EDWARD O. THOPR

Quantitative Strategies at Princeton/Newport Partners (PNP)

Edward O. Thorp co-founded Princeton/Newport Partners in 1974 – one of the first market-neutral quantitative hedge funds. At PNP, Thorp applied mathematical models to exploit mispricings in securities like stock warrants, convertible bonds, and options. By hedging these instruments against their underlying stocks, PNP generated high returns with low risk, largely insulated from market swings. In fact, PNP earned about 20% annualized after fees for nearly 20 years without a single losing quarter. This market-neutral approach proved its worth during major downturns – PNP gained +6.5% in 1973 and +9% in 1974 even as the S&P 500 plunged 15% and 27% in those years. Thorp’s reliance on statistical arbitrage (trading many small pricing discrepancies) and rigorous hedging helped the fund avoid the typical volatility of equity markets.

• Convertible Arbitrage Example: Thorp’s early strategy (detailed in Beat the Market, 1967) was to buy undervalued stock warrants or convertible bonds and short the equivalent stock. This locked in profit if the warrant was mispriced relative to the stock. In one series of actual trades starting in 1961, Thorp and co-author Sheen Kassouf earned roughly 25% annual returns for five years using this hedged warrant strategy. Such trades were designed to be market-neutral – “high profit with low risk” as Thorp described it – so that even a market crash would not wipe out the positions.
• 1987 Crash Arbitrage: Thorp’s probabilistic thinking shone during the Black Monday crash of October 1987. As panic hit, index futures collapsed far below the level of the S&P 500 index itself. Thorp recognized an extraordinary arbitrage: S&P futures were trading ~15% lower than the equivalent basket of stocks. Normally, traders would buy the cheap futures and short stocks to profit when prices converged, but fear (and short-sale restrictions) kept others on the sidelines. Thorp calmly devised a plan: his traders bought S&P futures heavily and simultaneously short-sold a double-sized basket of stocks, expecting only half the short orders to fill due to the uptick rule. This way, they’d end up roughly 100% hedged. The strategy succeeded – PNP got roughly half the desired shorts, ending with about $9 million long in futures versus $10 million short in stocks, locking in a ~$1 million profit in a matter of days. While the market crashed over 20%, Thorp’s fund emerged unscathed (even slightly up), demonstrating his risk-controlled opportunism in a crisis.

(PNP eventually closed in 1988, not due to market losses but because a legal investigation into a third-party (the Milken junk bond case) entangled the fund. Thorp and his team were cleared of wrongdoing, but the costly RICO probe forced PNP’s liquidation. Thorp’s colleagues later reformed as TGS Management to continue quantitative trading.)

Thorp’s Personal Investments and Notable Trades

Beyond his hedge funds, Ed Thorp applied his mathematical rigor to personal investments and unique trades – often finding asymmetric bets with big upside and limited downside:

