It’s the spring of 2000 and another warm sunny day in Newport Beach. From my home six hundred feet high on the hill I can see thirty miles across the Pacific Ocean to Wrigley’s twenty-six-mile-long Catalina Island, stretched across the horizon like a huge ship. To the left, sixty miles away, the top of the equally large San Clemente Island is just visible above the horizon. The ocean starts two and a half miles from where I sit, separated by a ribbon of white surf from wide sandy beaches. An early trickle of boats streams into the sea from Newport Harbor, one of the world’s largest small-boat moorings, with more than eight thousand sail and power vessels, and some of the most expensive luxury homes in the world. Whenever I leave on vacation I wonder if I have made a mistake.
As I finish breakfast the sun is rising above the hills behind me, illuminating the financial towers to the west in the enormous business and retail complex of Fashion Island. By the time the skyscrapers are in full sunlight I drive three miles to my office in one of them. The statistical arbitrage operation that Steve and I restarted in 1992 has been running successfully now for eight years.
Our computers traded more than a million shares in the first hour and we are ahead $400,000. Currently managing $340 million, we have purchased $540 million worth of stocks long and sold an equal amount short. Our computer simulations and experience show that this portfolio is close to market-neutral, which means that the fluctuations in the value of the portfolio have little correlation to the overall average price changes in the market. Our level of market neutrality, measured by what financial theorists call beta, has averaged 0.06. When beta is zero for a portfolio, its price movements have no correlation with those of the market, and it is called market-neutral. Portfolios with positive beta tend to move up and down with the market, more so for larger beta. The beta of the market itself is chosen to be 1.0. Negative beta portfolios tend to fluctuate oppositely to the market. Our risk-adjusted excess return, the amount by which our annualized return has exceeded that from investments of comparable risk and called alpha by finance theorists, has averaged about 20 percent per year. This means that our past annual rate of return (before fees) of 26 percent can be thought of as the sum of three parts: 5 percent from Treasury bills with no risk, about 1 percent due to our slight correlation to the market, plus the remaining 20 percent, the amount by which our return exceeds investments with comparable risk.
Using our model, our computers calculate daily a “fair” price for each of about one thousand of the largest, most heavily traded companies on the New York and American stock exchanges. Market professionals describe stocks with large trading volume as “liquid”; they have the advantage of being easier to trade without moving the price up or down as much in the process. The latest prices from the exchanges flow into our computers and are compared at once with the current fair value according to our model. When the actual price differs enough from the fair price, we buy the underpriced and short the overpriced.
To control risk, we limit the dollar value we hold in the stock of any one company. Our caution and our risk-control measures seem to work. Our daily, weekly, and monthly results are “positively skewed,” meaning that we have substantially more large winning days, weeks, and months than losing ones, and the gainers tend to be bigger than the losers.
Scanning the computer screen, I see the day’s interesting positions, including the biggest gainers and the biggest losers. I can see quickly if any winners or losers seem unusually large. Everything looks normal. I walk down the hall to Steve Mizusawa’s office, where he is watching his Bloomberg terminal, checking for news that might have a big impact on one of the stocks we trade. When he finds events such as the unexpected announcement of a merger, takeover, spin-off, or reorganization, he tells the computer to put the stock on the restricted list: Don’t initiate a new position and close out what we have.
Steve has just persuaded the broker where we do most of our business to cut our commissions by 0.16 cents per share. The savings are big. Our entire holding of stocks, long and short, turns over about once every two weeks, or twenty-five times per year. At current levels this means we sell $540 million of stocks held long and replace them with $540 million of new stocks, a total value traded of $1.08 billion. We do the same with our shorts, for another $1.08 billion worth of trades. Trading both sides twenty-five times a year means we do $54 billion, or 1.5 billion shares annually. When famed hedge fund manager Michael Steinhardt retired, he astonished many by announcing he had traded a billion shares in one year.
The reduction Steve negotiated saves us $1.6 million a year. Even after this, our brokers are collecting $14.3 million per year from us. Our broker was smart to stay competitive.
Why is statistical arbitrage so-called? Arbitrage originally meant a pair of offsetting positions that lock in a sure profit. An example might be selling gold in London at $300 an ounce while at the same time buying it at $290 in New York for a $10 gain. If the total cost to finance the deal and to insure and deliver the New York gold to London were $5, it would leave a $5 sure profit. That’s an arbitrage in its original usage.
