Arbitrage


In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices at which the unit is traded. When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs. For example, an arbitrage opportunity is present when there is the possibility to instantaneously buy something for a low price and sell it for a higher price.
In principle and in academic use, an arbitrage is risk-free; in common use, as in statistical arbitrage, it may refer to expected profit, though losses may occur, and in practice, there are always [|risks] in arbitrage, some minor, some major. In academic use, an arbitrage involves taking advantage of differences in price of a single asset or identical cash-flows; in common use, it is also used to refer to differences between similar assets, as in merger arbitrage.
The term is mainly applied to trading in financial instruments, such as bonds, stocks, derivatives, commodities, and currencies. People who engage in arbitrage are called arbitrageurs.
Arbitrage has the effect of causing prices of the same or very similar assets in different markets to converge.

Etymology

"Arbitrage" is a French word and denotes a decision by an arbitrator or arbitration tribunal. In the sense used here, it was first defined in 1704 by Mathieu de la Porte in his treatise "La science des négociants et teneurs de livres" as a consideration of different exchange rates to recognise the most profitable places of issuance and settlement for a bill of exchange

Arbitrage-free

If the market prices do not allow for profitable arbitrage, the prices are said to constitute an arbitrage equilibrium, or an arbitrage-free market. An arbitrage equilibrium is a precondition for a general economic equilibrium. The "no arbitrage" assumption is used in quantitative finance to calculate a unique risk neutral price for derivatives.

Arbitrage-free pricing approach for bonds

This refers to the method of valuing a coupon-bearing financial instrument by discounting its future cash flows by multiple discount rates. By doing so, a more accurate price can be obtained than if the price is calculated with a present-value pricing approach. Arbitrage-free pricing is used for bond valuation and to detect arbitrage opportunities for investors.
For the purpose of valuing the price of a bond, its cash flows can each be thought of as packets of incremental cash flows with a large packet upon maturity, being the principal. Since the cash flows are dispersed throughout future periods, they must be discounted back to the present. In the present-value approach, the cash flows are discounted with one discount rate to find the price of the bond. In arbitrage-free pricing, multiple discount rates are used.
The present-value approach assumes that the yield of the bond will stay the same until maturity. This is a simplified model because interest rates may fluctuate in the future, which in turn affects the yield on the bond. For this reason, the discount rate may be different for each of the cash flows. Each cash flow can be considered a zero-coupon instrument that pays one payment upon maturity. The discount rates used should be the rates of multiple zero-coupon bonds with maturity dates the same as each cash flow and similar risk as the instrument being valued. By using multiple discount rates, the arbitrage-free price is the sum of the discounted cash flows. Arbitrage-free price refers to the price at which no price arbitrage is possible.
The ideas of using multiple discount rates obtained from zero-coupon bonds and discounting a similar bond's cash flow to find its price is derived from the yield curve, which is a curve of the yields of the same bond with different maturities. This curve can be used to view trends in market expectations of how interest rates will move in the future. In arbitrage-free pricing of a bond, a yield curve of similar zero-coupon bonds with different maturities is created. If the curve were to be created with Treasury securities of different maturities, they would be stripped of their coupon payments through bootstrapping. This is to transform the bonds into zero-coupon bonds. The yield of these zero-coupon bonds would then be plotted on a diagram with time on the x-axis and yield on the y-axis.
Since the yield curve displays market expectations on how yields and interest rates may move, the arbitrage-free pricing approach is more realistic than using only one discount rate. Investors can use this approach to value bonds and find mismatches in prices, resulting in an arbitrage opportunity. If a bond valued with the arbitrage-free pricing approach turns out to be priced higher in the market, an investor could have such an opportunity:
  1. Investor shorts the bond at price at time t1.
  2. Investor longs the zero-coupon bonds making up the related yield curve and strips and sells any coupon payments at t1.
  3. As t>t1, the price spread between the prices will decrease.
  4. At maturity, the prices will converge and be equal. Investor exits both the long and short positions, realizing a profit.
If the outcome from the valuation were the reverse case, the opposite positions would be taken in the bonds. This arbitrage opportunity comes from the assumption that the prices of bonds with the same properties will converge upon maturity. This can be explained through market efficiency, which states that arbitrage opportunities will eventually be discovered and corrected. The prices of the bonds in t1 move closer together to finally become the same at tT.

