months, they had a theoretical 44% edge from choosing the most likely “octant” in which the ball would fall.

  • They built the world’s first wearable computer so that an observer could time the ball and transmit the data (via switches in his shoes) to the guy who was betting.

They tested the system in Vegas in August 1961.

  • Shannon was the timer and Thorp the bettor.
  • Betting only dimes, they proved that the system worked, despite a lot of hardware problems.

Thorp switched his attention back to blackjack, and never made significant profits from the roulette system.

Back to blackjack

Thorp’s work on blackjack “went viral” (( As we say today )) after a lecture he gave to the American Mathematical Society.

  • He got 20,000 letters and had six secretaries replying to all of them (until the MIT math department shut that down).
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A gambler from New York named Emanuel Kimmel offered to bankroll Thorp with $100K, but Thorp would only risk £10K at first, betting a maximum of $10 per hand.

  • Within a couple of days, his maximum bet was $500 (the house limit).
  • After two more days, he had doubled the $10K to $21K.

After Beat the Dealer was published, thousands of players tried to implement the system.

  • Thorp worked out that most players were so bad that the casinos should have made more money, but they didn’t see it that way.
  • Profitable blackjack players were often beaten up.

Eventually the casinos changed the rules, adding six decks to a shoe and shuffling.

  • See the movies “Casino” and “21” for more details.

Thorp moved on to baccarat, and in particular the “side bets”. (( This is not a game I know well, though I remember playing at college – I seem to recall it pops up in James Bond, too, alongside chemin-de-fer ))

On the first trial of the system, Thorp won $600 a day (what he figured the casinos could tolerate).

  • By the third day they had resorted to spiking his drinks.
  • He switched casinos and was kicked out after three hours (and $2,500 profit).

On the trip home the car accelerator locked out on a curvy mountain road at 80 mph, but Thorp was able to stop. (( He shifted into low gear, turned off the engine and used the brake and the emergency brake ))

  • Thorp decided to switch to the financial markets, about which he knew nothing at the time.
Technical analysis

He quickly decided against technical analysis.

One could come up with a rational explanation of why chart analysis might work -namely that the charts reflect the net impact of all the fundamentals and the psychology of all the market participants. I can’t prove it doesn’t work.


After two years of reading, he started to focus on the pricing of warrants.

  • This was basically because they were simpler – stock prices had too many inputs.

Warrants are like options, and the determining factors are:

  1. the price of the underlying stock
  2. the strike price
  3. the volatility
  4. the time to expiration, and
  5. the interest rate.

Using these he (and Sheen Kassouf) came up with a version of the Black-Scholes option pricing formula before they did.

  • He didn’t publish it because it was his edge in the market.

They found that warrants with less than two years to run typically traded at too high a price.

  • They shorted the warrant and hedged by buying the stock.

They were successful, and began managing other people’s money as well as their own.

  • But Kassouf thought he could predict the movement of stock prices, whilst Thorp was market neutral, so they split.

Thorp was back to managing his own money, and didn’t have enough to buy (and hedge) a diversified (mis-priced) warrant portfolio.

  • Instead he identified warrants selling at two or three times what his formula predicted.

Being naked short warrants left him exposed to a market rally, which duly happened in 1967-8 (small caps more than doubled).

  • But he still broke even.

Thorp set up Princeton Newport Partners (PNP) in 1969 with an East Coast broker, James Regan, who handled the execution, admin and marketing for the fund.

In 1988, the East Coast office was raided by the Feds, and eventually Regan and four others were found guilty of stock manipulation.

  • They were later cleared, and none went to jail.
  • Observers now feel that they were accused in order to pressure them to testify against Michael Milken and Drexel, with who they traded.

Thorp was never charged or even interviewed, but PNP’s reputation was damaged and he closed down the firm.

  • He went back to trading his own account.

PNP used the warrant formula to trade convertible bonds, which act like a combination of a corporate bond and a call option.

  • The value of the option means that convertibles have lower yields, but initially this option was underpriced.
  • Arbitrage funds would by the convertibles and hedge by shorting the stock (delta hedging).
Kelly criterion

Thorp used the Kelly criterion to work out optimal bet sizes.

