The Challenges of Regulation of Derivatives

Abstract

Derivatives are the functional form that speculative capital assumes in markets. The notional amount of derivatives in 2015, as reported by the Bank for International Settlement, was $550 trillion. That number does not include the synthetic derivatives, so it grossly – by a factor of many multiples – underestimates the size of capital earmarked for derivatives-type trading. Speculative capital operating as derivatives is the glue that holds the financial markets together. This chapter explains the nature of that mechanism. We offer no policy recommendations, only a description of the conditions that prevail in the markets and the potential effects of disturbing them through regulation.

Nasser Saber is the author of Interest Rate Swaps (Business One Irwin, 1993) and the three volumes of Speculative Capital (Financial Times). The fourth and final volume is due to be released in 2017. He holds a master’s degree in engineering from Case Western Reserve University and an MBA in quantitative analysis and finance from NYU.

1 Introduction

It is commonplace that to act is to act in the confines of the given conditions. That is another way of saying that to act one must know the conditions, or “what the shot is.” The American colloquial expression captures the implied exigency and hints at the dangers of failing to do so.

The “shot” for the markets regulator is the role of derivatives in global financial markets. According to the Bank for International Settlements, the outstanding notional amount of derivatives in 2015 was $550 trillion.¹ That sum does not include synthetic derivatives, so it grossly—by a factor of many multiples—undercounts the size of capital earmarked for derivatives-type trading.² I have shown elsewhere that such capital is the anima mundi of financial markets. What that means is the subject of the current chapter. We prescribe no policy here, only an adequate description of the conditions that exist in the markets with a focus on derivatives. Knowing those conditions is the prerequisite for regulation. An adequate explanation is an explanation in full. It accounts for the market dynamics in a precise manner, permits of no inconsistencies, and no future development will contradict it.

2 Structure of Derivatives

A derivative is a bet. That this bet is used in finance or that its outcome is determined with reference to the price of some security does not change the matter in the least.

A bet involves the realization of an event in the future. This definition applies to traditional commerce as well.³ The maritime trade that gave rise to capitalism is entirely based on the forward delivery of goods, due when (and if) the ship arrived. The owners of the goods who needed money sold the bill of goods of as-yet-to-arrive merchandise in financial centres. Since there was always a risk of loss until the ship actually arrived, the buyers of the bills bought for less than full face value. Hence discount bills were born, one of the early securities.

A discount bill is a security because it represents a claim on existing merchandise. In agriculture, by contrast, a forward contract to deliver, say, wheat pertains to wheat that does not yet exist. That is why the contract to deliver it—unlike the existing goods travelling on a ship—is not a security but a derivative.

Independent farmers used derivatives to hedge their harvest.⁴ A wheat farmer, for example, could enter into a forward contract to deliver wheat at, say, $1 a bushel. If by the time of harvest the price fell, he was guaranteed the $1 contract price.⁵ On the other hand, by locking the price he would have to forego the benefit of any price appreciation above $1.20. That is how hedging works: it stabilizes the price in either direction.

But if there was no commodity to deliver, that is, nothing to be owned yet, speculators could also pretend to be farmers, i.e., mimic farmers’ actions. They, too, could sell the commodities forward, hoping that by delivery time the prices would increase. Farmers had mixed feelings about the intrusion of speculators in “their” market. On one hand, speculators provided additional buying and selling opportunities which meant more liquidity. But precisely for that reason, they could also create price volatility that damaged the farmers. We see this tension between the producers and speculators as early as the early twentieth-century USA in the rise of bucket shops and attempts to regulate them.

Bucket shops were the nascent form of present day exchanges and clearing houses. They connected buyers and sellers of forwards and earned a profit from the spreads.

The early capitalists who started the bucket shops did not grasp the importance of capital—and if they did, they had no means to account for it.⁶ Taking their chances, they lost not infrequently; if the market volatility was low so was the capital base of the bucket shops, so even small price changes led to their ruin. In the free-wheeling nineteenth-century USA such ruins in speculative markets carried little reputational risk.⁷ When a bucket shop failed, its owner started a new one across the town. But farmers lost money. That is how “bucket shops” acquired their name and a pejorative connotation.⁸ Bucket shops “bucketed”, that is, discarded, the trade tickets because they had no intention of delivering the underlying commodity. But that was true of all exchanges and clearing houses, including the Chicago Board of Trade (CBT) and the Chicago Mercantile Exchange (CME), the two largest bucket shops, which thrived because they were well capitalized.

Under the pressure of farmers and populist politicians, the states passed bucket shop laws that forbade offering forward contracts without the ability and intent to deliver. But the practical difficulties of the law—making a distinction between who had the intent to deliver and who did not—proved insurmountable. The two exchanges claimed that their trading reduced the price risk of commodities by offering hedging facilities to farmers. The bucket shops, by contrast, were interested in the price changes and speculation. Bucket shops disagreed. In 1912, the dispute reached the Supreme Court via Board of Trade v. Christie. ⁹

The BOT sued Christie, a bucket shop, to prevent it from using the Board’s price quotes. Christie claimed that the BOT was itself a bucket shop. The Court disagreed. Writing for the Court, Chief Justice Holmes said:

Purchase made with the understanding that the contract will be settled by paying the difference between the contract and the market price … stands on a different ground from purchases made merely with the expectation that they will be satisfied with the offset.¹⁰

Note the Justices’ struggle to distinguish between trading and speculation by talking of “different ground.” The implication was that there was an opposition between “good and beneficial” trading and “bad” speculation. But such moralizations could not resolve the issue and the question of trade versus speculation, why one deserved support and the other censure, remained. As the uncertainty posed legal risk to the exchanges, they lobbied Congress, which passed the Futures Trading Act (FTA) in 1921. The Act mandated that all “contracts for future delivery” be traded in official, licensed exchanges. Over-the-counter forwards were banned.¹¹

That is where things remained for half a century.

