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Gold Delta Hedge Trap (Parts I & II)

by Adam Hamilton

As this essay has exploded outward with all the force of NASDAQ slamming into the concrete wall of cold fundamental cashflow reality, it has been necessary to split it up for your own safety. Part 1 discusses the origins of the infamous Black and Scholes Option Pricing Model and outlines the tremendous risks of writing naked gold call options. Part 2 discusses Delta Hedging, how it should be used to mitigate naked call writing risk, and describes the growing peril of the delta hedge trap in which the gold shorts find themselves.

Gold Delta Hedge Trap  (Part 1)

As an exceptionally volatile week in the world gold markets draws to a close, the growing peril in which the gold shorts find themselves is becoming much more evident. Unlike the odd and manipulated four weeks of glassy calm in the gold markets last month (we discussed this in our November Gold essay), we have finally observed what looks like a long-slumbering giant beginning to awaken and stir. With investor interest in gold and gold equities spreading like wildfire, the winds of change blow new gold tidings fiercely along the horizon.

As gold makes a few tentative shuffles higher in its long-anticipated quest to attain its true value, at the price where global mined gold supply is in equilibrium with global gold demand, the entities around the world that owe physical gold that they do not have are getting very nervous. And they have darned good reason to be.

One specific area of tremendous risk for the gold shorts that has not been discussed much lately is Delta Hedging. Delta hedging is a methodology of hedging, or protecting, written naked call options from catastrophic increases in the market price of the underlying asset. It is a common practice for large option writers, and has been proven incredibly successful after nearly three decades of real-world application.

In the recent small rallies in gold, reliable reports from the gold trading pits surfaced that indicated large money-center banks short gold had not been buying gold, as their delta hedging requirements call for, but had actually been massive net sellers of gold into the rallies. If this is the case, we believe the managers of these prestigious Wall Street corporations may be acting in a criminally negligent manner and putting their shareholders into an unacceptably risky and dangerous position. 

As the delta hedging of naked call options written has long been accepted as the standard way to mitigate risk, not maintaining proper delta hedges is the financial equivalent of a commercial airline pilot ignoring his preflight check, taking off in a faulty jumbo jet, and causing the fiery deaths of several hundred people. It is unacceptable, and may border on criminal negligence if there was an explicit decision made NOT to maintain delta hedges. If our suspicions that the gold shorts are not actually maintaining their delta hedges in gold rallies is true, the shareholders of these large and venerable money center banks need to know how reckless and foolish these actions their managers have intentionally undertaken are in reality.

Unfortunately, delta hedging is a complex topic that requires a bit of background to fully comprehend. In the first half of this essay, we look at the origins of the famous Black and Scholes Option Pricing Model and examine the risk profile of gold calls. In the second half, we explore delta hedging and the implications for corporations writing naked gold calls if they are not maintaining properly balanced delta hedges.

Delta hedging and even the widespread use of options themselves are based on the amazing foundational work completed by Fischer Black, Myron Scholes, and Robert Merton over 25 years ago. The importance of the Black and Scholes Option Pricing Model (BS) they developed cannot be easily overstated. The achievement of the logic and solution for pricing options in continuously changing markets has been hailed as having the equivalent impact on the world of finance as the discovery of the double-helix DNA strand had on the world of genetic engineering. The BS is a triumph in human financial achievement, and enabled vast new frontiers to be opened and exploited in global financial markets.

One of the brilliant men who created the BS model, Myron Scholes, actually grew up near gold and silver mining operations in northern Canada. Young Myron observed that his family and family friends would often purchase gold or silver stocks on a rumor that some great new discovery was about to be announced. Sometimes the rumors were true and large gains were realized, but many times the rumors did not play out, and losses accrued. Myron was fascinated by the concept of volatility. As he watched others play the gold and silver mining (and penny stock mining) sectors, he became increasingly curious about why price fluctuations occur, how they occur, and how they could possibly be predicted. With the heavy application of the BS model in the world of gold options today, it is fitting and poetic that Myron Scholes' initial spark of interest was nurtured firsthand on the precious metals frontier of the Great White North.

Scholes would go on to become an assistant professor of finance at the ultra-prestigious Massachusetts Institute of Technology. In 1969, when he was 28 years old and teaching at MIT, Scholes met Fischer Black. Black was a 31 year old independent finance contractor with a Harvard Ph.D. in applied mathematics. Black and Scholes soon became friends and began to study the arcane world of options.

