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Authors: Emanuel Derman

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I was Mike's lieutenant in charge of research on adjustable rate mortgages (ARMs, for short), something I knew little about when I arrived. I had never had any formal education in mortgage markets; flung into the middle of this, and supposedly supervising people who knew more about it than I did, I began to read the Salomon Brothers research papers on the topic.

The American mortgage market, I learned, was gigantic, comparable to that of Treasury bonds. At the individual level, savings banks all over the country lend money to homeowners who need to finance their housing purchase. In exchange, homeowners contract to repay the loan over 15 or 30 years in equal monthly installments of interest and principal. ARMS are mortgages with an
adjustable
rate of interest that, every six months, for example, floats up or down in approximate synchrony with short-term Treasury interest rates according to some specified formula. Correspondingly, every six months, the homeowner's monthly mortgage payment changes, too.

ARMs have all sorts of additional wrinkles. They start out the first year with a “teaser,” an unusually low and tempting interest rate. Then, over time, as the rate adjusts, there is a cap on how high it can float and a floor on how low it can sink. Finally, although a mortgage may have a nominal life of 15 or 30 years, a homeowner can choose to terminate the loan early by prepaying the unpaid balance—a smart thing to do if interest rates have fallen so low that a totally new mortgage with a lower interest rate is preferable.

Banks who lend to homeowners own the mortgage, the claim to the homeowner's future monthly repayments. Periodically, the banks turn around and sell the mortgages they have acquired to GNMA, FNMA, and FHLMC, government agencies that act as financial intermediaries by pooling together vast quantities of similar but not identical mortgages into more standardized securities. They then resell these pools to large investors—mutual funds, pension funds, insurance companies, hedge funds, and the like—in search of interest-bearing investments. This process of asset acquisition, pooling, standardization, and subsequent sale provides a liquidity that frees the savings banks to make more loans. As a result, the percentage of residents who own their own homes is greater in the United States than anywhere else in the world.

Mortgages are messy, though it takes only a little careful high-school math to work out the monthly mortgage payment that will draw the loan down to zero over 15 years. But that's just the start. Everything about an adjustable rate mortgage pool—the interest payments, the principal repayments, and so on—varies with the future level of interest rates, so an ARM is really a complex option whose payments are contingent on interest rates.

To estimate what a mortgage pool is worth, you have to rely on a model of future interest rates, something like the BDT model I had worked on, in fact. You then simulate the pool's future cash flows, averaging over thousands of interest-rate scenarios generated by the model. You want to represent the future evolution of long- and short-term interest rates as realistically as possible, and then, for each future scenario, compute the adjustment in the floating ARM interest rate that a homeowner will pay each month. You also want to try to estimate from past experience what percentage of homeowners will prepay their mortgage as a consequence of the change in rates on each scenario, since this prepayment alters the cash flows, too. The output of this Monte Carlo simulation model is the current value of the mortgage pool.

Mortgage valuation models involve a witch's brew of assumptions about yield curve movements and how homeowners respond to them, none of them well-tested. Even the ZIP code of the homeowners who owned the houses that were financed by the mortgages in a pool is important—some localities, based on their socioeconomic classification, had a greater tendency to prepay than others—and I had heard of investors who actually went to check out the neighborhoods for themselves. Compared to the rigor and predictability of physics or even the simple elegance of the Black-Scholes formalism, mortgage valuation is ugly. I once remarked on this to Steve Ross whose investment company, Roll & Ross Asset Management, specialized in mortgages. “Whenever I see something complex and confusing in the investment area,” he retorted, “I see the scope for getting a little extra benefit out of being smart.”

It's a good answer, and probably true, but I still find mortgages unattractive. Black-Scholes is clean and simple, like the theory of the hydrogen atom. Modeling mortgages is involved and approximate, more like trying to explain the structure of the energy levels in the uranium isotope U
238
. I prefer clean problems. Still, mortgages were what I had signed on to deal with.