3 Collapse of Bretton Woods and the Rise of Hedging

The collapse of the Bretton Woods system of fixed exchange rates in 1971 threw currency relations into chaos and exposed multinational companies to new risks.

Take a corporation like IBM and assume it had a contract with a Japanese customer to deliver computers for ¥3 billion in three months. At the current exchange rate of $1 = ¥300, that translated to $10 million which included a $1 million built-in profit. If in the interim the yen weakened to $1 = ¥330, the contract price of ¥3 billion would be worth $9 million, wiping out the profit.¹² This was intolerable. The multinationals pressed their banks for a solution. The banks, taking a page from the old playbook of farmers, came up with hedging.

Take an international bank such as J.P. Morgan with long standing relations with leading industrial companies such as IBM and General Motors. Let us assume that GM, too, had negotiated to purchase land in Japan for a car assembly plant. The contract was expected to be signed in a few months for the agreed upon price of ¥3 billion. With the prevailing exchange rate that translated to $10 million. If in the interim the yen were to strengthen to say, $1 = ¥270, the land price would rise to $11 million. GM, too, wanted to protect itself against this eventuality. So it, too, went to J.P. Morgan for advice.

By placing itself in the middle, the bank could help both clients. From the diagram of the funds flow below, the solution is self-suggesting.

The bank entered into a contract to buy ¥3 billion from IBM for $10 million in three months. It also entered into a contract to sell ¥3 billion to GM for $10 million in three months. On the delivery date, IBM received ¥3 billion from its customer, which it paid to J.P. Morgan, which then passed it to GM. In return, the bank received $10 million from GM, which it paid IBM in exchange for the ¥3 billion it had received.

Superficially, that is, out of context, the arrangement resembles a bucket shop transaction: the Japanese yen is wheat, IBM is the farmer, GM the industrial food processor and the bank the bucket shop operator. But the same arrangement—a series of interlinked transactions—when adopted by speculative capital that was rising from the ashes of the Bretton Woods system, became the blueprint of the modern world, the key to its understanding.

4 Transformation of Hedging into Arbitrage

Speculative capital is capital engaged in arbitrage. It is the latest form in the evolution of capital that has come to dominate the financial markets in the twenty-first century.¹³

The genesis of speculative capital, like any other form of capital, is buying low and selling high; no one has yet invented another way of making money. Historically, the difference between the purchase and sales price was a function of space and/or time: to realize profit, commodities had to be either transported from one location to another or hoarded from one time to the next.¹⁴

But making a profit was never certain. Commodities could perish while being transported—or be stolen or confiscated. The borrowers could die, go broke or flee. And there was the ever-present risk that the price could drop for economic, natural or social reasons. As all these events took place in time, the early capitalists—they were merchants, traders and usurers before the rise of industrial capital—came to see time as the source of risk. The longer the time between the purchase and sale, the greater the risk. Conversely, if by some magic one could buy a commodity and simultaneously sell it for a profit one could realize riskless profit. That was the Holy Grail of finance that had to remain in the realm of dreams until the collapse of the Bretton Woods system produced the conditions for its realization.

The Bretton Woods system was a regime of fixed exchange rates created by the governments; the exchange rate of $1 = ¥360 that held immediately in the post-war years between the US dollar and Japanese yen was a matter of agreement between the governments of the USA and Japan. Governments stabilize rates through decree.

The collapse of the system meant that governments washed their hands of exchange rates. Into the vacuum stepped private finance. Private finance stabilizes rates through arbitrage. Let us return to Fig. 7.1 and elaborate this point.

Fig. 7.1

Back-to-back transactions creating a currency hedge

First, notice that what we have are private parties signed into private contracts. Yet the overall effect of the agreements is to isolate them from their economic “eco system.” No matter how volatile the USD–JPY exchange rate, that is, no matter what happens in the “world,” IBM and GM will exchange USD and JPY at the rate of $1 = 300¥. That is hedging, which insulates the companies’ assets against market fluctuations. Setting aside counterparty default risk for now, IBM and GM have eliminated exchange rate risk.

As the middle man, J.P. Morgan faces no risk either, as it merely collects and forwards the payments to the main parties. In fact, strictly speaking, IBM and GM do not need the bank; they could have dealt with one another directly, if they knew of one another’s need. That is exactly what “FinTech,” the technology driven financial app industry backed by venture capital, is aiming at: it wants to “disrupt” the business model of the bank intermediaries.¹⁵

But in the 1970s only the international banks with corporate contacts could arrange such multiparty deals. Naturally, they charged for their service either directly or, more commonly, by taking a “cut” from the deal by buying yens slightly cheaper from IBM and selling them slightly more expensively to GM.

