Gold Delta Hedge Trap (Part 1)
Adam Hamilton December 8, 2000 2702 Words
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 will discuss Delta Hedging, how it should be used to mitigate naked call writing risk, and describes the dangerous Gold Delta Hedge Trap into which the gold shorts may be wandering.
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 large naked written 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 banks’ short gold derivative positions could be extraordinary.
With this critical background, we are ready to wade fearlessly into the second half of this essay. Part 2 will discuss Delta Hedging, how it should be used to mitigate gold call writing risk, and how neglecting it is increasing the growing peril in which the gold shorts find themselves these days. The thrilling finale will be published next week. We hope you can stand the breathtaking, cliffhanging suspense!
Adam Hamilton, CPA December 8, 2000