Conditions for arbitrage

Arbitrage is possible when one of three conditions is met:
  1. The same asset does not trade at the same price on all markets.
  2. Two assets with identical cash flows do not trade at the same price.
  3. An asset with a known price in the future does not today trade at its future price discounted at the risk-free interest rate.
Arbitrage is not simply the act of buying a product in one market and selling it in another for a higher price at some later time. The transactions must occur simultaneously to avoid exposure to market risk, or the risk that prices may change on one market before both transactions are complete. In practical terms, this is generally possible only with securities and financial products that can be traded electronically, and even then, when each leg of the trade is executed, the prices in the market may have moved. Missing one of the legs of the trade is called 'execution risk' or more specifically 'leg risk'.
In the simplest example, any good sold in one market should sell for the same price in another. Traders may, for example, find that the price of wheat is lower in agricultural regions than in cities, purchase the good, and transport it to another region to sell at a higher price. This type of price arbitrage is the most common, but this simple example ignores the cost of transport, storage, risk, and other factors. "True" arbitrage requires that there is no market risk involved. Where securities are traded on more than one exchange, arbitrage occurs by simultaneously buying in one and selling on the other.
See rational pricing, particularly § arbitrage mechanics, for further discussion.
Mathematically it is defined as follows:
where and denotes the portfolio value at time t.

Price convergence

Arbitrage has the effect of causing prices in different markets to converge. As a result of arbitrage, the currency exchange rates, the price of commodities, and the price of securities in different markets tend to converge. The speed at which they do so is a measure of market efficiency. Arbitrage tends to reduce price discrimination by encouraging people to buy an item where the price is low and resell it where the price is high.
Arbitrage moves different currencies toward purchasing power parity. Assume that a car purchased in the United States is cheaper than the same car in Canada. Canadians would buy their cars across the border to exploit the arbitrage condition. At the same time, Americans would buy US cars, transport them across the border, then sell them in Canada. Canadians would have to buy American dollars to buy the cars and Americans would have to sell the Canadian dollars they received in exchange. Both actions would increase demand for US dollars and supply of Canadian dollars. As a result, there would be an appreciation of the US currency. This would make US cars more expensive and Canadian cars less so until their prices were similar. On a larger scale, international arbitrage opportunities in commodities, goods, securities, and currencies tend to change exchange rates until the purchasing power is equal.
In reality, most assets exhibit some difference between countries. These, transaction costs, taxes, and other costs provide an impediment to this kind of arbitrage. Similarly, arbitrage affects the difference in interest rates paid on government bonds issued by the various countries, given the expected depreciation in the currencies relative to each other.

Risks

Arbitrage transactions in modern securities markets involve fairly low day-to-day risks, but can face extremely high risk in rare situations, particularly financial crises, and can lead to bankruptcy. Formally, arbitrage transactions have negative skew – prices can get a small amount closer, while they can get very far apart. The day-to-day risks are generally small because the transactions involve small differences in price, so an execution failure will generally cause a small loss. The rare case risks are extremely high because these small price differences are converted to large profits via leverage, and in the rare event of a large price move, this may yield a large loss.
The main day-to-day risk is that part of the transaction fails; this is called execution risk. The main, rare risks are counterparty risk, and liquidity risk: that a counterparty to a large transaction or many transactions fails to pay, or that one is required to post margin and does not have the money to do so.
In the academic literature, the idea that seemingly very low risk arbitrage trades might not be fully exploited because of these risk factors and other considerations is often referred to as limits to arbitrage.