The difference in buy–sell prices established the bid-offered “spreads.” But recall that these were private deals. J.P. Morgan’s USD–JPY spreads were different from those of Citibank or Credit Lyonnais. As these prices were posted in the shared interbank networks, traders took notice of arbitrage opportunities.

Now suppose a trader saw the following prices between the USD, JPY and Deutschmark (DEM)

$$ 1\kern0.2em USD=2.25\kern0.2em DEM $$

$$ 1\kern0.2em DEM=150\kern0.2em JPY $$

$$ 1\kern0.2em USD=330\kern0.2em JPY $$

The trader could buy 2.25 MM DEM for $1MM USD and sell marks for 337.5MM JPY and pay that to buy $1,022,700 for a profit of about $22,700. The buying and selling was done through the phone so orders rapidly followed one another. This near simultaneous profitable buying and selling is arbitrage. Arbitrage means simultaneously buying low and selling high for a riskless profit. Capital earmarked for arbitrage is speculative capital.

Figure 7.2 shows the flows of funds in our example. Note the critical changes that have taken place compared to Fig. 7.1. The industrial corporations are gone. What began as a service to bank clients is now currency transactions between generic buyers and sellers. Absent corporations, there can be no talk of their hedging needs. Indeed, there is nothing to hedge. Hedging is transformed into arbitrage.

Fig. 7.2

USD–JPY arbitrage flow

The importance of this point is easy to miss, so let us develop it more methodically. The accounting equation is the place to start:

$$ \mathrm{A}=\mathrm{L}+ OE $$

(7.1)

In Eq. 7.1 A is assets, L is liabilities and OE is owners’ equity. If an entity has $100 (A), either all of it is borrowed (L), or all of it belongs to the owner (OE), or, as is always the case for a corporation, a mix of the two, say L = $90 and OE = $10.

The objective of hedging is to insulate the capital against market fluctuations. That would be the owners’ capital, OE. Rewriting Eq. 7.1 with respect to it, we get:

$$ OE=\mathrm{A}\hbox{--} \mathrm{L} $$

(7.2)

In hedging, OE must remain constant “no matter what happens in the world.” That is another way of saying that its value must not change. Denoting the change by Δ, we can express this condition mathematically as follows:

$$ \varDelta OE=0 $$

(7.3)

If the left-hand side of Eq. 7.2 is to remain unchanged, its right-hand side must remain unchanged:

$$ \varDelta A\hbox{--} \varDelta L=0 $$

Or:

$$ \varDelta A=\varDelta L $$

(7.4)

Equation 7.4 is the condition of hedge. It states that for the equity of the entrepreneur to be preserved, the change in assets must equal the change in liabilities—or assets and liabilities must match.

That is also the condition of arbitrage. In the example above, J.P. Morgan successively converted

• 1) $1MM USD to 2.25MM DEM

• 2) 2.25MM DEM to 337.5MM JPY

• 3) 337.5 JPY to 1.022MM USD

In each stage, equivalents were exchanged so the bank had no risk. Yet, at the end, it earned a profit of $22,700. That is profit without exposure, or riskless profit, which is the driver as well as the condition of arbitrage.

To summarize, comparing hedging and arbitrage, hedging is matching assets and liabilities to insulate the existing capital. It is a defensive and conservative strategy.

Arbitrage is matching assets and liabilities to wangle a profit from “inefficiencies.” An arbitrageur has neither an asset nor a liability. He looks for any two positions whose purchase and sale would create a profit for him. Arbitrage is an aggressive and predatory strategy.

After the fact, it is impossible to tell hedging from arbitrage; one only sees an asset matched by a liability, a long position matched by a short position. What conceptually separates the two is the raison d’être of the trades reflected in their order of execution. If the trades are sequential—an existing position is followed by another—the operation is hedging. If the trades are simultaneous, it is arbitrage.

In practice, the line between the two is easily crossed, hence the endless confusion about the “propriety” of the transactions after losses and wondering what went wrong in a conservative strategy.¹⁶

Since the difference between hedging and arbitrage is closely linked to their purpose and, from there, to the user, it would seem that one could draw a distinction between them by focusing on users. That is what the Christie Court tried to do but failed. The US Congress, as we saw, gave up trying and forbade non-regulated derivatives trading altogether.

More than a century later, the European Commission took the same track. Since there could be no talk of forbidding derivatives in the twenty-first century, the Commission went in a roundabout way, by increasing capital requirements for the use of derivatives. But unlike the US Congress which had earlier accommodated the farmers it made no exemption for the modern-day hedgers, the industrial user of derivatives. The result was an outcry from them:

Ford, IBM, Airbus, BP and General Electric are among dozens of global businesses that have sharply criticised Europe’s rules for the use of derivatives, claiming they unfairly push up costs for companies “that did not cause the financial crisis” … More than 40 institutions have written to policymakers at the European Commission urging them to rewrite the rules to be more like those in the US, which exempt non-financial corporations from some of the more onerous requirements.¹⁷

“Non-financial corporations” above is a byword for corporations that use derivatives for hedging. In light of their influence in Western capitals there is little doubt that the Commission will relax its rules. So it would seem that the regulation of derivatives could be bifurcated along the hedging-speculation divides. But the modern-day regulator of derivatives faces a far more complex challenge because the shell of derivatives is now claimed by the most potent force in the markets: speculative capital.