  • Kelly was a former colleague of Shannon, and Shannon told Thorp to use it to work out bet sizes.

The Kelly criterion seemed like the best strategy over the long run. A week playing blackjack might not sound very long, but I would be placing thousands of bets. In the stock market, it’s not the same thing.

There are, however, safer paths that have smaller drawdowns and a lower probability of ruin.

With Kelly, if you bet too big, then even with an edge, returns are reduced because of volatility.

  • Betting more than double the Kelly number produces expected losses.
  • Betting half the Kelly number reduces profits by 25%.

The Kelly formula is:

%age to bet = probability of winning - (probability of losing / (win size / loss size))

To use a simple example, if wins and losses were £1K, and the probability of winning were 60%, then:

Trade size = 0.6 - (0.4 / (1000/1000)) = 0.2

You should bet 20% of your pot (portfolio).

Or if you can win £2K or lose £1K with 50% probability (something close to the situation in disciplined spread betting), then:

Trade size = 0.5 - (0.5 / (2000/1000) = 0.5 - 0.25 = 0.25

You would bet 25%

This is an interesting result, since most traders would bet closer to 2% of their portfolio on one trade.

  • This is largely to protect the pot from a sequence of losing bets, yet the Kelly approach implicitly does this by using the new pot size for each bet. (( Note that with minimum bet sizes, your portfolio might eventually be too small to gamble with ))
  • This anomaly is something I will look at in a future post.

Schwager doesn’t like the way that Kelly assumes that your cut-out point is zero (rather than a maximum drawdown).

Since I personally am only ever likely to actively trade 20% to 30% of my net worth (( I’m currently trading much less than that )) the concept of a zero cut-out doesn’t seem that problematic to me.

  • By adjusting the size of your Kelly bankroll, the bet size will shrink appropriately, as Thorp points out.

Thorpe used Kelly in blackjack, but PNP used hedging, so Kelly would have implied a degree of additional leverage that Thorp wasn’t able to use (the brokerages wouldn’t lend him the money).

  • Thorp thinks that he wouldn’t have done it anyway, since trading K/2 produces 75% of the return with half the volatility.

I believe that betting half Kelly is psychologically much better.

Given the uncertainty of the probability of winning in trading combined with the inherent asymmetry in returns, the rational choice is to always bet less than Kelly.

Thorp points out that marginal utility is asymmetric, too (loss aversion).

Indicators project

In 1979, we looked for indicators that might have some forecasting power – earnings surprises, dividend payout rates, book to price. We had a list of about 30 or 40.

We found that the stocks that were most up tended to underperform the market in the next period, while the stocks that were most down tended to outperform the market.

That led to a strategy of buying a diversified portfolio of the most down stocks and selling the most up stocks. This had a 20% annual return before costs.

We called it MUD for most up, most down. My friend William Donoghue used to joke “buy low and sell high.”

Thorp also discovered:

A U-shape curve that favored buying stocks with no dividends and high dividends and selling stocks with low dividends.

Earnings surprises also seemed to have an impact for a considerable period of time–weeks and even months–suggesting the market was slow to assimilate this type of information.

Statistical arbitrage

In the 1980s, Thorp returned to a strategy he had been too busy to try during the warrants and convertibles years.

  • He created a joint venture with Gerry Bamberger, who had significantly reduced the risk of statistical arbitrage by using long/short portfolios within each industry sector. (( I am working towards a simple version of this strategy myself ))
  • Thorp felt that he would have come up with the idea himself in time.

It wasn’t a matter of paying Bamberger for the idea, but rather the execution of the idea.

After a couple of years returns tailed off and Bamberger decided to retire.

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Thorp decided to make the strategy “factor neutral”.

  • These were “abstract factors” derived from the historical data rather than economic / real-wrold factors (equity index prices, oil prices, etc).

Another name for this approach is principal component analysis. (( This is bit like finding multi-dimensional trend lines at right angles to each other ))

  • It works better than using economic factors since the latter are closely related to each other rather than independent.
  • Note that some abstract factors will closely correlate with real-world factors (the stock index value is usually one of the abstract factors).

After this change in direction, Thorp’s returns went up and the volatility went down.

Hedge funds

After Thorp closed his statistical arbitrage fund in 2002, he managed his own money through other people’s hedge funds.