Execution risk

Generally it is impossible to close two or three transactions at the same instant; therefore, there is the possibility that when one part of the deal is closed, a quick shift in prices makes it impossible to close the other at a profitable price. However, this is not necessarily the case. Many exchanges and inter-dealer brokers allow multi legged trades.
Competition in the marketplace can also create risks during arbitrage transactions. As an example, if one was trying to profit from a price discrepancy between IBM on the NYSE and IBM on the London Stock Exchange, they may purchase a large number of shares on the NYSE and find that they cannot simultaneously sell on the LSE. This leaves the arbitrageur in an unhedged risk position.
In the 1980s, risk arbitrage was common. In this form of speculation, one trades a security that is clearly undervalued or overvalued, when it is seen that the wrong valuation is about to be corrected. The standard example is the stock of a company, undervalued in the stock market, which is about to be the object of a takeover bid; the price of the takeover will more truly reflect the value of the company, giving a large profit to those who bought at the current price, if the merger goes through as predicted. Traditionally, arbitrage transactions in the securities markets involve high speed, high volume, and low risk. At some moment a price difference exists, and the problem is to execute two or three balancing transactions while the difference persists. When the transaction involves a delay of weeks or months, as above, it may entail considerable risk if borrowed money is used to magnify the reward through leverage. One way of reducing this risk is through the illegal use of inside information, and risk arbitrage in leveraged buyouts was associated with some of the famous financial scandals of the 1980s, such as those involving Michael Milken and Ivan Boesky.

Mismatch

Another risk occurs if the items being bought and sold are not identical and the arbitrage is conducted under the assumption that the prices of the items are correlated or predictable; this is more narrowly referred to as a convergence trade. In the extreme case this is merger arbitrage, described below. In comparison to the classical quick arbitrage transaction, such an operation can produce disastrous losses.

Counterparty risk

As arbitrages generally involve future movements of cash, they are subject to counterparty risk: the risk that a counterparty fails to fulfill their side of a transaction. This is a serious problem if one has either a single trade or many related trades with a single counterparty, whose failure thus poses a threat, or in the event of a financial crisis when many counterparties fail. This hazard is serious because of the large quantities one must trade in order to make a profit on small price differences.
For example, if one purchases many risky bonds, then hedges them with CDSes, profiting from the difference between the bond spread and the CDS premium, in a financial crisis, the bonds may default and the CDS writer/seller may fail, due to the stress of the crisis, causing the arbitrageur to face steep losses.

Liquidity risk

Arbitrage trades are necessarily synthetic, leveraged trades, as they involve a short position. If the assets used are not identical, or the margin treatment is not identical, and the trader is accordingly required to post margin, the trader may run out of capital and be forced to sell these assets at a loss even though the trades may be expected to ultimately make money. In effect, arbitrage traders synthesize a put option on their ability to finance themselves.
Prices may diverge during a financial crisis, often termed a "flight to quality"; these are precisely the times when it is hardest for leveraged investors to raise capital, and thus they will lack capital precisely when they need it most.

Types

Spatial arbitrage

Also known as geographical arbitrage, this is the simplest form of arbitrage. In spatial arbitrage, an arbitrageur looks for price differences between geographically separate markets. For example, there may be a bond dealer in Virginia offering a bond at 100-12/23 and a dealer in Washington bidding 100-15/23 for the same bond. For whatever reason, the two dealers have not spotted the difference in the prices, but the arbitrageur does. The arbitrageur immediately buys the bond from the Virginia dealer and sells it to the Washington dealer.

Merger arbitrage

Also called risk arbitrage, merger arbitrage generally consists of buying/holding the stock of a company that is the target of a takeover while shorting the stock of the acquiring company.
Usually the market price of the target company is less than the price offered by the acquiring company.
The spread between these two prices depends mainly on the probability and the timing of the takeover being completed as well as the prevailing level of interest rates.
The bet in a merger arbitrage is that such a spread will eventually be zero, if and when the takeover is completed. The risk is that the deal "breaks" and the spread massively widens.