5 Speculative Capital

The subject of finance is not people. It is capital in circulation. The mind arrives at that conclusion through the compulsion of its reasoning as it moves from arbitrageur as a person to capital as a thing.

An arbitrageur’s motive for trading is riskless profit. It goes without saying that to place the trade or write the algorithms, the arbitrageur acts as a person. But he cannot employ his capital in a development project in an emerging market or some long-term infrastructure project. If he does, he ceases to be an arbitrageur. An arbitrageur must employ capital in arbitrage trades. In consequence, he becomes an “agent” of capital, someone who must conform to capital’s modus operandi. Capital then becomes the grammatical subject of the sentence as if it were alive: capital seeks arbitrage opportunities. Such capital is speculative capital. It is impossible to understand either the real life or theoretical developments in finance in the past 40 years without knowing speculative capital, its properties and the effects of its operations on markets. I have examined them in detail elsewhere. We briefly review them here as the prelude to the regulation of derivatives.

6 Characteristics of Speculative Capital

Arbitrage opportunities cannot exist in the open. Such situations would imply an infinite supply of fools on the receiving end of arbitrage who buy high and sell low. Arbitrage opportunities, rather, must be discovered. In Fig. 7.2, in addition to access to information, the bank trader must have some basic mathematical skills to unearth the hidden USD–JPY profit opportunity that passes through the USD–DEM intermediation. From there arises the need for mathematicians—later the “quants” and “rocket scientists”—who were recruited into finance in the rising era of speculative capital in the 1980s.

Precisely because arbitrage opportunities could appear at any time and anywhere, the manager of speculative capital must have the freedom to act quickly. He cannot operate with the traditional mutual funds bylaws which tie him to a particular strategy—say, value investing or growth. Hence the need for a legal structure that would give the investment officer carte blanche to invest in any form and fashion as he sees fit. These are hedge funds. They are the legal/organizational form that speculative capital assumes in the market.¹⁸

In terms of its main characteristics, speculative capital is, first and foremost, self-destructive: it eliminates the arbitrage opportunities that give rise to it. Buying low and selling high increases the price of what was low and decreases the price of what was high, creating a condition of “equilibrium” between the two.¹⁹

A system in equilibrium is a dead system.²⁰ Meanwhile, speculative capital is self-destructive by virtue of its modus operandi but it is not suicidal. Quite the contrary. It turns markets, societies and laws upside down to survive. So, after an arbitrage opportunity is grazed, it moves to the next.

Arbitrage pricing is relative-value pricing par excellence. It prices A by comparing it against the price of B and in doing so, “links” A and B and synchronizes their price movement. That destroys portfolio diversification, which assumes that asset prices move asynchronously.

What is more, speculative capital does not have a command and control centre. It is dispersed amongst all the hedge funds and high-frequency trading desks and all arbitrage-seeking strategies in the world. The managers of these capitals use the same pricing sources and employ similar mathematical and algorithmic skills. So, when an arbitrage opportunity opens up, they all rush in. “Rushing in” is necessary because opportunities are short lived and the fastest arbitrageur will get the lion’s share of profits.

Rushing in results in overshooting the target; what was overpriced becomes underpriced, and vice versa. The result is an increase in volatility that is transferred from one market to another. Market volatility, ironically, is the side effect of the attempts of speculative capital to restore equilibrium to the markets.

In search of virgin opportunities, speculative capital pushes for laws that facilitate globalization and transparency. Globalization expands the universe of arbitrage opportunities. Transparency enables it to uncover those opportunities.

Speculative capital, however, is not invincible. Temporarily setting its self-destructive nature aside, two potential threats to it always loom on the horizon. One is internal and hits the profit directly. The other is external and works in a roundabout way, but its impact is no less real or pernicious.

The internal threat is the counterparty default risk. It exists by virtue of the nature of private transactions from which speculative capital is born. If the party to the arbitrage defaults, the arbitrage fails and speculative capital incurs loss. The riskless profit which defined arbitrage is not truly riskless unless counterparty default risk is resolved.

Then there is the external threat that is regulation. Unlike the law which is enacted by the legislature, regulation is issued by regulatory agencies. Compared to the law, regulation is more focused and directly hits the areas it targets. The result is that the wiggle room is reduced, which is why regulation is the bane of speculative capital. It interferes with speculative capital’s free movement and, by doing so, impairs and disrupts it.

Speculative resolves both problems through derivatives.

7 Forwards and Forward-like Derivatives

Derivatives are the functional form that speculative capital assumes in the market; one who speaks of derivatives speaks of speculative capital. To explain, let us examine the form. All derivatives are either forward-like or option-like.²¹ We begin with the simple forward.

Forward contracts, as we saw, appeared in relation with agriculture. Let us take a commodity such as wheat and assume it is selling at $1 per bushel. If we have a contract to deliver a bushel of wheat in three months at the price of $1.15, we have a forward contract, as shown in Fig. 7.3.

Fig. 7.3

A forward time line

S is spot price and F is the forward price.

How is F determined?

