When Black and Scholes published their formula, the same one I was already using, I knew that to maintain PNP’s trading edge I would have to develop my tools for valuing warrants, options, convertible bonds, and other derivative securities rapidly enough to stay ahead of future marching legions of PhDs hungry for academic advancement through publication. Though I had to keep important results secret for the benefit of our investors, I could publicize lesser ideas that I thought would soon be found by others.
Before the work of Black and Scholes, I had moved beyond their basic formula, having generalized it to include cases where short-sale proceeds were withheld by the broker (to his benefit, since he got the use of the money) until the short sale was closed. Once they published, I presented these at a meeting of the International Statistical Institute in Vienna, where I was speaking. I also had extended the model to include dividend-paying stocks, since I was trading call options and warrants on many such stocks. Then the CBOE announced it would start trading put options sometime in the following year, 1974. These options, like the call options we were already trading, were called American options, as distinguished from European options. European options can be exercised only during a short settlement period just prior to expiration, whereas American options can be exercised anytime during their life.
If the underlying stock pays no dividends, the Black-Scholes formula, which is for the European call option, turns out to coincide with the formula for the American call option, which is the type that trades on the CBOE. A formula for the European put option can be obtained using the formula for the European call option. But the math for American put options differs from that for European put options, and—even now—no general formula has ever been found. I realized that I could use a computer and my undisclosed “integral method” for valuing options to get numerical results to any desired degree of accuracy for this as-yet-unsolved “American put problem.” In a productive hour in the fall of 1973 I outlined the solution, from which my staff programmed a computer to produce precise calculated values. My integral method also had another advantage over the Black-Scholes approach. Whereas the latter was based on one specific model for stock prices, one with limited accuracy, my technique could value options for a wide range of assumed distributions of stock prices.
In May 1974 I had dinner with Fischer Black in Chicago, where he had invited me to give a talk at the semiannual CRSP (Center for Research in Security Prices) meeting at the University of Chicago. Then in his thirties, Fischer was trim and tall, with combed-back black hair and “serious” glasses. Focusing intently on whatever finance topic was being discussed, he spoke articulately, logically, and concisely. His notes, compact and ultra-legible, reflected this. He would go on to become one of the most innovative and influential figures in academic and applied finance. Since a computational method for pricing American puts had been easy for me, I brought it to show Fischer and to learn from him how others had solved it. I laid the answer on the table between us but before I could speak Fischer began telling me about his approach to the problem and the difficulties that had so far stopped him. Earlier, I had explored his approach and believed it would work but, as my integral method was so easy, I used it. If Fischer Black didn’t know the answer, no one else did. Owing it to my partners to preserve our competitive advantage, I unobtrusively returned my work to my briefcase. Two other computational methods for finding American put prices were eventually published in scholarly journals in 1977.
As with my method for valuing American puts, my associates and I continued to solve problems for valuing so-called derivatives before the discovery and publication by academics. From 1967 until PNP closed at the end of 1988, this gave us a significant edge in trading the expanding array of new financial instruments.
Some of our trades were easy to explain to partners without using theory. One of these involved warrants issued by the Mary Carter Paint Company. Founded in 1958 as the successor to a 1908 company, it started as an acquirer of other paint companies, then evolved into a resort and casino developer in the Bahamas. Changing its name to Resorts International, it divested itself of the paint business and name. In 1972 the company had warrants that sold for 27 cents when the stock traded at $8 share. The warrants were so cheap because they were worthless unless the stock traded above $40 a share. Fat chance. Since our model said the warrants were worth $4 a share, we bought all we could at the unbelievable bargain price of 27 cents each, which turned out to be 10,800 warrants at a total cost, after commissions, of $3,200. We hedged our risk of loss by shorting eight hundred shares of the common stock at $8. When the stock later fell to $1.50 a share, we bought back our short stock for a profit of about $5,000. Our gain now consisted of the warrants for “free” plus about $1,800 in cash. The warrants were trading close to zero but below the tiny amount the model said they were worth, so I decided we should put them away and forget them.
Six busy years passed. Then in 1978 we started getting calls from people who wanted to buy our warrants. The company had purchased property in Atlantic City, New Jersey, after which it successfully lobbied, along with others, to bring casino gambling to the state, limited to Atlantic City. On May 26, 1978, Resorts opened the first US casino outside Nevada. Having received early approval, they had no competition and reaped windfall profits until other casinos opened late in 1979. With the stock now trading at $15 a share, ten times its earlier lowest price, and the warrants trading between $3 and $4, the model said they were worth about $7 or $8. So, instead of selling and reaping a $30,000 to $40,000 profit, I bought more warrants and sold stock short to hedge the risk of loss. As the stock broke through the $100 mark, we were still buying warrants and shorting stock. We finally sold the 27-cent warrants and others for above $100 each. We ultimately made more than $1 million. At the same time, blackjack teams using my methods were exploiting the casino boom in Atlantic City with its temporary friendly environment and reasonable blackjack rules. Ironically, as they were extracting millions of dollars from the blackjack tables at Resorts and elsewhere, I was profiting from Resorts’ securities.