Municipal bond arbitrage

Also called municipal bond relative value arbitrage, municipal arbitrage, or just muni arb, this hedge fund strategy involves one of two approaches. The term "arbitrage" is also used in the context of the Income Tax Regulations governing the investment of proceeds of municipal bonds; these regulations, aimed at the issuers or beneficiaries of tax-exempt municipal bonds, are different and, instead, attempt to remove the issuer's ability to arbitrage between the low tax-exempt rate and a taxable investment rate.
Generally, managers seek relative value opportunities by being both long and short municipal bonds with a duration-neutral book. The relative value trades may be between different issuers, different bonds issued by the same entity, or capital structure trades referencing the same asset. Managers aim to capture the inefficiencies arising from the heavy participation of non-economic investors as well as the "crossover buying" arising from corporations' or individuals' changing income tax situations. There are additional inefficiencies arising from the highly fragmented nature of the municipal bond market which has two million outstanding issues and 50,000 issuers, in contrast to the Treasury market which has 400 issues and a single issuer.
Second, managers construct leveraged portfolios of AAA- or AA-rated tax-exempt municipal bonds with the duration risk hedged by shorting the appropriate ratio of taxable corporate bonds. These corporate equivalents are typically interest rate swaps referencing Libor or SIFMA. The arbitrage manifests itself in the form of a relatively cheap longer maturity municipal bond, which is a municipal bond that yields significantly more than 65% of a corresponding taxable corporate bond. The steeper slope of the municipal yield curve allows participants to collect more after-tax income from the municipal bond portfolio than is spent on the interest rate swap; the carry is greater than the hedge expense. Positive, tax-free carry from muni arb can reach into the double digits. The bet in this municipal bond arbitrage is that, over a longer period of time, two similar instruments—municipal bonds and interest rate swaps—will correlate with each other; they are both very high quality credits, have the same maturity and are denominated in the same currency. Credit risk and duration risk are largely eliminated in this strategy. However, basis risk arises from use of an imperfect hedge, which results in significant, but range-bound principal volatility. The end goal is to limit this principal volatility, eliminating its relevance over time as the high, consistent, tax-free cash flow accumulates. Since the inefficiency is related to government tax policy, and hence is structural in nature, it has not been arbitraged away.
However, many municipal bonds are callable, and this adds substantial risks to the strategy.

Convertible bond arbitrage

A convertible bond is a bond that an investor can return to the issuing company in exchange for a predetermined number of shares in the company.
A convertible bond can be thought of as a corporate bond with a stock call option attached to it.
The price of a convertible bond is sensitive to three major factors:
Given the complexity of the calculations involved and the convoluted structure that a convertible bond can have, an arbitrageur often relies on sophisticated quantitative models in order to identify bonds that are trading cheap versus their theoretical value.
Convertible arbitrage consists of buying a convertible bond and hedging two of the three factors in order to gain exposure to the third factor at a very attractive price.
For instance an arbitrageur would first buy a convertible bond, then sell fixed income securities or interest rate futures and buy some credit protection.
Eventually what he'd be left with is something similar to a call option on the underlying stock, acquired at a very low price.
He could then make money either selling some of the more expensive options that are openly traded in the market or delta hedging his exposure to the underlying shares.

Depository receipts

A depositary receipt is a security that is offered as a "tracking stock" on another foreign market. For instance, a Chinese company wishing to raise more money may issue a depository receipt on the New York Stock Exchange, as the amount of capital on the local exchanges is limited. These securities, known as ADRs or GDRs depending on where they are issued, are typically considered "foreign" and therefore trade at a lower value when first released. Many ADR's are exchangeable into the original security and actually have the same value. In this case there is a spread between the perceived value and real value, which can be extracted. Other ADR's that are not exchangeable often have much larger spreads. Since the ADR is trading at a value lower than what it is worth, one can purchase the ADR and expect to make money as its value converges on the original. However, there is a chance that the original stock will fall in value too, so by shorting it one can hedge that risk.