In the early twentieth-century USA, the forward price was “discovered” in the negotiation between farmers, silo owners, food companies and speculators.²² Each day these actors came into a consensus after considering everything from national politics to foreign wars and, of course, the weather,²³ as to what price the various commodities should be in three, four, five months. Each price was an estimate and could change during the day in response to new information. But it was an estimate nonetheless, more art than science.

In “modern finance,” the forward price F, of any asset whose spot price is S, is determined by the following equation:

$$ \mathrm{F}=\mathrm{S}+ CC $$

CC is the cost of carry. It includes all costs—actual as well as opportunity loss—associated with carrying the asset into the delivery. If the spot price of an asset is $100 and one-year interest .5%, the one-year forward price would be $100.5:

$$ \mathrm{F}=100+100\mathrm{x}.005=100.5 $$

The $.5 “cost of carry” in the above calculation arises from the opportunity cost of carrying the asset: if we had not purchased the asset we could have earned $.5 on our $100 with the prevailing rate. To make an investor “indifferent” between lending and purchasing the assets, the forward price of the asset must include that cost.

What happens if the forward price is not $100.5? In that case an arbitrageur could make a riskless profit.

• If the forward price is less, say $100, the arbitrageur could:

  • (1) Buy forward at $100

  • (2) Sell the asset short and place $100 at .5% with one year

  • (3) At the end of the year, take the delivery of the asset (from 1) at $100, deliver it to satisfy the short position at (2) and keep the $.5 profit.

Buying forward and selling spot would increase the price of the forward and decrease the price of the spot, bringing them into the equilibrium, non-arbitrageable relation.

If the forward is more than $100.5, say, if it is $101, the arbitrageur could

• (1) Sell forward at $101

• (2) Borrow $100 and buy spot

• (3) At delivery date, deliver the asset to satisfy forward, receive $101 (from 1), pay $100.5 towards the loan and its interest for a net profit of $.5

Selling forward and buying spot would restore the equilibrium.

The above reasoning, which is the basis of pricing of all derivatives, presupposes speculative capital: capital engaged in arbitrage.²⁴ Speculative capital is the mechanism that restores equilibrium to the markets.

A forward-like structure is too simple to be of practical use. Any discrepancy between the forward and spot prices would be detected and eliminated at once. That is why they are used almost exclusively for hedging. Vigilance of arbitrageurs ensures liquidity and tight bid/asked spreads.

Profitable arbitrage opportunities must be discovered as they lie hidden beneath the avalanche of data that is continually produced in financial markets. Speculative capital discovers them through option-like derivatives.

8 Options and Option-like Derivatives

All students of finance know of the Black–Scholes option valuation model. The problem of logically valuing options remained unsolved until in 1973 Robert Merton and, independently from him, Fischer Black and Myron Scholes produced a solution. In 1997 Merton and Scholes received the Nobel Memorial Prize in Economics for their discovery.²⁵

The Black–Scholes formula has an imposing form. But that is because of the equation of stock price dynamics.²⁶ Otherwise the concept and the reasoning behind the valuation are simple. That a simple concept took more than a quarter of a century of work to be grasped—and was finally grasped in a misunderstood way, the way speculative capital operates—confirms what we stated earlier about the link between speculative capital and derivatives. Prior to the breakdown of the Bretton Woods system, speculative capital had not impressed itself sufficiently on the minds of traders and scholars for an option valuation formula to be possible.

We explain.

The Black–Scholes model begins with hedging, by creating a riskless portfolio of “Δ share of stock and one short call.”

Assume the stock is trading at S = $100. We would like to price a one-year call option on this stock with the strike price of K = $100. At expiration, the asset price could be $105 or $95.²⁷

A call option is a “right but not the obligation” to purchase the stock at the strike price. If the asset goes up to $105, the holder of the call who has the right to buy it at the strike price ($100) will make $5 profit. If the stock drops to $95, the holder would have no reason to pay $100 for an asset that is trading at $95. The option will expire worthless. Our problem is finding the value of this option.

• (1) We create a riskless portfolio with Δ shares of stock and 1 short call, C.²⁸ The value of this portfolio would be 100Δ – C. C is what we want to value.

• (2) In 1 year, the stock price F, would be either $105 or $95.

  • (i) F = $105: The call option we have sold will be presented to us as demand for payment. The strike price of the call was $100. With the stock price at $105, the owner of the call will have the right to buy it for $100, that is, $5 cheaper than the market. Since we sold the call, we must bear the cost. The value of the portfolio would be 105Δ – 5.

  • (ii) F = $95: The call would expire worthless; the purchaser of the call option will not demand to buy the asset for $100 if the asset is $95. The value of the portfolio would be 95Δ.

  These scenarios are shown in Fig. 7.4

  Fig. 7.4

  

  Stock option pay-off

• (3) If the portfolio is riskless, its value must remain the same whether under condition (i) or (ii).²⁹ That is:

  $$ 105\varDelta \hbox{--} 5=95\varDelta \Rightarrow \varDelta =.5 $$

• (4) Substituting for Δ, the value of the original riskless portfolio would be 100 × .5 – C

• (5) This value must remain unchanged at expiration:

$$ 100\times .5\kern0.2em \hbox{--} \kern0.2em \mathrm{C}=95\times .5=105\times .5\kern0.2em \hbox{--} \kern0.2em 5\Rightarrow \mathrm{C}=\$2.5 $$

Like the forward price we calculated, this call price is “rational” in the sense that it permits of no arbitrage. If the price is not $2.5 but, say, $3, an arbitrageur could sell the call at $3, and borrow $50 to buy .5 share of stock. The value of his portfolio is thus 100 × .5 + 3 = $53. At expiration

• (1) If F = $105

  He would deliver half a share of stock equal to $52.5 to the call and keep $.5 profit.