For two centuries, the Holy Grail of cutting edge economics had been the problem of trying to correctly price options. In the complex and interrelated financial markets, changes in a myriad of variables that affected the value of a particular option happened continuously in realtime. Trading in options and other derivatives was very limited because it was impossible to quantify the risk and proper price of an option at any moment in time.

One hundred years ago a French graduate student named Louis Bachelier wrote a thesis called The Theory of Speculation where he compared the behavior of buyers and sellers in a financial market to random movements of gas particles within a fluid. Ignored at the time, his work was rediscovered in the 1950s and led leading economic minds to once again begin thinking on how to properly price an option.

While Black and Scholes were working on the problem twenty years later, they met Robert Merton. Merton was a brilliant financial genius well known for using exotic mathematics to study complex financial contracts. He was always thinking outside the box, and had recently been studying the mathematical formulas developed by a Japanese rocket scientist named Kiyosi Ito.

When launching a rocket into the atmosphere, it is critically important that its trajectory is precisely tracked so any necessary minute adjustments can be made. It is not good enough to know where a rocket is every second or so -- rocket scientists need to know exactly where a rocket is continuously. Kiyosi Ito developed a mathematical way to divide time into infinitely small packets, so that a rocket's trajectory could be computed in an uninterrupted continuum.

Robert Merton recognized that financial markets are also instantly and continuously changing, and was able to build on Ito's math and apply the solution to Black and Scholes problem. Black and Scholes used Merton's math to examine raw data from the Chicago Board Options Exchange. A theory emerged from their meticulous research, and the result was the Black and Scholes Option Pricing Model. Interestingly, although now absolutely critical for pricing gold options, the sixteen commodities on which options were offered in the early 1970s by the Chicago Board Options Exchange did not include gold, which was then illegal for US citizens to own.

Although the first draft paper of the BS model was initially rejected by prestigious economics journals in 1973, with the help of Nobel Laureate Merton Miller from the University of Chicago Black and Scholes were able to revise their theory enough for a resubmission. The paper was finally published and it immediately became one of the most widely accepted and successful financial models in all of history.

Active floor traders, who needed to know exactly how much an option was worth at a given moment in time, rapidly put the theory to work. Although the BS formula itself looks complex, it is easy to program into a pocket calculator for rapid computation. 

The BS model spread far and wide, and soon it was the standard and undisputed methodology for calculating option prices. It allowed the derivatives business to mushroom, enabling risk to be efficiently and rapidly transferred from those who did not want to bear it (hedgers) to those who were willing to accept it (speculators) to try and profit. Applied mathematics as manifested in the BS model is the foundation for the multi-trillion dollar derivatives markets around the world today.

In 1997, 25 years after their discovery, Dr. Scholes and Dr. Merton received the Nobel Prize for Economics, the most prestigious honor in the economics field. Unfortunately, Dr. Fischer Black had passed away by then. He also would have no doubt been a co-recipient for the Nobel Prize for the theory and pricing model that still bears his name.

The BS model undergirds and prices all the gold call options traded around the world today. The large money center banks that are shorting gold have written vast quantities of call options, and the background of the BS model is necessary to understand the almost unfathomable risk in which they have placed themselves.

Although there are several ways to short gold, including borrowing it and selling it in the open market, we are focusing specifically on the writing of call options in this essay. In order to understand the risk of being on the short side of a gold call option, it is useful to understand the long side first.

If you buy a gold call option at a strike price of $325, you have the right, but not the obligation, to buy gold at $325 regardless of what the actual price of gold does. You pay a premium for purchasing the option. The actual price you pay in the open market is determined by the BS formula. With gold around $275, the option is deep out of the money and has a chance of expiring worthless. The worst thing that can happen to you, the buyer, is that the option will indeed expire worthless. In that case, you lose 100% of the money you paid for the option. If gold would rise in price above $325 before the option expired, however, the profits would be enormous. 