Later the term was expanded to describe investments where risks are expected to be largely offsetting, with a profit that is likely, if not certain. For instance, in what is called merger arbitrage, company A trading at $100 a share may offer to buy company B, trading at $70 a share, by exchanging one share of company A for each share of company B. The market reacts instantly and company A’s shares drop to, say, $88 while company B’s shares jump to $83. Merger arbitrageurs now step in, buying a share of B at $83 and selling short a share of A at $88. If the deal closes in three months, the arbitrageur will make $5 on an $83 investment or 6 percent. But the deal is not certain until it gets regulatory and shareholder approval, so there is a risk of loss should the negotiations fail and the prices of A and B reverse. If the stocks of A and B returned to their preannouncement prices, the arbitrageur would lose $12 = $100 − $88 on his short sale of A and $13 = $83 − $70 on his purchase of B, for a total loss of $25 per $83 invested, or 30 percent. The arbitrageur won’t take this lopsided risk unless he believes the chance of failure to be small.
Our portfolio has the risk-reducing characteristics of arbitrage but with a large number of stocks in the long side and in the short side of the portfolio, we expect the statistical behavior of a large number of favorable bets to deliver our profit. This is like card counting at blackjack again, but on a much larger scale. Our average trade size is $54,000 and we are placing a million such bets per year, or one bet every six seconds when the market is open.
As I walk back to my office, I think about how our statistical arbitrage venture came to be. While teaching finance in the UCI Graduate School of Management, I had many stimulating discussions with Dr. Jerome Baesel, the professor in the next office. I invited him to work full-time at Princeton Newport Partners. A major responsibility for him was to direct the indicators project, a research program I conceived. Neither Jerry nor I believed the efficient market theory. I had overwhelming evidence of inefficiency from blackjack, from the history of Warren Buffett and friends, and from our daily success in Princeton Newport Partners. We didn’t ask, Is the market efficient? but rather, In what ways and to what extent is the market inefficient? and How can we exploit this?
The idea of the project was to study how the historical returns of securities were related to various characteristics, or indicators. Among the scores of fundamental and technical measures we considered were the ratio of earnings per share to price per share, known as the earnings yield, the liquidation or “book” value of the company compared with its market price, and the total market value of the company (its “size”). Today our approach is well known and widely explored but back in 1979 it was denounced by massed legions of academics who believed market prices already had fully adjusted to such information. Many practitioners disagreed. The time was right for our project because the necessary high-quality databases and the powerful new computers with which to explore them were just becoming affordable.
By luck, one of our researchers almost immediately found the basic idea behind statistical arbitrage. He ranked stocks by their gain or loss over the previous two weeks. The stocks that had gone up the most did worse as a group than the market in the next few weeks, and the stocks that were the most down did better. Historically, the annualized return was 20 percent from buying the one-tenth of stocks that had fallen most and selling short the tenth that had risen most. We called the system MUD, as it was constructed from the “most-up, most-down” stocks. As UCI mathematician William F. Donoghue would joke, “Thorp, my advice is to buy low and sell high.” The portfolio of long stocks tracked the market and the short portfolio did the opposite, so the two sides together mostly canceled the movement of the market. This gave us what we liked, a market-neutral portfolio. But that portfolio still had larger fluctuations in value than our usual investments, so we put statistical arbitrage aside for the time being.
Unknown to us, a couple of years later an ingenious researcher at Morgan Stanley invented a product similar to ours but with substantially less variability. Trading probably began in 1983. With experience, his confidence increased and his investments expanded. Statistical arbitrage had become a significant profit center at Morgan Stanley by 1985 but the credit for its discovery, and the rewards from the firm, did not attach to the discoverer, Gerry Bamberger. While his boss Nunzio Tartaglia continued to expand the operation, a dissatisfied Bamberger handed in his notice.
As part of our plan to add diversified profit centers, Princeton Newport Partners was seeking to bankroll people who had successful quantitative strategies. Bamberger, now out of a job, contacted us. He described his strategy as high-turnover, market-neutral, and low-risk, with at any one time a large number of stocks held long and a large number held short. It sounded very much like our statistical arbitrage strategy, so even though we knew only the general characteristics of the portfolio and none of the details of how trades were chosen, we followed up. Once I gave my word that I would tell no one else unless either he okayed it or the information entered the public domain by some other route, I met with Gerry and he told me how his strategy worked.