• Berkshire Hathaway Stake: Thorp has famously invested much of his personal wealth in Berkshire Hathaway. After meeting Warren Buffett in 1968, Thorp realized Buffett’s conglomerate was an ideal long-term investment. He finally bought in by 1982, and to this day Berkshire is his single largest stock holding. Thorp likens Berkshire to a broad value index fund but with a key advantage: no dividends. This allows compounding without annual taxes, as Buffett reinvests earnings instead of paying them out. Thorp notes that holding Berkshire in place of an index fund achieves roughly similar returns “with no current taxes to pay” – a rational tax-efficient choice. At age 85, Thorp said he’s content earning ~10% long-term with virtually no effort, rather than chasing extra return: “The marginal value of time is higher [now] and the marginal value of money is lower”.
• Early Options Arbitrage: Thorp was a pioneer in pricing derivatives. In the 1960s he devised an options pricing formula years before Black-Scholes was published. Using this edge, he could spot mispriced options and warrants. For example, if a stock warrant was underpriced relative to the stock’s volatility, Thorp would buy the warrant and short the stock. He described trading with a superior model as “firearms versus bows and arrows” on the trading floor– giving him accurate values while others guessed. This quantitative arbitrage yielded consistent profits. By hedging each position, Thorp essentially built a “betting the spread” approach: whichever way the stock moved, the long warrant and short stock combo would converge to a gain. Such derivative arbitrage was the core of PNP’s strategy and also boosted Thorp’s personal portfolio. Through nearly 30 years, Thorp’s own investments compounded about 20% annually, a testament to these methods.
• Oil Tanker “Scrap Value” Play: In the early 1980s, Thorp partnered with famed trader Bruce Kovner in an unconventional asset play. Kovner observed that oil supertankers were so oversupplied that older ships sold for scrap metal prices. They formed a partnership to buy a large used tanker (the Empress Des Mers) for only $6 million – roughly its scrap value. Thorp joined as a limited partner, attracted by the low-risk, high-reward profile. The downside was minimal (the ship could always be sold for scrap, recouping most of the cost) while the upside was significant if tanker lease rates recovered. Indeed, over the next few years global oil transport demand rebounded. The Empress Des Mers was soon profitably hauling oil and ultimately yielded about 30% annualized returns for the investors. After a long and lucrative run, the tanker was finally sold for scrap around 2004 for $23 million – far above its purchase price. Thorp cites this as a favorite example of an “interesting option” in investing: a deal with a floor under the losses and open-ended upside.
• Exploiting the 2008–09 Crash (SPAC Arbitrage): Thorp’s rational approach led him to special opportunities amid the 2008 financial crisis. He focused on SPACs – Special Purpose Acquisition Companies – that had raised cash but not yet made any acquisitions. These SPACs held their IPO proceeds in trust (often U.S. Treasury bills) and would return the cash to investors if no deal was done. During the panic of late 2008, many such SPACs traded at deep discounts to their net asset value (despite holding only cash). Thorp recognized an almost risk-free arbitrage: he could buy SPAC shares at, say, 90 cents on the dollar, wait a few months, and redeem for $1 plus interest. In some cases he locked in 10–12% annualized returns on essentially Treasury-backed assets

– a huge yield with near-zero risk, given short-term T-bills were yielding ~0% then. This is a classic Thorp move: when most investors were fearful or forced to sell, he used cold math to scoop up free money. By December 2008, Thorp was buying these discounted cash-shells and reaping double-digit safe returns while the market slowly recovered.

• Gold Futures Arbitrage (1981): In the inflationary early 1980s, Thorp identified a pricing anomaly in the gold futures curve. In 1981, short-term gold futures (2 months out) were about $400/oz, while gold futures for late 1982 (14 months out) were around $500/oz. Such a steep $100 price gap (25% difference) was unusual – essentially the market anticipated significant inflation. Thorp executed a trade to capture this spread: he committed to buy gold in the near-term at $400 and planned to later deliver it at $500 via the long-dated contract. In practice, this meant going long the cheaper near-term futures (or physical gold) and short the more expensive far-term futures. By holding the gold for a year, he could lock in a 25% profit (the $100 spread) minus carrying costs. This trade was a bet on convergence: as time passed, the price of physical gold rose toward the higher future price. Thorp’s insight was that the extreme inflation fears baked into long-term gold prices could be arbitraged with a straightforward long/short hedge. It paid off handsomely, illustrating how he leveraged economic analysis (inflation expectations) into a low-risk profit.
• Sidestepping the Madoff Scam: Thorp’s quantitative skepticism also saved investors from pitfalls. A notable example: Bernie Madoff’s “too good to be true” returns. In 1991 – long before Madoff was unmasked – Thorp analyzed the trading reports of Madoff’s investment program. He found glaring irregularities, such as Madoff claiming trades in volumes that exceeded the entire market on certain days. Realizing the results were impossible, Thorp concluded it was likely a fraud (or at least not actually following the stated strategy). He promptly warned his network in the early 1990s, predicting Madoff’s hedge fund was an expanding Ponzi scheme that would eventually collapse. Thorp himself of course refused to invest. His suspicions proved correct years later when Madoff’s $50bn Ponzi scheme imploded in 2008. This episode highlights Thorp’s uncompromising due diligence – he trusted the numbers over reputation, avoiding a bubble of fake returns that ensnared many others.