• (2) If F = $95

  The call expires worthless. He sells half a share of the stock at 95 × .5 = $47.5 and together with $3 from the sale of the call he returns the borrowed $50 for a profit of $.5

The driver of this way of option valuation is the equivalent position. The original portfolio of Δ shares of stock and one short call, 100Δ – C, is riskless because its value remains constant. That, recall from the condition of hedge in Eq. 7.4, can only happen if the change in the value of Δ share of stock and the change in the value of the call is the same. The call is valued from that equivalence.

An appropriately levered position in stock will replicate the future returns of a call. This is, if we buy shares and borrow against them in the right proportion, we can, in effect, duplicate a pure position in calls.³⁰

In our example, .5 share of stock will earn $2.5 if the stock rises to $105; it will lose $2.5 if the stock falls to $95. That is exactly the call option’s payoff. It will make $5 if the stock rises to $105, from which must be subtracted the call price of $2.5 for a total profit of $2.5. Otherwise, the option expires worthless and the initial $2.5 is lost.

That is how speculative capital operates, a process which the authors of Black–Scholes followed and uncomprehendingly copied.³¹

But beneath this procedural movement of speculative capital something deeper is going on. The clue to this is in the critical leveraged position. Why must the option valuation begin with a leveraged position? Why can we not assume that the owner of the stock—someone who has already fully paid for it—is valuing the option?

Let us return to our forward contract and assume a mispricing that an arbitrageur wants to exploit. Recall that he has no position or equity. To buy the asset, he needs to borrow $100. So he goes to a lender. The following is an imaginary conversation between the arbitrageur (A) and the lender (L):

A::

I would like to borrow $100 to buy a stock currently at $100. I will pledge the asset as the collateral for the loan.

L::

Do you think that the stock will go up?

A::

Yes. It will go up to $105.

L::

Does the stock only go up? Can it drop to say, $95?

A::

Yes, it can. But you and I would not care because I have shorted a forward on the stock with the strike price of $100. So no matter how low the asset drops, my counterparty has to buy it from me for $100.

L::

Your forward counterpart is a bucket shop. Why would he buy the asset from you for $105 if the price has fallen to $95? And if you tell me the bucket shops no longer exist allow me to remind you of the carnage in the US housing market when the prices dropped below the outstanding mortgage: the borrowers just walked away.

At that point the conversation comes to a halt, the counterparty default risk being the central point of contention. That is what the US legislature in the early twentieth century tried to address by banning bucket shops and limiting derivatives to well-capitalized exchanges. And that is exactly what the European Union (EU) Commission attempted to do with its capital ruling on the use of derivatives.

After the crisis of 2008, the US legislators tightened the reins still further through the Volker Rule, which banned most propriety trading by banks, “proprietary trading” being a byword for (speculative capital driven) arbitrage trading. The reasoning was that banks should not expose “other people’s money” to risky ventures.

Such banning is foreign to private finance. It is a diktat that is imposed from without, and like any “foreign” element it has the potential to disturb the environment to which it is introduced. Speculative capital solves the problem that arises out of finance using the tools of finance. Let us return to the conversation between the arbitrageur and the lender:

A::

I have a way to address your concern. I will buy only half a share of the stock.

L::

Some solution! In that case if the price goes down to $95 and your counterparty defaults, I will lose $2.5 instead of the previous $5. Your new solution reduces my loss but the fundamental problem of exposure remains, unless you have $2.5 to pay me in advance.

A::

I do not. But I know how to get it. I will sell a call option for $2.5 to a gambler.

A::

What is a call option and why would a gambler give you $2.5 for it?

A::

Come and see.

Together they go to Gambler. Arbitrageur addresses him:

A::

There is this stock trading at $100. I think it will go up in price. Would you like to share in its appreciation?

G::

I would like to. But I don’t have $100. And what happens if its price drops?

A::

You don’t need $100. All you need is $2.5. That sum will also take care of your concern re price drop. Here is how it works. The diagram below would help (Fig. 7.5):

Fig. 7.5

Option outcome scenarios

Arbitrageur continues:

A::

You bet on the price increase of the stock. It goes to $105, you make $5. Or more. The sky is the limit, really! Now you are concerned that the stock might drop to $95 in which case you would lose $5. But I will enter into a contract with you that if the stock drops, you could walk away without any obligation—no matter how far it drops, even to zero! All you need to pay for this all upside, no downside deal is $2.5.

G::

How do I know that you could deliver on the “up” movement of the stock?

A::

Because I will have the stock. I am going to buy half a share of the stock. When the price increases from $100 to $105 it would result in a $2.5 gain.

G::

Where do you get the other $2.5 to pay me $5?

A::

Why, that would be the $2.5 that you are going to pay me in return for entering into this contract!

G::

Does this contract have a name?