Gerry Bamberger was a tall, trim Orthodox Jew with an original way of looking at problems and a wry sense of humor. We worked together for several weeks in Newport Beach to test his system exhaustively. If I was satisfied, we would bankroll a joint venture with Gerry. He brought a brown bag for lunch, and it always contained a tuna salad sandwich. I finally had to ask, “How often do you have a tuna salad sandwich for lunch?” Gerry said, “Every day for the last six years.” He was a heavy smoker and I’m extremely sensitive to tobacco smoke—to the extent that we did not hire smokers or allow smoking in our office—so we negotiated how to handle this. We compromised. Whenever Gerry needed a cigarette he would step outside our ground-floor garden office. This is not the ordeal in Southern California that it could have been during an East Coast winter.
The source of gain in the Bamberger version of statistical arbitrage was the most-up, most-down effect we had discovered in 1979–80. We hedged market risk but Gerry reduced risk even more by trading industry groups separately. To measure the historical performance of his system and to simulate real-time trading, we used Princeton Newport’s 1,100-square-foot computer room filled with $2 million worth of equipment. Inside were banks of gigabyte disk drives as large as washing machines, plus tape drives and central processing units, or CPUs, the size of refrigerators. All this sat on a raised floor consisting of removable panels, under which snaked a jungle of cables, wires, and other connectors.
The room also had its own safety system. In case of fire, the air was automatically replaced by noncombustible halogen gas within eighty seconds. Once this happened the room had too little oxygen for fire to burn or for people to breathe. We practiced how to get out in time and to trigger the halogen manually, if necessary.
Our facility was high-tech in the mid-1980s, but with the enormous increase in computer miniaturization, speed, and cheapness, now even cellphones store many gigabytes. The room was chilled to a constant sixty degrees Fahrenheit by its own cooling system and had sealed doors and dust filters to keep the air clean. Since smokers strongly emit tiny particles for an hour or more after even a single cigarette, Gerry agreed, with a lot of good-natured kidding, that the computer room was off limits.
When I was totally satisfied, we set up a joint venture, funded by PNP and run in New York by Gerry as a turn-key operation. We called it BOSS Partners, for “Bamberger (plus) Oakley Sutton Securities”—the latter an entity created by us to assist PNP. On capital ranging from $30 million to $60 million, BOSS earned between 25 and 30 percent in 1985. Returns gradually declined to 15 percent or so by 1988. The waning profitability and the mounting Giuliani attack on our Princeton office discouraged Gerry from continuing in the securities industry. He elected to retire a millionaire.
Meanwhile, I took the statistical arbitrage concept a step further. Trading started with my improved approach in January 1988, thus by chance missing the crash of 1987. How would we have done? Despite a 22 percent drop in the S&P 500 Index, BOSS made 7 percent for October 1987. Computer simulations showed our new statistical arbitrage product would also have had a good day and a record month. This was a ship for riding out cataclysms.
To control risk further, I replaced Bamberger’s segregation into industry groups by a statistical procedure called factor analysis. Factors are common tendencies shared by several, many, or all companies. The most important is called the market factor, which measures the tendency of each stock price to move up and down with the market. The daily returns on any stock can be expressed as a part that follows the market plus what’s left over, the so-called residual. Financial theorists and practitioners have identified a large number of such factors that help explain changes in securities prices. Some, like participation in a specified industry group or sector (say, oil or finance) mainly affect subgroups of stocks. Other factors, such as the market itself, the levels of short-term and long-term interest rates, and inflation, affect nearly all stocks.
The beauty of a statistical arbitrage product is that it can be designed to offset the effects of as many of these factors as you desire. The portfolio is already market-neutral by constraining the relation between the long and short portfolios so that the tendency of the long side to follow the market is offset by an equal but opposite effect on the short side. The portfolio becomes inflation-neutral, oil-price-neutral, and so on, by doing the same thing individually with each of those factors. Of course, there is a trade-off: The reduction in risk is accompanied by limiting the choice of possible portfolios. Only those that are market-neutral, inflation-neutral, oil-price-neutral, et cetera, are now allowed, and so the attempt to reduce risk also tends to reduce return.
We called the new method STAR, for “STatistical ARbitrage.” At the request of one of our investors we sent a trading history to Barra, a world leader in researching and developing financial products. They tested STAR with their model E2, which had fifty-five industry factors and thirteen macroeconomic factors. They found that our returns were essentially factor-neutral, and did not appear to result from lucky bets.