Probabilistic Thinking and Risk Management in Action

Throughout his investing career, Thorp applied principles of probability, statistics, and risk management learned from gambling. His book A Man for All Markets (2017) and other writings illustrate how he balanced risk and reward rationally:

• The Kelly Criterion: Thorp was a strong proponent of the Kelly criterion for bet sizing – a formula that maximizes long-term growth by sizing bets according to one’s edge. In blackjack, he used Kelly to manage his bankroll, and he carried this optimal bet philosophy into investing. For example, at PNP he would scale positions in proportion to their expected profit and inverse to their risk, rather than make all bets equal. Kelly sizing prevents overbetting – a lesson many over-leveraged investors learned the hard way. Thorp often pointed out that LTCM’s 1998 collapse and other hedge fund blow-ups were due to overbetting (far beyond Kelly limits). In his words: “The lesson of leverage is this: Assume that the worst imaginable outcome will occur and ask whether you can tolerate it. If the answer is no, then reduce your borrowing.”. This cautious approach kept Thorp’s funds alive while others perished. He never had a single losing year in 30+ years of managing money, partly because he never bet the farm on any one trade.
• Rigid Risk Controls: Thorp’s scientific mindset led him to quantify and limit risk wherever possible. At PNP he maintained meticulous hedges and monitored correlations between positions. “We tracked a correlation matrix… if two markets were highly correlated and our system went long both, we would take a smaller position in each,” Thorp recalls. By keeping the overall portfolio uncorrelated and market-neutral, he ensured that even in worst-case scenarios (market crashes, etc.), losses would be contained. Thorp also stress-tested for extreme events. He famously contemplated scenarios like the 1987 crash long before they happened, so when such an event occurred, he was prepared (as demonstrated in the 1987 arbitrage story). His maxim was to assume the worst-case daily loss is possible – far beyond statistical VaR models – and size positions so that such a loss would not be catastrophic. This prudence is why Thorp never fell prey to bubbles or crashes. During the dot-com mania of the late 1990s, for instance, he did not chase overvalued tech stocks; his hedge fund remained market-neutral and continued its steady ~18% yearly returns through the 2000 crash. And in 2007–2008, he avoided subprime mortgage bets and instead hunted for safe harbors (like the SPAC trade). In short, Thorp’s probabilistic risk management let him play offense and defense at the same time: he aggressively pursued small edges, but always with protective hedges or position limits to guard against tail events.
• Rational Detachment and “Expected Value” Mindset: Thorp approaches investing much like a gambler playing many hands – focus on process and probabilities, not emotions. An anecdote from A Man for All Markets illustrates this: Thorp’s very first stock trade (Electric Autolite) taught him about emotional bias. He bought the stock, and it dropped 50% over two years. Instead of cutting the loss, he “anchored” on his purchase price and waited years just to get back to even – a mistake he later recognized. Thorp reflected: “What I had done was focus on a price that was of unique significance to me – my purchase price”. The lesson cured him of anchoring bias. Thereafter, he treated investments like bets with given odds; if the facts changed or the price no longer offered an edge, he had no attachment to the original price. This dispassionate style is akin to folding a poker hand that no longer has positive expected value. Similarly, Thorp advises not to get swept up by market narratives or media headlines. He observed that financial news often ascribes big meanings to tiny market moves. In one example he noted a headline about stocks “slumping on earnings concern” – yet the Dow had fallen only 2.96 points (0.03%) that day. Statistically, that move is indistinguishable from noise, occurring on the majority of trading days. Thorp’s point: always distinguish signal vs. noise – use data (like comparing moves to daily volatility) to avoid being misled by hypewould exit positions when the odds turned unfavorable, even if others were still bidding up the price).

In summary, Thorp ran his investments like a casino with the odds in his favor – making many calculated bets, size-limited by the Kelly criterion, and relentlessly eliminating any bets where he couldn’t quantify the edge or the risk. This scientific approach to finance enabled him to consistently profit while sidestepping disasters that caught less disciplined investors.

How Thorp Compares to Other Legendary Investors

Despite his extraordinary track record, Ed Thorp isn’t as publicly famous as some investing legends. His style and philosophy both differ from and overlap with figures like Warren Buffett, Jim Simons, and Benjamin Graham:

Thorp vs. Warren Buffett – Quantitative Hedging vs. Value Investing

On the surface, Thorp’s and Buffett’s approaches seem almost opposite. Buffett is a classic long-term value investor – he conducts deep fundamental analysis to estimate a business’s intrinsic value, then buys stocks that trade far below that value, often holding them for decades. Thorp, by contrast, is a quantitative trader – he identifies statistical mispricings and puts on hedged bets, often holding positions for shorter periods until the pricing gap closes. As one analysis put it, when Thorp and Buffett first met over a bridge game in 1968, “a deep philosophical chasm” separated their strategies. Buffett focuses on companies’ earnings, moats, and cash flows, largely ignoring short-term market fluctuations. Thorp focuses on prices and probabilities, largely ignoring subjective business quality.