Imagine you had to pay $2 per ounce to buy the $325 gold call option. If gold languished under $325, your option's value would rapidly dwindle. The closer the option moves to its expiration date, the less time and uncertainty exists, and the lower the option price. BUT, if gold rallies and trades above your $325 strike price, your option shoots up in value dramatically. If gold jumps to $350, your $2 option is now worth $25 ($350 gold spot price minus the $325 option strike price) in the open market. The leverage evident in options is absolutely phenomenal and is readily apparent. From a buyer's perspective, call options are a way to bet on future market direction with fantastic leverage, but the buyer's potential loss is limited to 100% of the initial price paid for the options.

In order for there to be options to buy, someone has to be selling them. The folks selling the most gold options are the large gold shorting money-center banks and gold mines themselves. We will focus here on the money-center banks because they are writing "naked" call options, and save the gold mines for another essay.

The banks' motivations for selling (or writing) call options are purely profit. That $325 gold call they sold you had a price of $2. If gold stays under $325, it is a source of easy profits for the banks. After all, they do not have to produce anything, the entire $2 premium is profit, and they can write these call options in virtually unlimited numbers. When writing a lot of options, the small premiums for which one can sell each option soon add up and can yield a lot of cash.

The risk profile for the banks is exactly the opposite as for the gold call option buyer. For the banks, if gold stays under $325, they make a 100% profit on the option premium. If the gold price goes over $325, however, they rapidly lose money -- a LOT of money. 

When the banks write gold option contracts, in the vast majority of cases they do not have the physical gold on hand to back their call options. They are writing "naked" call options. The bank is considered "naked" and unprotected because it does not have the asset in the vault that it promised to deliver at the strike price. A naked call is the functional equivalent of a short sale. The banks have contractually promised to provide gold at $325, no matter what trajectory the spot price of gold attains. Unlike the gold call option buyer, the banks selling the call options have the very real potential for an unlimited loss. 

Imagine gold rockets to $1,325 per ounce on the spot markets, for example. That $2 option is now worth $1,000 ($1,325 gold spot price minus the $325 option strike price) to the individual who purchased it. When the option buyer exercises his or her contract, the bank is obligated to sell an ounce of physical gold to that person for $325. Since the bank wrote a naked call option, it has to go to the open market and pay cash for gold at $1,325 for ounce, and then sell the gold to the option contract holder at $325. The potential $2 profit the bank forecasted has turned into a mind-boggling $1,000 CASH loss, a 500x negative increase. 

With banks writing hundreds of thousands of naked gold call option contracts, and each contract representing 100 ounces of gold, the scope of the problem is truly mind-blowing. Thus far into our discussion, it is easy to see why the large money-center banks that are short gold are utterly terrified at the price of gold rising. As soon as gold trades above the strike price of a particular naked call option contract, the bank watches enormous losses grow at dizzying speeds. What had once seemed like a prudent strategy to milk a "dead" market where a "barbaric relic" trades soon seems like the dumbest macro-bet in the history of humanity.

Because of the nature of the vast amounts of naked gold calls gold-shorting banks have written, you can be absolutely sure they are sweating out ANY rally in gold, even if it is only a few dollars. Some of these banks sport notional amounts of gold derivatives that exceed their entire capital base. They are controlling, through various financial derivatives including options, tens of billions of dollars of gold. Most independent analysts in the gold community believe the lion's share of these massive gold derivative positions are on the short side of the ledger. If gold rallies even a mere 25% from current levels, some of these banks, which include old, venerated, and widely respected blue-chip names, will be totally eviscerated from the massive losses they will sustain in their gold derivative operations. As such, they have to do everything in their power to hold down the price of gold or else watch their corporations suddenly leap to a fiery death in bankruptcy.

There IS one widely accepted method for reducing the risk of writing naked calls, and that is the Delta Hedge. Delta hedging is a strategy derived from the BS option pricing formulas. It is absolutely essential to follow this strategy when writing large amounts of naked gold calls.

Are the banks, however, properly deploying delta hedges on their naked call positions? If not, the financial and legal consequences for the gold-shorting banks could be catastrophic. Disturbing reports emerged from the trading floors in recent gold rallies that indicate the very gold-shorting banks having written large naked gold call option positions were actually SELLING physical gold into the rallies, not buying physical gold as the important discipline of delta hedging demands.

We believe these banks may have fallen into a gold delta hedge trap. The implications of this course of action they may have chosen, in terms of potential capital destruction, shareholder lawsuits against the money-center banks themselves, and shareholder lawsuits against the individual managers involved in accumulating and neglecting the banksí short gold derivative positions could be extraordinary.