A::

Yes. It is a call option.

The arbitrageur receives $2.5 from the gambler for the call. He pledges it to the lender and receives $50 from him with which he buys half a share of stock.

Note the position of the parties. The arbitrageur and lender are fully hedged. They have also eliminated the default risk, an ever-present risk in private contracts. For the lender, the loan is fully collateralized; for the borrower, the potential default is prepaid.

As for the option buyer, he is a bit player. He does not have enough money to invest in securities markets as capital demands a minimum size to be acquired. So he risks the meagre sum he has on a double or nothing bet that is the stock-in-trade of gamblers. More often than not, he loses.³²

And yet he is a critical link in the circulation of speculative capital, which is why he is wooed, brought in and woven into the global network of capital markets.³³ Without the option buyer’s money, the loan to purchase the stock would not be granted to the arbitrageur, meaning that arbitrage opportunities would go unexploited and the options could not be priced.³⁴

9 Synthetic Derivatives

In creating the option structure, speculative capital scores two hits. We are forced to describe them sequentially but there is no “first” and “second,” as they are intertwined and inseparable.

First, speculative capital makes itself impregnable through option structure. It can now confidently roam the global markets for arbitrage opportunities, having eliminated one scourge of private transactions, namely counterparty default risk. Little wonder that it creates this structure anywhere it can. Risk-parity, smart alpha, smart beta, exchange-traded funds, high-frequency trading:³⁵ these are the most recent names under which the synthetic structure is put to work. The extent to which speculative capital dominates the markets in that form is clear from the daily reporting of the financial press. A few examples should suffice:

Risk-parity

• (1) The “systemic/technical investors” include risk parity funds and momentum investors known as CTAs. Initially commodity focused, they now invest across futures markets and are often computer driven. These investors, along with “smart beta” passive equity strategies that have become increasingly popular, adjust their exposures according to algorithms in response to market moves, meaning spikes in volatility can trigger a rash of automatic selling.³⁶

• (2) So-called risk parity is a next-generation passive strategy that seeks to give equity-like returns, while providing the relative stability of bonds in a crisis. Risk parity funds typically invest in a basket of stocks, bonds, and commodities, but “leverage” the traditionally safer fixed-income bets through derivatives to ensure each asset class contributes equally to a portfolio.³⁷

• (3) [Risk parity] is now a $400bn industry, and assuming an average 355 % leverage ratio—derived from the funds that issue public reports—it controls assets worth about $1.4 trillion. Even that figure is probably conservative, as it does not include in-house risk parity funds that have been established in some pension funds and insurers, which could easily bring the number up to $600 billion.³⁸

Exchange-Traded Funds (ETFs)

• (1) ETFs were introduced only 25 years ago but now manage more than $3tn globally.³⁹

• (2) Many of the [exchange traded] funds are now “synthetic,” relying on derivatives to deliver promised returns rather than holding the actual basket of goods as “physical” ETFs do. And despite the name, many exchange traded products change hands over the counter rather than on an exchange.⁴⁰

• (3) Synthetic ETFs, which use derivatives or structured products, have exploded; [they] account for 45 % of the market in Europe. And some ETFs are now using leverage; others are starting to purchase riskier assets such as risky loans.⁴¹

High Frequency Trading (HFT)

• (1) Stock market: “[B]y any measure, HFT is a dominant component of the current market structure and likely to affect nearly all aspects of its performance.”⁴²

• (2) Bond market: “More than $500bn in US Treasuries are traded daily and electronic trading accounts for 40 per cent of that, a number Nasdaq believes will increase. Nor is Nasdaq likely to stop at Treasuries. The group is planning geographical expansion, with new markets such as gilts, Japanese government bonds, repos and European sovereigns under consideration.”⁴³

• (3) Currency market: “The gains are most visible in foreign exchange, where the global market share of high-frequency trading has soared to 40 per cent up from just a quarter in three years.”⁴⁴

• (4) Commodities market: “The world’s top sugar traders have attacked ‘parasitic’ computer traders, criticizing the New York-based exchange that hosts the main sugar futures contract for failing to clamp down on their activities.”⁴⁵

Any farmer in 1910 would have understood the complaint of the sugar traders above, only that the “parasite” they complain about is no longer an tenuously solvent speculator but a force commanding trillions in euros, dollars, yens—what have you.⁴⁶

Second, speculative capital uses derivatives to neutralize the external threat of regulation by performing a vanishing act. It shape-shifts from product to strategy and disappears in plain sight.

The derivative product form, you recall, was always tenuous; an option and a forward presuppose constantly arbitraging speculative capital to be priced. But this point was not adequately understood. Options, swaps, futures, captions—all were thought of, and presented as, products. The regulatory agencies claimed jurisdiction over them as products.

In its latest form, speculative capital goes a step further down the abstraction ladder. It decomposes the derivative structure to its constituent transactions—shorting Treasuries here, buying stock there—and executes them following a “strategy.” To an outside observer these trades appear as innocuous, routine and unrelated.⁴⁷ There could be no talk of regulating them. Indeed, there is nothing to regulate. The booming business of index construction, for example, has little relation to derivatives. It revolves around creating the “best” index. That is, the most strongly correlated with a market segment and the cheapest to emulate index. The index is then used by the ETFs for arbitrage purpose.