Salomon was a tough place. The first thing I noticed when I started work was that everyone came late for meetings. The most senior people arrived last, each of them popping their heads into the door to see if everyone else was there and then quickly leaving again if they weren't. The junior people took advantage of this chronic lateness to be late themselves. Everyone was so determined to not have his or her own time wasted that they collectively wasted everyone else's. This would not have happened at Goldman.

The level of fear that permeated Salomon was more evident, too. Friends of mine who wanted to leave the firm were semiparanoid that their bosses would discover that they were interviewing elsewhere and then fire them before they left. I never heard anyone at Goldman speak this way; despite the natural tension between employer and employee, most Goldman workers never imagined that exercising their right to look at other jobs would naturally lead to being fired.

There were other signs of Salomon's take-no-prisoners culture. In the 1980s, the BPA group had written a series of renowned reports for clients on valuing swaps and other recently invented derivatives contracts. Each report's distinctive light brown cover bore the names of its authors printed in a darker brown. Then, over the years, as one or more of the original authors left the firm for other banks or trading houses, BPA would reprint the report, having removed the departed authors' names. Eventually there were old but popular reports still being distributed that apparently had no author at all. This Orwellian rewriting of history struck me as particularly petty and ineffective, an affront to the notion of research.

At Goldman the enemies were competing firms; at Salomon the enemies were competing colleagues. Shortly before they were acquired by Citigroup, I met with an old friend still working there and asked him what had caused a well-known acquaintance of ours to have been laid off by the firm. “Oh him,” my friend said, “It turned out he couldn't even code a Black-Scholes model!” Now, the Black-Scholes model is so fundamental and ubiquitous that I had little doubt that this was false. But, more interestingly, I asked, how did anyone actually know that our friend couldn't code the model? Who had put him to the test?

Everyone in the Salomon quant group, I was told, had to recreate their own computer code for even the simplest things that other people could already do, because no one who had created something independently was willing to share it. This was in diametric contrast to the situation at Goldman, where, because this kind of backstabbing was frowned upon, software was shared. At Goldman it would have taken longer to find out that someone couldn't do something as straightforward as code a simple model.

The most impenetrable barrier was the wall between Meriwether's group and everyone else. Occasionally I would catch distant glimpses of the arb group. Meriwether, Haghani, Hawkins, Krasker and their colleagues sat together in the center of the trading floor, a world apart from everyone else, a little Persian carpet marking the center of their privileged domain, an exalted clique of happy people who awed everyone and knew it. They had their own inviolably secret models, their own inaccessible data, their own computer systems and system administrators, all exclusively theirs. They also had access, if they wanted it, to the best models and minds in BPA, via a one-way street that ran only in their direction. They were an elite force, a Republican guard who could do whatever they wanted, and everyone half-envied, half-resented them for it. They had it all—knowledge, independence, prestige, and lots of money.

I attributed many of these cultural divergences between Salomon and Goldman to the structural differences between a public company and a private partnership. Goldman, then still private, functioned more smoothly because it was run by partners seeded uniformly throughout the firm. They were the daily overseers who didn't possess a liquid stock to sell, and so their long-term profit depended on the firm remaining intact. As a result, any excessive egotism was eventually squelched, sooner rather than later, because someone in control, despite his or her desire to win that particular battle, realized that it was harmful to the firm. Goldman people always told you that Goldman people were nicer, worked better together, were less political. Though this was not entirely true, the constant talking about it helped make it a self-fulfilling prophecy. No matter how self-interested the partners were, their long-term interests were tied up in the entire company, not just in their little piece of it.

In the words of a famous Goldman ex-partner, Gus Levy, Goldman was long-term greedy rather than short-term greedy. At Salomon, I thought, it was every man for himself and God against them all.

The key responsibility of my research group was to support the ARMs dealers, who, unlike the arb group, were more interested in earning a spread by servicing clients than in carrying out genuine proprietary trading. We helped them by writing short quantitative marketing reports that provided generally truthful ammunition for use by the salespeople. When the desk acquired some new pool of mortgages, we ran our models on them and tried to explain where their value lay.