December 8, 2000

Gold Delta Hedge Trap  (Part 2)

Armed with the perspective from our previous discussion, it should be pretty obvious by now that writing naked call options in a market trading slightly above 25 year real lows is near the height of financial audacity. A massive bet has been placed by the money-center gold shorting banks. By writing vast quantities of naked call options on gold, they are making critical assumptions that the gold market is not cyclical, that gold is dead as an investment, and that governments can control gold. Fat chance! Unless the lessons of six thousand years of human history are suddenly and miraculously voided, the probability of success for these bets against gold is effectively zero.

Fortunately for the gold shorts, the brilliant men who created the Black and Scholes Option Pricing Model (BS) designed a way to mitigate SOME of the risk of a gold rally for call option writers. Enter delta hedging.

Using calculus, partial derivatives can be calculated using the BS model. There are five major partial derivatives, and all were given Greek letter names in order to identify them. Delta, gamma, theta, vega, and rho are all BS partial derivatives, but the most important and widely known is the delta. The delta variable encompasses an estimate of the probability that the option purchaser will exercise an option. The delta variable is used by gold shorts writing gold call options in order to reduce their ultimate exposure and risk of loss in response to gold rallies.

The delta is computed by taking into account changes in the spot price of gold (volatility), the time to expiration of an option contract, and the difference between the strike price of the option and the spot price of gold. As these underlying factors fluctuate, the delta variable changes in response and the writer of the call options must buy or sell physical gold in order to keep the option contract properly delta hedged. In general, if gold prices rise, physical gold must be purchased in the open market to maintain an acceptable delta hedge on a written gold call. Conversely, if gold prices fall, physical gold may be sold. If the BS delta hedging methodology is scrupulously followed, a delta-neutral position can be attained in a written call option portfolio.

Digging deeper into this concept, think about when you would want to exercise an option as the purchaser. In our $325 strike price gold call option example from the first half of this essay, would you want to exercise if gold was trading at $300? The answer, of course, is no. Why use the option contract to pay $325 for gold that you could buy in the open market for only $300? The probability of exercise is low in these "deep out of the money" options. In delta hedging terms, the probability of exercise approaches zero the further away the spot price moves downward from the strike price.

Now imagine gold is trading at $350. Would you want to exercise your $325 call option now? Absolutely! You can use the option to buy gold for $325 and then immediately sell it in the open market for $350, netting a $25 profit. The probability of exercise of an option is very high for "deep in the money" options. In delta hedging terms, the probability of exercise of a gold call option approaches or equals one the higher the spot price of gold moves above the strike price of the option.

If the strike price of the option EQUALS the spot price of gold, the option is considered "at the money". In our example, this occurs when the spot price of gold is at $325, the same as our option strike price. Black and Scholes delta hedging assigns a probability of exercise of 0.5 in this case, indicating there is a fifty percent chance of the option being exercised. The reason is explained below.

The gold shorts, in order to attempt to protect themselves from that unlimited loss potential we discussed in the first half of this essay, employ standard delta hedging practices to reduce the risk of their written gold calls. Delta hedging is executed by using BS formulas to tell the gold shorts what amount of physical gold they should have on hand in case their options are exercised. When the gold price is rising and is approaching the strike price of the call options they have written, they buy physical gold. Delta hedging is designed so that as the gold price rises, a higher and higher percentage of the naked gold calls written are protected with actual physical gold. The naked calls become covered calls through the purchase of physical gold. This occurs on a sliding scale based on the general delta hedging probability framework discussed above.

When the options are deep out of the money, the gold short may only need enough physical gold to cover a few percent of the total option contracts written. As gold rises in price, however, the amount of physical gold needed to delta hedge increases. When the spot price reaches the strike price, per delta hedging theory the gold shorting bank should have purchased enough physical gold to cover 50% of the call options they have written. 

The theory is really elegant in concept and practice, as it is designed so ALL the naked call options will end up being covered at an average gold price equal to the original strike price of the call options written. 50% of the physical gold needed to delta hedge is purchased below the strike price, then the remaining 50% is purchased above the strike price. The net result is an average price for the physical gold purchased to delta hedge that equals the strike price of the written call option.

