Gold Delta Hedge Trap (Part 2)
Adam Hamilton December 15, 2000 3616 Words
As this essay has exploded outward with all the force of NASDAQ slamming into the unyielding concrete wall of cold fundamental cashflow reality, it has been necessary to split it up for your own safety. Part 1 discussed the origins of the infamous Black and Scholes Option Pricing Model and outlined the tremendous risks of writing naked gold calls. Part 2 discusses Delta Hedging, how it should be used to mitigate call writing risk, and discusses the growing peril of the delta hedge trap in which the gold shorts find themselves.
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
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.
Adam Hamilton, CPA December 15, 2000