It was good that we advanced beyond the Bamberger model because, in simulation, its returns continued to fall. Moreover, after finishing with a good 1987, Morgan Stanley reportedly expanded their investment in it to $900 million long and $900 million short, which had to drive down returns for everyone using the method. The rumor was that they lost between 6 percent and 12 percent, leading to the winding down of the product.
People at Morgan Stanley began leaving the quantitative systems group that was in charge of statistical arbitrage. Among those to depart was David E. Shaw, a former professor of computer science at Columbia University. He had been wooed to Wall Street to use computers to find opportunities in the market.
In the spring of 1988, Shaw spent the day in Newport Beach. We discussed his plan to launch an improved statistical arbitrage product. PNP was able to put up the $10 million he wanted for start-up, and we were impressed by his ideas but decided not to go ahead because we already had a good statistical arbitrage product. He found other backing, creating one of the most successful analytic firms on Wall Street, and later would become a member of the president’s science advisory committee. Using statistical arbitrage as a core profit center, he expanded into related hedging and arbitrage areas (the PNP business plan again), and hired large numbers of smart quantitative types from academia. In 2014, Forbes ranked him as the 134th richest American, at $3.8 billion. One of his hires was Jeff Bezos, who, while researching business opportunities in 1994 for Shaw, got the idea for an online bookstore and left to start a company called Amazon.com. At $30 billion in 2014, Bezos was the fifteenth richest American.
As PNP began winding down in late 1988, despite the stress we developed yet another approach to statistical arbitrage that was simpler and more powerful. But as PNP phased out, I wanted simplicity. We focused on two areas that could be managed by a small staff, Japanese warrant hedging and investing in other hedge funds. Both went well.
I had no immediate plans to use our new statistical arbitrage technique and I expected that continuing innovations by investors using related systems would, as is the way of things, gradually erode its value. Four years passed, and then, my friend and former partner Jerry Baesel came to me with tales of extraordinary returns from statistical arbitrage. Besides D. E. Shaw & Company, the practitioners included former Morgan Stanley quants who were starting their own hedge funds, and some of my past PNP associates. I asked the former Morgan Stanley people if they knew how statistical arbitrage started at their firm. No one did. A couple had heard rumors of a nameless legendary “discoverer” of the system, who of course, was Gerry Bamberger—so thoroughly had recognition for his contribution been erased.
If our statistical arbitrage system still worked, Jerry Baesel told me that one of our former investors, a multibillion-dollar pension and profit sharing plan that was his current employer, wanted most or all of the capacity. Every stock market system with an edge is necessarily limited in the amount of money it can use and still produce extra returns. One reason is that buying undervalued securities tends to raise the price, reducing or eliminating the mispricing, and selling short overpriced securities tends to lower the price, once again shrinking the mispricing. Thus, opportunities for beating the market are limited in size by how trading them affects market prices.
Since our statistical arbitrage method was mostly computerized, Steve and I could run the managed account with help from our small office staff. It would let me have time to enjoy life. We decided to go ahead. The venture began auspiciously. Our software ran smoothly, first in simulation and then with real money, starting in August 1992.
I also wanted to invest my own money. I could do this efficiently and profitably by creating a new investment partnership. This led to the launching of Ridgeline Partners in August 1994 to trade alongside our institutional account. Limited partners gained 18 percent per year over its eight and a quarter years of operation.
Appendix E shows results for the large managed account, which for confidentiality I call XYZ. The annualized return of 7.77 percent and the annualized standard deviation of 15.07 percent for the S&P 500 during this period are somewhat below its long-term values. The unlevered annualized return for XYZ before fees, at 18.21 percent, is more than double that of the S&P; the riskiness, as measured by the standard deviation, is 6.68 percent. The ratio of (annualized) return to risk for XYZ at 2.73 is more than five times that of the S&P. Estimating 5 percent as the average three-month T-bill rate over the period, the corresponding Sharpe ratios are 0.18 for the S&P versus 1.98 for XYZ.
The graph in Appendix E, XYZ Performance Comparison, displays two major “epochs.” The first, from August 12, 1992, to early October 1998, shows a steady increase. The second epoch, from then until September 13, 2002, has a higher rate of return, including a remarkable six-month spurt just after the collapse (after four years) of the large hedge fund called, ironically, Long-Term Capital Management. Following the spurt during the last quarter of 1998 and the first quarter of 1999, the growth rate reverts for the rest of the time to about what it was in the first epoch. However, the variability around the trend is greater.