In the three years and ten months from the start of 1973 through October 1976, limited partners in PNP gained 48.9 percent. During this time, ordinary investors had a wild ride in the stock market. The S&P Index fell 38 percent in the first two years and then surged 61 percent from 1975 through October 1976, for a net gain of just 1 percent. Meanwhile, Princeton Newport gained in every quarter.
That the market’s good years have to be better than its bad years just to come out even is a general rule. As an extreme example to make the point, using only month-end values throughout, the S&P 500 fell by 83.4 percent from its peak at the end of August 1929 to the close in June 1932. A dollar invested was reduced to 16.6 cents. For this 16.6 cents to become $1 again, the index needed to become 6.02 times as large, an increase of 502 percent. The wait was over eighteen years, until the end of November 1950. The rate of growth per year during this long recovery period was 10.2 percent, near the long-term historical average.
During the 1970s, the range and sophistication of our investments expanded. Companies came with families of securities, which included convertible bonds and preferreds, warrants, and put and call options. These derived most of their value from that of the underlying stock and were called derivatives. They proliferated in number, type, and quantity in the decades to follow, as so-called financial engineers invented new ones to possibly decrease risk and certainly increase fees. I used my methodology to price these derivatives and the others that followed. This enabled Princeton Newport Partners to price convertible bonds more accurately than anyone else. Hedging with derivatives was a key source of profits for PNP during its entire nineteen years. Such hedging also became a core strategy for many later hedge funds like Citadel, Stark, and Elliott, which each went on to manage billions.
Convertible bonds today may have complex terms and conditions. However, the basic idea is simple. Consider the hypothetical XYZ 6s of 2020. Each bond was originally sold for approximately $1,000 on July 1, 2005, to be redeemed by the company for exactly $1,000, the “face amount,” on July 1, 2020. The bond promises to pay 6 percent of the face amount in interest for each year of its life, in two semiannual installments of 3 percent, or $30, payable to holders of record on January 1 and on July 1. So far these are like the terms of a typical ordinary bond. However, the convertible has one more feature. At the option of the owner, it can be converted into twenty shares of XYZ common stock anytime until bond maturity on July 1, 2020. So this bond combines the features of both an ordinary bond and an option. The market price of the bond can be thought of as the sum of two parts. The first is the value of a comparable bond without the conversion feature, which will fluctuate with the level of interest rates and the financial soundness of the company. This sets a “floor” to the price.
The second part is the option value of the conversion feature. In our example, if the stock is at $50, the bond can be exchanged for twenty shares of stock, worth $1,000, which the bond is worth anyhow when it matures so there is no benefit from the conversion feature. However, if the stock were to rise at any point to $75, twenty shares of stock would be worth $1,500. The bond, which can be exchanged immediately for this amount of stock, should trade in the market then for at least that amount.
Why do companies issue such bonds? Because the value of the extra option or conversion feature, which gives the buyer a lottery ticket on the company’s future, allows the company to reduce the interest rate they need to pay on the bonds in order to sell them.
Just as PNP used option valuation methods to build models for pricing convertible bonds, it did the same with other derivatives. Our hedges individually had low risk. Of two hundred that I tracked in the early 1970s, 80 percent were winners, 10 percent ended approximately even, and 10 percent lost. The losses were considerably smaller on average than the gains.
To produce even steadier returns, we hedged the overall risk from our entire collection of hedges by neutralizing the impact on our portfolio of shifts in interest rates (across the spectrum of quality and maturity). We also offset the danger to the portfolio from sudden large shifts in overall stock market prices and in the volatility level of the market. From the 1980s on, some of these techniques came into usage by modern investment banks and hedge funds. They also adopted a notion we rejected, called VaR or “value at risk,” where they estimated the damage to their portfolio for, say, the worst events among the most likely 95 percent of future outcomes, neglecting the extreme 5 percent “tails,” then acted to reduce any unacceptably large risks. The defect of VaR alone is that it doesn’t fully account for the worst 5 percent of expected cases. But these extreme events are where ruin is to be found. It’s also true that extreme changes in securities prices may be much greater than you would expect from the Gaussian or normal statistics commonly used. When the S&P 500 Index fell 23 percent on October 19, 1987, a leading academic finance professor said that if the market had traded every day for the thirteen-billion-year life of the universe, the chance of this happening even once was negligible.