There was a range of different models and corresponding metrics that you could use to gauge the value of a pool. The simplest measure was the total profit that the pool would yield to a purchaser over its lifetime, assuming interest rates in the future remained unchanged. The most complex, which used interest-rate simulation models of the BDT type I had helped develop at Goldman, was Salomon's option-adjusted spread model that reported the spread over Treasury bonds the pool would generate, on average, over all future interest-rate scenarios.

We ran daily reports on the desk's inventory using both these models. Different clients preferred different metrics, depending on their sophistication and on the accounting rules and regulations to which they were subject. We also did some longer-term, client-focused research, developing improved statistical models for homeowner prepayments or programs for valuing the more exotic ARM-based structures that were growing in popularity.

The traders on the desk used the option-adjusted spread model to decide how much to bid for newly available ARM pools. The calculation was arduous. Each pool consisted of a variety of mortgages with a range of coupons and a spectrum of servicing fees, and the option-adjusted spread was calculated by averaging over thousands of future scenarios, each one involving a month-by-month simulation of interest rates over hundreds of months. Because the number and size of the monthly payments received from the pool varied in a complex path-dependent way with changes in interest rates, in 1989, on even the fastest computers, it took vast amounts time to perform the calculations that led to the model's recommended bid.

What made all of this complex work so unpleasant was the extreme urgency of the demands from the desk coupled with the archaic nature of the computer models we used. Often, we had less than thirty minutes to prepare a bid for a pool. The outdated and unfriendly FORTRAN program used to calculate the option-adjusted spread had been written many years earlier. In order to value the pool, the program needed the parameters that described its constituents: how many subgroups of mortgages it contained, each subgroup's coupon and maturity, the caps and floors on the interest rate, and so on. You had to type these numbers into a file in a prespecified order with exactly the right number of blank spaces between each number. Then the program ran on a powerful supercomputer bought solely for this purpose.

On a typical day, the starting gun fired when the desk received a page-long fax from a savings-and-loan with the pool's parameters. We then had a half-hour to type the parameters into the input file and submit it to the supercomputer, which in ideal circumstances took about ten minutes to complete its calculations. So, every ten minutes impatient traders would call from the desk for the answer.

Unfortunately, the program was totally unforgiving about input: If there were just one blank character too many or too few, the program silently hiccupped, and then went into an infinite loop, pointlessly churning away on misread data without ever producing an answer. As a result, for the first ten or fifteen minutes you would sit there nervously waiting for the program to terminate and an answer to appear on the screen, all the while wondering whether the supercomputer was simply running a little slowly that day, or whether you had mistyped the number of blanks and were now in purgatory. If fifteen minutes elapsed without an answer, you could assume you had made a mistake; you then killed the program and started over. It was agonizing.

This schedule of pool valuations dominated our life. Someone always had to be on duty, preferably someone who could type very fast. It was maddening to stand by and watch the one slow typist in our group chicken-peck her way across the keyboard when there was a rush to bid. If you left your desk for a while, you had to tell the secretary where you could be reached. No one thought of taking more than a one-week vacation. When I did take two weeks in the summer of 1989, I could sense Mike's displeasure at my lack of professionalism.

Once a week there was an early-morning meeting of S, T, and R, as the hollowly upbeat sales manager liked to refer to sales, trading, and research, linking their names together in an effort to give equal status to research. Occasionally I had to deliver a brief two-minute presentation to the salespeople on the attractive characteristics of some new ARMs pool we had acquired. The first time I did this I was still shaky and insecure about the peculiarities of mortgages, and a consultant was brought in to prep me on how to talk from a script without seeming to look at it. His trick was to use very large type, so you could invisibly scan ahead and memorize one phrase at a time with a quick glance down, all the while maintaining apparent eye contact with your audience. The rehearsals and videotaping were demeaning, but it was an illustration of their totally professional approach.

BOOK: My Life as a Quant
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