Buffett once argued that successful investing doesn’t require “arcane formulae or computer programs,” just good business judgment and the ability to tune out market emotions. Thorp, on the other hand, championed the use of mathematics and scientific models. In the introduction to Beat the Market, he wrote that he and Kassouf had developed “the first scientifically proven method for consistent stock market profits” using math and computers– a direct counterpoint to the idea that numbers-driven investing can’t work. Thorp also diverged from Buffett (and Ben Graham) in his view of classic value investing. In Beat the Market he noted the practical difficulties of pure fundamental investing: accurately forecasting a company’s future is extremely hard, and even if you find an undervalued stock, you might wait years for the market to realize its value. “Many ‘undervalued’ stocks remain bargains for years, frustrating an owner who may have made a correct and ingenious calculation,” Thorp wrote. This impatience with sitting on idle value led Thorp to prefer strategies where the catalyst for profit was built-in (e.g. an arbitrage that will converge in a known timeframe) rather than simply hoping the market comes around to his view.

Despite their different methods, Buffett and Thorp also share important similarities. Both had confidence that markets are beatable with skill and discipline, defying the efficient market hypothesis. Both achieved superior long-term returns by sticking to their circle of competence (Buffett in selecting businesses, Thorp in pricing anomalies). Interestingly, both men placed huge emphasis on risk management and avoiding ruin. Buffett’s rule “Never lose money” echoes Thorp’s rigorous loss control – they just implement it differently (Buffett insists on a margin of safety in the business value, Thorp insists on a hedged or limited-risk position). The two became friendly – Thorp was greatly impressed by Buffett’s mind and even predicted in 1968 that “Buffett would one day be the richest man in America”. In turn, Buffett respected Thorp; in later years Buffett acknowledged that position sizing (Kelly criterion) and probabilistic thinking – hallmarks of Thorp’s approach – do have merit in investing. Notably, Thorp ended up investing heavily in Buffett’s Berkshire as a proxy for the value approach, essentially outsourcing that side of investing to Buffett. Thus, while Buffett and Thorp started from very different philosophies, they found common ground in believing in rationality over emotion and in aiming for high returns with carefully controlled risk.

Thorp vs. Jim Simons – The First Quant vs. The Ultimate Quant

Jim Simons, founder of Renaissance Technologies, is often considered the most successful quantitative hedge fund manager in history – Medallion Fund’s astronomical returns (over 30 years of ~66% annual gross returns) dwarf even Thorp’s record. But in many ways Thorp paved the way for Simons. Both men were mathematics professors who left academia to apply math in the markets. Both believed in systematic, model-driven trading rather than fundamental analysis or gut feel. Thorp in the 1960s–70s developed pricing models and statistical arbitrage by hand and with early computers; Simons in the 1980s–90s took it to another level with advanced algorithms, massive computing power, and teams of PhDs mining data. Thorp’s strategy often involved identifying a known mispricing (e.g. a warrant trading too cheap relative to its stock) and constructing a specific hedge to exploit it.

Simons’ strategy, as far as is public, involves finding subtle patterns in market data – often short-term statistical signals – and trading many of them in a diversified, automated fashion. In essence, Simons turned quant trading into a high-speed, high-complexity operation. Thorp’s operations were comparatively lower frequency and focused on more structural arbitrages.

There are interesting points of contact between the two. Simons has acknowledged Thorp’s influence – calling Thorp “the godfather of quants”. In fact, Thorp nearly became an investor in Simons’ Medallion Fund in the late 1990s. He set up a meeting in 1998 to potentially allocate money to Medallion, but (as Thorp humorously recounts) he was dissuaded by Simons’ incessant chain-smoking during the meeting– an example of Thorp’s personal risk calculus (he joked he couldn’t spend time in smoke-filled meetings). While that cost Thorp a chance at even greater returns, it reflects a difference in style: Simons, a smoker and famously secretive, built a large organization and kept its techniques ultra-confidential; Thorp, ever the educator, published books and papers openly sharing many of his methods. Both Simons and Thorp emphasize risk management and model refinement. Simons has said Renaissance constantly improves models and controls risk, aware that old edges decay– a mindset Thorp would agree with. Thorp’s performance was extraordinarily steady (never a down year in decades), and Simons likewise achieved remarkably steady gains (Medallion had only a handful of small down months in 30+ years). One telling comparison: Simons initially had money invested in Madoff’s scheme (through Renaissance’s partners and family accounts) and pulled it out only when he couldn’t understand how Madoff made money. Thorp, by contrast, figured out Madoff was a fraud from day one and avoided it entirely – indicating Thorp’s perhaps sharper skeptical instincts in that case. Overall, Thorp and Simons are kindred spirits in using math to outsmart markets. Thorp was the pioneer who proved quant strategies work on a smaller scale, and Simons built on that to create a quant empire. If Buffett is proof of concept for value investing, Thorp is proof of concept for quant investing – and Simons is the extreme realization of what quant can do.