This can be a fuzzy concept at first, but it is really important to understand. Building on our example, let's assume our gold shorting bank wrote call options on 10,000 oz of gold at a $325 strike price. While gold trades at $275, the bank may only need 500 oz of actual physical gold on hand from a delta hedging perspective. When gold rallies and runs to $325, however, and the options contracts have not expired, delta hedging calls for 5,000 oz of gold to be on hand at the bank to meet expected orders to exercise the call options. 

A delta hedge ensures 50% of the call options written are covered by physical gold once the spot price reaches the call option's strike price. In this example, the bank has to purchase 4,500 oz of gold (5,000 oz needed minus 500 oz on hand) in the open market while gold is rallying in order to ensure the delta hedge is maintained. As gold continues to trend higher above the $325 strike price, the bank will buy more and more gold until it has the physical gold on hand to back ALL its written calls.

Theoretically, if delta hedging is properly maintained, scrupulously employed, and assumptions about the volatility of an asset are correct, delta hedging enables the call option writer to cover its written in the money calls at an average cost equal to the option strike price. If this is attained, the call writer gets to keep its profits for writing the option contract even if the price of gold rises high enough to put the call options in the money.

Delta hedging is INCREDIBLY important for someone writing naked calls, as it vastly mitigates the risk of unlimited losses in response to a rising gold price. Using delta hedging, the gold short is able to mathematically scale up its gold buying to cover its shorts before it is forced by the market to cover later at a much higher price for a catastrophic loss.

Since the Black and Scholes model is so ubiquitous and so widely revered, an option manager who has written naked calls and is NOT delta hedging is taking a monstrous risk. Not backstopping a large naked call writing campaign with delta hedging is foolhardy and potentially suicidal. It borders on criminal negligence to not have a proper delta hedge in place when large amounts of naked calls are outstanding.

As the price of gold rises, the large money center gold shorts with outstanding naked written gold calls HAVE to purchase ever increasing amounts of physical gold to maintain their delta hedges. This presents a huge problem, however.

The gold price rises as physical demand exceeds available physical supply during any given trading period. The gold shorts do NOT want gold to rise in price, as they risk seeing their sophisticated gold derivatives implode at tremendous losses in a gold rally. The price of gold, and any trading asset, is determined at the margin. If the price is rising slowly, and more physical gold buy orders hit the market, the price of gold will accelerate to the upside. Often, even a relatively small amount of additional buying or selling of gold will have a substantial impact on the spot price of gold.

The gold shorts are faced with a potentially disastrous dilemma. Prudence would dictate they must INCREASE their physical gold buying as the gold price rallies, in order to maintain a balanced delta hedge. On the other hand, if they initiate physical gold buy orders in a rising gold price environment, the gold price rate of increase will accelerate. As it accelerates, they will have to buy MORE gold to keep their delta hedges intact. Other banks will also see the price rise and they too will initiate buying to delta hedge their own naked written gold call options. The net effect will be a vicious circle, where gold short covering begets more gold short covering, and a classic short covering rally ensues as the gold price spirals higher and higher.

And this is not even considering the gargantuan increase in gold investment demand that will occur as the price begins to rise in a continually increasing trajectory to the upside!

Since the large money-center banks shorting gold are publicly held and traded, and since corporate managers have a fiduciary responsibility to their bosses the shareholders, they face a very difficult decision. The proper thing to do in a rising gold price environment is to buy physical gold in the open market to backstop the naked calls, maintaining a balanced delta hedge. If they do this, however, they risk furthering the gold rally that will decimate their other shorting activities, including gold loans they have taken from central banks. When the gold shorts borrowed gold from central banks, they sold it immediately in the open market and used the cash to finance equity investments. If their delta hedging purchases force up the gold price, they will have to buy back more expensive gold to repay their gold loans at a loss. The losses compound and compound on multiple fronts for gold shorts as the price of gold rises.

If the gold shorting banks decide NOT to maintain proper delta hedges on written gold calls in a rising gold market, and a moderate spike in the price of gold leads to the exercising of options, they face potentially enormous cash losses. They would have to buy gold in the open market with cash to sell at a much lower price to the folks who bought the call options. With the large amount of options written, this scenario would lead to either massive derivatives losses or the bankruptcy of the money-center bank.