Or take risk-parity, which is the age-old “60 percent stock, 40 percent bond” portfolio selection with only a change in the accent.⁴⁸

It is only at the local command centre of speculative capital—a hedge fund, an asset management firm or a HFT shop—that the trades “come together” to form a de facto or synthetic derivative. This transformation of the product to strategy outmanoeuvres the regulator, a development which has not gone unnoticed:

The ban on proprietary trading … has seemingly had a big impact since it was introduced in 2010. But are banks getting round this in part by dealing in exchange-traded funds? … While the industry does not talk freely about its strategies, it is known that many revolve around index arbitrage, where traders exploit mispricing between ETFs and their underlying assets.”⁴⁹

The writer has the gist of the story right but it is not “banks”; it is speculative capital which resides increasingly in non-bank entities and, especially, these days, in asset managers that control trillions of dollars of individual investments including pensions.

Now it must be clear why we said speculative capital is the anima mundi of finance. It derives the innovation in finance and the technology serving it. It creates products, indexes and strategies and sees that they are implemented and used in serving its end. It links markets, products, securities and currencies through price relations that are transparent and fair; buyers and sellers would agree that they could not get any better prices. And it is efficiency-mad: it constantly drives down the bid/asked spreads to make trading in capital markets cheaper. These are the benefits of “modern financial markets” that finance professors teach without knowing their cause.⁵⁰

This complex system is balanced on a razor’s edge. The self-destructive tendency of speculative capital is ready to tip the balance any time and anywhere. The “mysterious” flash crashes that have plagued the US financial markets provide ample proof of that.

Treasury bond yield do not tumble 35 basis points in a few minutes every morning. There is no possible explanation for such a fall in the economic data that normally move the bond market, so yesterday’s plunge in Treasury yield … suggests the market pathologies we grew to know during the crisis of 2008 are returning … Such a fall in such a liquid market implies someone, somewhere is under stress. Much like the “flash crash” of early 2010, which presaged a long period of volatility before the post-crisis rally resumed late the next year, it is a symptom of distress that cannot be ignored … The broader picture suggests the conventional wisdom is about to face a severe test. … There was no space in this world view for yield to fall, and certainly not to the 1.86 per cent level they briefly hit yesterday morning.⁵¹

How speculative capital causes crashes is beyond our subject. The mechanics of the crash and whether it become a crisis is a function of many idiosyncratic factors.⁵² The main point to note is that the much praised “efficiency” has two faces. On one hand, it ensures razor-thin spreads which is the good and the beneficial side that free-market supporters highlight.

But “in the most adequate and satisfactory tool, there is a hidden violence which is the reverse of its docility.”⁵³ The efficiency also means that the margin of error is reduced, so that a small disturbance can trigger a crash—or a crisis. There, too, traders have noticed the vulnerability before the academics:

The markets don’t really need a Lehman or even Lehman-lite event for a credit dislocation,” says [a hedge fund manager]. “You just need spreads to widen out or rates to go up for a significant impact on collateral movement for derivatives.⁵⁴

Derivative products, qua products, are a small subset of this system. Nevertheless, because of the sensitivity of the system to outside stimulus, their regulation disturbs price relations. The protracted dispute between the USA and EU over derivatives regulated by the Commodities Futures Trading Commission that only recently led to an agreement is a case in point.⁵⁵ Each side claimed that an unfavourable collateral requirement made their derivatives more expensive, never mind that the dispute involved the relatively benign matter of minimizing default risk.

The effect is more pronounced when regulation targets the movement of speculative capital or bans it altogether, as in the Dodd–Frank Act and the Volker Rule. What results is a permanent dislocation of prices:

Attention has focused on the sharp move in the spread between US Treasury yields and interest rate swaps … But it is not just US Treasury asset swap spreads that are behaving oddly. In foreign exchange markets, the so-called “cross-currency-basis” has rocketed. … Since the 2008 financial crisis, the difference between the theoretical and actual forward exchange rate, the “basis”, has become more volatile. Recently, it has collapsed again. Credit and equity markets have not been immune either. In both cases cash and derivatives markets have diverged, with the underlying cash assets cheapening significantly versus their related derivatives.⁵⁶

Dislocated prices impact indices, and indices are the reference points for allocating trillions of investment capital. Their mispricing has serious implications for returns of investment portfolios and pensions alike. It is with consideration of all these matters that a derivatives regulator must act.

10 Conclusion

Highlighting the vulnerability of the financial system and its sensitivity to regulation is not a manifesto for laissez-faire or regulatory inaction. Quite the contrary. The vulnerability and sensitivity we discussed arise from the complexity of the markets: a dense web of interrelated segments kept in place by a self-destructive force whose incessant buying and selling is the condition of an equilibrium balanced on a razor’s edge. Regulators approaching this complex web must do so with a firm theoretical grasp of the system. Only then will they be able to see what is happening, that is, what is changing and in what direction the changes are headed. That is the latest condition that arbitrage-driven speculative capital imposes on the markets: not only arbitrageurs but regulators, too, must recognize and adhere to the objective, mathematical relations that keeps markets in place. The days of regulation based on the “gut feelings” or moral considerations such as “prudence,” “public good” or “common sense” are behind us.