Thorp vs. Benjamin Graham – Arbitrageur vs. Deep-Value Sage

Benjamin Graham, known as the father of value investing, represents an earlier generation’s approach focused on fundamental value and margin of safety. Superficially, Graham and Thorp seem very different: Graham hunted for severely undervalued stocks (net-nets, bargain issues) and held a diversified portfolio of them, waiting for the market to correct the mispricing; Thorp hunted for pricing inefficiencies in warrants, options, and other instruments that he could mathematically arbitrage fairly quickly.

Graham’s style was long-only and fundamentally driven, whereas Thorp’s was typically market-neutral and mathematically driven. However, there are notable parallels. Both Graham and Thorp were intensely focused on risk minimization. Graham insisted on a “margin of safety” – buying at a big discount to intrinsic value – to limit downside. Thorp achieved a margin of safety by hedging – constructing a position that would be safe in most market conditions. In essence, Graham used fundamental cushions, Thorp used statistical and structural cushions, but the goal – don’t lose big – was the same.

Another similarity: diversification and rationality. Graham advised spreading bets across many independent opportunities (since any one stock could stay undervalued or even go bankrupt). Thorp similarly ran portfolios of many small uncorrelated bets (since any single arbitrage could go awry due to unforeseen events). Both men also took a very rational, evidence-based approach. Graham was known for his analytical, almost clinical, approach to stocks as pieces of a business – trying to remove emotion from investing decisions. Thorp, as we’ve seen, treated investing like a science experiment or a gambling strategy – also stripping out emotion. In practice, Graham’s investments sometimes took years to pay off (e.g. waiting for a stock trading at 2/3 of its net asset value to appreciate), whereas Thorp’s trades often had more immediate catalysts (a warrant approaching expiration, a convertible bond with a known redemption date, etc.). This meant Thorp’s holding periods were shorter and his portfolio turnover higher, while Graham might patiently hold a cheap stock for 5+ years.

Importantly, Thorp did not rely on economic forecasts or management analysis as Graham might; instead, he relied on pricing formulas and market psychology quirks. For example, Graham might buy a cyclical company when it’s out of favor (betting on mean reversion in fundamentals), whereas Thorp might buy a mispriced option because the market maker used the wrong implied volatility. These are different domains, but both exploit others’ mistakes: Graham exploited investors’ emotional or informational mistakes about a business’s value, and Thorp exploited investors’ analytical mistakes in pricing complex securities. In the long run, both approaches worked exceedingly well – Graham achieved ~20% annual returns for decades; Thorp achieved ~20% (or more) with far lower variance. The key difference is that Graham’s style accepts market risk (but tries to buffer it with cheap prices), while Thorp’s style tries to cancel out market risk entirely and profit purely from the relative mispricing. In a sense, Thorp’s strategy is a descendent of the “workout” or arbitrage operations that Graham also engaged in (Graham did merger arbitrage and other specials), but Thorp expanded that to a whole quantitative system.

In summary, Thorp’s legacy in investing is unique – he combined the intellect of an academic, the odds-making of a gambler, and the cool discipline of a risk manager. Real-world examples from his career – from beating blackjack and roulette, to arbitraging stock warrants, to buying tanker ships and SPACs – all show his consistent application of mathematical rigor and rational decision-making. While his style differs from buy-and-hold fundamental investors, they all share a common thread of exploiting market inefficiencies (whether in securities prices or in human behavior) and managing risks so that no single mistake would knock them out. Thorp demonstrated that with enough edge and discipline, one truly can “beat the market” – not by predicting every twist and turn, but by systematically betting when the odds are favorable and limiting damage when they’re not. His story and strategies continue to inspire quants and investors who aim to marry mathematics with real-world markets.