The managers of these large, well-known, money-center banks that are shorting gold are damned if they do and damned if they don't!

We suspect they are so terrified of rising gold deep-sixing their derivatives portfolios that they are not scaling up their delta hedges as Black and Scholes dictates they should. Since the BS model is so widely accepted, this inaction in the face of a growing threat to capital has widespread implications.

The United States of America is unfortunately one of the most litigious societies on the planet. We Americans sue each other for sport over the most trivial of things. Sadly, lawsuits are now as American as rock and roll music and apple pie. When the shareholders of the gold shorting banks find out that their expected $4 per share profits turned into $10+ per share losses because corporate managers did not properly employee standard delta hedging, the proverbial excrement is going to slam into the whirling blades. Lawsuits will fly faster than snow in a North Dakota blizzard.

Even worse for the corporate derivatives managers of these banks, there is a high probability they will be held PERSONALLY criminally negligent if they have indeed made an explicit decision to not maintain their delta hedges. The managers have a fiduciary responsibility to shareholders. Not delta hedging a naked written call option position is like flying a loaded 747 without ensuring the airplane is mechanically sound. In either case, the probability of a disaster may be small, but the results of the unthinkable are always catastrophic.

In EVERY gold rally of significance in the year 2000, reliable reports from professional traders directly from the trading floors have indicated that THE very handful of large banks shorting gold have been heavy, heavy sellers of physical gold in an effort to cap each rally. The weight of evidence would suggest that these gold shorts are SO desperate to stave off any meaningful rally in gold that they are putting their shareholders' money at unbelievable levels of risk by not maintaining delta neutrality in their written call option portfolios.

We honestly do not know how the managers actively and complicity involved in the gold shorting scheme can sleep at night. In addition to risking all the capital their companies have ever earned on the faulty premise that gold is dead, they are risking being found personally liable for gross criminal negligence in neglecting an essential and common safeguard of the derivative world. We suspect that these managers will be turned into the scapegoats when gold rallies and the gold shorting banks face the consequences of their brazen bets. They will be tarred and feathered, the courts will strip all wealth from them and their families, and they may end up in prison for white-collar crimes. It will not be pretty.

The gold delta hedge trap has been set, and the folks in charge of gold operations at the money center banks will be shredded when the trap is sprung. If they have not been diligently delta hedging their written gold calls, they have already written their own professional obituaries.

Provocatively, even if the gold-shorts WERE delta hedging, they still face leviathan risks on the short side of the gold market.

Although an excellent theory, the BS model does have significant limitations.

For instance, in order to obtain the delta variable, estimates of the probability of option exercise must be made. These estimates are based on historical volatility and price trends. In effect, because gold has not been very volatile in recent years, the assumption is made that future volatility of gold will also be very sedate. This is a potentially lethal hole in delta hedging logic. Making linear assumptions in a non-linear world is very foolish in the chaotic age in which we live. A couple examples illustrate this point:

In August 1999, European central banks gathered in secret (ie the anti-gold US and British governments were not invited) to make a deal to limit the leasing and sale of central bank gold into the open market. When the news of the meeting went public, the price of gold unexpectedly roared up $45 in a few days, from $255 to $300+. This was a non-linear market event that was completely unpredictable using estimates based on historical volatility data.

Gold shorts with naked written call options outstanding had no opportunity to delta hedge in this swift and unexpected gold rally. Many had very large paper losses and they were rescued by a desperate official sector effort to hammer the price of gold back down to lower levels. Since the BS delta hedging model is based on the theory that volatility is generally predictable, even a good faith delta hedging effort would have failed in this case.

A massive spike up in the spot price of an asset underlying an option is known as a Gamma Spike. Gamma spikes are rare, but they are very possible in the gold market. Since gold is the ultimate real form of wealth and the flight capital safe harbor of choice, unpredictable geopolitical events around the world have the potential of creating a massive increase in gold investment demand resulting in a gamma spike virtually all the time. Everything from wars, to stock market difficulties, to oil disruptions carry the potential of igniting a highly dangerous gamma spike in gold. Linear assumptions that assume future volatility will reflect near past volatility are highly treacherous.

A second example of the danger of making linear assumptions in a non-linear world revolves around the brilliant men who created the Black and Scholes Option Pricing Model themselves, Myron Scholes and Robert Merton.