I have run low on hedge fund candidates. Twenty years ago, I had a pretty good idea of which funds had an edge and which ones were just asset gatherers.

I screened out funds that had an annualized standard deviation greater than 15 percent or had an annualized return less than 12 percent or had a bad year.

There has been an explosion in the number of hedge funds and assets under management, accompanied by the entry of many more mediocre players. At the same time, the fees increased.

Schwager wonders whether:

The hedge fund industry is following the path of the mutual fund industry, which became equivalent to the market, or actually worse than the market once you account for costs.

Trend following

Schwager asks for Thorp’s thoughts on trend following.

I believe there are versions of the strategy that have a Sharpe ratio of about 1.0 or more, but that is low enough that there is a significant risk of getting shaken out.

I believe there are trends inherent in the markets.

Throp developed a trend-following strategy, but shelved it when his wife got sick.

We combined technical and fundamental information, which varied with the market sector. Backwardation vs contango, amount in storage relative to storage capacity, etc.

We also tracked a correlation matrix that was used to reduce exposures in correlated markets.

We found that 60 days [lookback] was best [for correlations]. If you use too short a window, you get a lot of noise; too long of and you get a lot of old information that isn’t relevant.

We also had a risk management process where if we lost 5%, we would shrink our positions with each additional 1% down. We were out at 20% down.

Our maximum drawdown was about 15%, by which point we were trading about one-third of normal size.

If you have a really strong conviction about your edge, then the best thing to do is sit there and take your lumps. If not, then you better have a safety mechanism that constrains your losses.

I would guess that we were probably using something equivalent to 1/10 or 1/20 of Kelly as a trade size on trend following.


In 1991, an institutional investor in PNP asked Thorp to review their pension fund allocation process.

  • One of their hedge fund managers had 1% to 2% positive returns every month.
  • This was Bernie Madoff, and Thorp quickly decided he was a fraud.

His purported strategy was to buy a stock, buy a put a little below the stock price, and sell a call a little bit above the stock price. The call premium approximately balanced the put premium.

Since he was doing the same strategy in all the stocks, he should have some very good months, but also some very bad months. But those results were not showing up.

Miraculous futures trades would be placed to get rid of the potential losing months and make them winners and get rid of the big winning months and make them moderate winners.

The trade confirmation statements came in bundles every few weeks, and the accountant was a friend of Madoff who ran a one-man shop. Madoff’s brother ran IT.

Thorp asked to visit, but Madoff’s brother said no.

He went through the daily confirmations and found that most of the option trades could never have been made.

  • They were for options that didn’t trade on the transaction date.
  • Others couldn’t have traded at the prices quoted.
  • Others didn’t have Madoff as a counterparty.

He told the institutional client to get out quietly.

Efficient markets

The question wasn’t “Is the market efficient?” but rather “How inefficient is the market?” and “How can we exploit the inefficiencies?”

I think inefficiencies are there for the finding, but they are fairly hard to find.

It has gotten harder for me, but that may only be because I am older and less interested, and have more money, which makes me less motivated.


This is a long and discursive chapter, with not much content that is directly useful to the private investor.

But Ed Thorp is a true legend, and an inspiration.

  • Beating the casinos at multiple games and then beating the markets in multiple ways makes him pretty much a one off.
  • Not to mention the first wearable computer, the early Black-Scholes equation and spotting Madoff.

As Schwager says:

Sometimes what seems impossible is entirely possible if approached from a completely different perspective.

We can only dream of contributing so much.

Takeaways for the private investor might include:

  1. vary the bet size when appropriate (or just don’t take on the low-probability bets)
  2. reduce exposure on losing trades, especially where you might not have an edge
  3. don’t bet more than you are comfortable with
  4. bet less than Kelly (half Kelly down to 1/10 K) unless the probabilities of winning and losing are clear (and you can tolerate a lot of volatility without abandoning the strategy)
  5. success in the markets is a process – there isn’t a single “holy grail” solution that won’t need to be refined and evolved

Until next time.

Mike is the owner of 7 Circles, and a private investor living in London. He has been managing his own money for 40 years, with some success.

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Ed Thorp – The Innovator

by Mike Rawson time to read: 12 min