Another tool used today is to “stress-test” a portfolio by simulating the impact of major calamitous events of the past on the portfolio. In 2008, a multibillion-dollar hedge fund managed by a leading quant used ten-day windows from the crash of 1987, the First Gulf War, Hurricane Katrina, the 1998 Long-Term Capital Management crisis, the tech-induced market drop in 2000–02, the Iraq War, and so forth. All this data was applied to the fund’s 2008 portfolio and showed that these events would have led to losses of at most $500 million on a $13 billion portfolio, a risk of loss of no more than 4 percent. But they actually lost over 50 percent at their low in 2009, brought to the brink of ruin before finally recovering their losses in 2012. The credit collapse of 2008 was different in kind from the past worst cases for which they tested, and their near-extinction reflects the inadequacy of simply replaying the past.
We took a more comprehensive view. We analyzed and incorporated tail risk, and considered extreme questions such as, “What if the market fell 25 percent in one day?” More than a decade later it did exactly that and our portfolio was barely affected. When, with our expanding range and size of trades, we moved our account to Goldman Sachs as our prime broker, one of the questions I asked was: “What happens to our account if Goldman Sachs New York is destroyed by a terrorist nuclear bomb smuggled into New York Harbor?” Their reply was: “We have duplicate records stored underground in Iron Mountain, Colorado.”
There is another kind of risk on Wall Street from which computers and formulas can’t protect you. That’s the danger of being swindled or defrauded. Being cheated at cards in the casinos of the 1960s was valuable preparation for the far greater scale of dishonesty I would encounter in the investment world. The financial press reveals new skulduggery on a daily basis.
With inflation approaching double digits and a spike in commodity prices, precious metals and options to buy or sell them were a booming business. Back in my office, I compared the XYZ Corporation’s prices to the “correct” model prices we used at PNP when we sold large amounts of such options to a major dealer.
To my astonishment, I found that XYZ Corp was offering to sell me options at less than half my expected payoff! After I collected financial statements from my friendly salesman and examined them, I discovered that when XYZ Corp sold an option it counted the proceeds as income, but did not set aside any reserve to pay off the options if and when they were cashed in by the buyer. Since the correct reserves on each option they sold should have been more than twice what they were being paid, proper accounting would show their net worth becoming more negative every time they sold another option.
It was clear that they had to sell more and more options, using the increasing cash flow to pay off any early “investors” who might cash in. Classic Ponzi, and bound to end badly. What to do?
I decided on a little educational experiment. After reviewing the scanty information available on sales, options outstanding, and early redemption rates, I estimated the company would survive for at least eight more months. It turned out to be ten. Buying $4,000 worth of six-month options, I doubled my money in four months and cashed out. A few months later the offices were shuttered, the operators gone, and another fraud investigation was under way.
The next big test of PNP’s investment approach came soon afterward. From 1979 through 1982 there were extreme distortions in the markets. Short-term US Treasury bill returns went into double-digit territory, yielding almost 15 percent in 1981. The interest on fixed-rate home mortgages peaked at more than 18 percent per year. Inflation was not far behind. These unprecedented price moves gave us new ways to profit. One of these was in the gold futures markets.
At one point, gold, for delivery two months in the future, was trading at $400 an ounce and gold futures fourteen months out were trading for $500 an ounce. Our trade was to buy the gold at $400 and sell it at $500. If, in two months, the gold we paid $400 for was delivered to us, we could store it for a nominal cost for a year, then deliver it for $500, gaining 25 percent in twelve months. There were a variety of risks, which we fully hedged, and several “kickers”—scenarios where we would make a higher—(often much higher) rate of return. We did similar trades in silver and copper and they worked as expected, with one tiny exception. After we took delivery of our copper, some of it was stolen from the warehouse our broker used and there was a short delay while we were reimbursed from the warehouse company’s insurance.
As the era of high interest rates unfolded, savings and loan companies began to lose massive amounts of money. Here’s why. Savings and loans borrowed money for a short term from depositors and lent much of it out long-term for home mortgages at fixed rates of interest. As short-term rates shot up, the cost of money to the S&Ls went up rapidly, whereas their revenue from the existing mortgage loans they had made earlier to homeowners at much lower fixed rates did not. This mismatch in interest rates between their short-term borrowing and their long-term lending would lead to the ruin of many S&Ls in the 1980s and a bailout cost to taxpayers of several hundred billion dollars.
The possible collapse of the S&Ls could have been predicted and prevented by suitable regulation, but wasn’t. The great financial crises that came later shared this characteristic.
Meanwhile, Princeton Newport Partners was expanding into new types of investments.