One cause for this greater variability might be the delayed and disputed election of George W. Bush. We also had an economic sea change from budget surpluses to massive deficits as a result of increased spending and tax rate reductions. More uncertainty came with the collapse of the dot-com bubble and the horrors of 9/11.
We charged Ridgeline Partners 1 percent per year plus 20 percent of net new profits. We voluntarily reduced fees during a period when we felt disappointed in our performance. We gave back more than $1 million to the limited partners. Some of today’s greedy hedge fund managers might say our return of fees was economically irrational, but our investors were happy and we nearly always had a waiting list. Ridgeline was closed a large part of the time to new investors, and current partners were often restricted from adding capital. To maintain higher returns, we sometimes even reduced our size by returning capital to partners.
Unlike some hedge fund managers who also had a waiting list, we could have increased our fees by raising our share of the profits or adding more capital, thereby driving down the return to limited partners. Such tactics by the general partner to capture nearly all the excess risk-adjusted return, or “alpha,” rather than share it with the other investors are what economic theory predicts. Instead, I preferred to treat limited partners as I would wish to be treated in their place.
In August 1998, the hedge fund Long-Term Capital Management (LTCM), a pool of $4 billion, lost nearly all its money. Highly leveraged, it threatened to default on something like $100 billion in contracts. Some claimed that the world financial system itself was threatened. The Federal Reserve decided LTCM was “too big to fail” and brokered a bailout by a consortium of brokers and banks, each of whom had a financial self-interest in saving LTCM. At about the same time several Asian economies got sick, and Russia defaulted on its debt.
The combination of events greatly increased volatility in the financial markets. Would these disruptions increase our potential rate of return or would they thwart our statistical arbitrage system? Hedge funds were suffering in multiple ways. Owners of Asian securities lost heavily. Financial institutions suddenly were less willing to extend credit, and leveraged hedge funds were forced to liquidate positions. We heard that large statistical arbitrage positions were being closed out. This seems likely because they are liquid and can be sold quickly to raise cash. This deleveraging and liquidity crisis foreshadowed a similar and far greater global rerun in 2008.
If there was such a large movement out of statistical arbitrage positions, we would expect our portfolios to lose while that was happening, because if others sell the stocks we own this drives the price down and our long positions show a loss. Similarly, if they have sold short the same stocks we have and they buy them back, this bids up the price of the stocks we are still short and we show a loss. Once the liquidation of portfolios winds down, we would expect a rebound. What actually happened was that after a small dip in the last four days of September, October began with six straight losing days during which our portfolio lost 4.2 percent, the sharpest blow we had ever experienced. Since this was just after the end of the quarter, I suspect it was due to involuntary liquidation of statistical arbitrage positions to raise cash to satisfy creditors. Fortunately we had just finished September with our best month ever.
Though October began badly, we recovered all our losses and continued the winning streak that started in September. It went on for six amazing months, through February 1999. During this time we made 54.5 percent. The result for the twelve months ending with August 1999 was that Ridgeline’s limited partners made 72.4 percent. This was from a market-neutral product using leverage of 2:1 or less. Several of our limited partners asked if we had ever seen anything like this. I told them that in thirty-five years of market-neutral investing I never had, but not to get used to it, as we were unlikely to repeat this performance.
Between Ridgeline and XYZ we managed as much as $400 million in statistical arbitrage and another $70 million in other strategies, whereas PNP’s peak was $272 million. Compared with PNP’s maximum of eighty employees, only six of us at Ridgeline faced our formidable competitors. Several of those had hundreds of employees, including scores of PhDs in mathematics, statistics, computer science, physics, finance, and economics. We were a highly automated, lean, and profitable operation.
We decided to close down in the fall of 2002. Returns, although respectable, had declined in 2001 and 2002. I believed this was due to the huge growth in hedge fund assets, with a corresponding expansion of statistical arbitrage programs. I had seen this happen before in 1988 when Morgan Stanley’s expansion of statistical arbitrage seemed to have a negative effect on our returns. The declining rate of return in statistical arbitrage seemed to be confirmed by the experience of most other hedge funds operating in the “space.”
The most important reason to wind down the operation was that time was worth more to me than the extra money. Vivian and I wanted to enjoy our children and their families, and to travel, read, and learn. It was time once again to change course in life.
And I had investments that remained interesting, such as the mutual savings and loan conversions in which my son, Jeff, and I began participating way back in 1990.