In 1994, legendary Salomon Brothers bond trader John Meriwether assembled a financial dream team that would ultimately live forever in infamy. He recruited 15 partners to found a new hedge fund, and Scholes and Merton were among them. The hedge fund was the ill-fated Long Term Capital Management.

LTCM was based on the sound theory that assets all over the world are usually under or overvalued, but they always ultimately seek their true values. The basic idea is valid, but LTCM implemented it with such extreme leverage that even small unpredictable discontinuities had the potential to greatly affect the capital base of the hedge fund. 

LTCM employed Scholes' and Merton's work to hedge and protect its bets. Through BS based hedging strategies, LTCM became one of the most highly leveraged hedge funds in history. It had a capital base of $3b, yet it controlled over $100b in assets worldwide, and some reports claim the total notional value of its derivatives exceeded an incredible $1.25 TRILLION. LTCM used extraordinarily sophisticated mathematical computer models to predict and mitigate its risks.

In August 1998, an unexpected non-linearity occurred that made a mockery of the models. Russia defaulted on its sovereign debt, and liquidity around the globe began to rapidly dry up as derivative positions were hastily unwound. The LTCM financial models told the principals they should not expect to lose more than $50m of capital in a given day, but they were soon losing $100m every day. Four days after the Russian default, their initial $3b capital base lost another $500m in a single trading day alone!

As LTCM geared up to declare bankruptcy, the US Federal Reserve believed LTCM's highly leveraged derivatives positions were so enormous that their default could wreak havoc throughout the entire global financial system. The US Fed engineered a $3.6b bailout of the fund, creating a major moral hazard for other high-flying hedge funds. (Expecting the government or counterparties will bail them out of bad bets once they get too large, why not push the limits of safety and prudence as a hedge fund manager?)

Persistent rumors exist that LTCM was short 400 tonnes of gold when it went belly up. The US government arranged for someone to supply this gold owed to counterparties very quietly, and forbade any LTCM principals to ever discuss the gold position and disposition in the future. Although the whole LTCM and gold scenario is incredibly intriguing, it is topic for a future essay.

In conclusion, even prudent delta hedging is risky because it makes the assumption that past volatility and option exercise rates will reliably predict future gold market activity. Markets never seem to operate as smoothly as expected, and vast quantities of capital has vaporized over the centuries due to the foolish assumption that the short-term status quo will continue indefinitely.

If the large money-center gold shorts DO delta hedge, they will change from net sellers of physical gold to net buyers in gold rallies. Since the spot price of gold is determined by buying and selling on the margin, even a small change in aggregate physical demand could ignite a gamma spike in gold, causing the price to go orbital and disembowel the gold shorts.

If the large money-center gold shorts DO NOT delta hedge, they risk bankruptcy in the next major gold rally, which is rapidly approaching. Gold is cyclical, and it has trended down for 20 years. It will not trend down forever, as physical gold demand greatly exceeds the fresh physical gold mined each year. In addition, corporate derivatives managers and high-ranking corporate officers probably face unlimited personal liability for criminal negligence if they neglect their fiduciary duty to protect shareholders' capital by properly delta hedging their naked written call options. Even more ominous, a gamma spike in gold will have the side effect of generating massive ripples that will affect US bonds, currencies, equities, and other derivatives markets. Are all those non-gold derivatives portfolios held by these banks properly delta hedged?

A gold delta hedge trap has been set. The gold shorts are smack in the middle of its massive steel jaws. If they do delta hedge their gold derivates as all prudent money managers should, they will have to become net buyers of physical gold and that would initiate a gold rally that will sign their own death warrants. If they do not delta hedge, they risk bankruptcy and corporate and personal lawsuits as the inevitable gold rally spawns unsustainable losses in their gold short positions.

There is no easy way out.

December 15, 2000

by Adam Hamilton, CPA, MCSE
December 8 - 15, 2000

Mr. Hamilton, a private investor and contrarian analyst, publishes Zeal Intelligence, an in-depth monthly strategic and tactical analysis of markets, geopolitics, economics, finance, and investing delivered from an explicitly pro-free market and laissez faire perspective. Please visit www.ZealLLC.com for more information.

Copyright 2000 Zeal Research. All Rights Reserved.

Reprinted by USAGOLD with permission of Adam Hamilton. No further reproduction without permission.

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