Cross-border arbitrage

Cross-border arbitrage exploits different prices of the same stock in different countries:
Example: Apple is trading on NASDAQ at US$108.84. The stock is also traded on the German electronic exchange, XETRA. If 1 euro costs US$1.11, a cross-border trader could enter a buy order on the XETRA at €98.03 per Apple share and a sell order at €98.07 per share.
Some brokers in Germany do not offer access to the U.S. exchanges. Hence if a German retail investor wants to buy Apple stock, he needs to buy it on the XETRA. The cross-border trader would sell the Apple shares on XETRA to the investor and buy the shares in the same second on NASDAQ. Afterwards, the cross-border trader would need to transfer the shares bought on NASDAQ to the German XETRA exchange, where he is obliged to deliver the stock.
In most cases, the quotation on the local exchanges is done electronically by high-frequency traders, taking into consideration the home price of the stock and the exchange rate. This kind of high-frequency trading benefits the public as it reduces the cost to the German investor and enables him to buy U.S. shares.

Dual-listed companies

A dual-listed company structure involves two companies incorporated in different countries contractually agreeing to operate their businesses as if they were a single enterprise, while retaining their separate legal identity and existing stock exchange listings. In integrated and efficient financial markets, stock prices of the twin pair should move in lockstep. In practice, DLC share prices exhibit large deviations from theoretical parity. Arbitrage positions in DLCs can be set up by obtaining a long position in the relatively underpriced part of the DLC and a short position in the relatively overpriced part. Such arbitrage strategies start paying off as soon as the relative prices of the two DLC stocks converge toward theoretical parity. However, since there is no identifiable date at which DLC prices will converge, arbitrage positions sometimes have to be kept open for considerable periods of time. In the meantime, the price gap might widen. In these situations, arbitrageurs may receive margin calls, after which they would most likely be forced to liquidate part of the position at a highly unfavorable moment and suffer a loss. Arbitrage in DLCs may be profitable, but is also very risky.
A good illustration of the risk of DLC arbitrage is the position in Royal Dutch Shell—which had a DLC structure until 2005—by the hedge fund Long-Term Capital Management. Lowenstein describes that LTCM established an arbitrage position in Royal Dutch Shell in the summer of 1997, when Royal Dutch traded at an 8 to 10 percent premium. In total, $2.3 billion was invested, half of which was long in Shell and the other half was short in Royal Dutch. In the autumn of 1998, large defaults on Russian debt created significant losses for the hedge fund and LTCM had to unwind several positions. Lowenstein reports that the premium of Royal Dutch had increased to about 22 percent and LTCM had to close the position and incur a loss. According to Lowenstein, LTCM lost $286 million in equity pairs trading and more than half of this loss is accounted for by the Royal Dutch Shell trade.

Private to public equities

The market prices for privately held companies are typically viewed from a return on investment perspective, whilst publicly held and or exchange listed companies trade on a Price to earnings ratio . Thus, if a publicly traded company specialises in the acquisition of privately held companies, from a per-share perspective there is a gain with every acquisition that falls within these guidelines. E.g., Berkshire Hathaway and Halydean Corporation. Private to public equities arbitrage is a term which can arguably be applied to investment banking in general. Private markets to public markets differences may also help explain the overnight windfall gains enjoyed by principals of companies that just did an initial public offering.

Regulatory arbitrage

Regulatory arbitrage "is an avoidance strategy of regulation that is exercised as a result of a regulatory inconsistency". In other words, where a regulated institution takes advantage of the difference between its real risk and the regulatory position. For example, if a bank, operating under the Basel I accord, has to hold 8% capital against default risk, but the real risk of default is lower, it is profitable to securitise the loan, removing the low risk loan from its portfolio. On the other hand, if the real risk is higher than the regulatory risk then it is profitable to make that loan and hold on to it, provided it is priced appropriately. Regulatory arbitrage can result in parts of entire businesses being unregulated as a result of the arbitrage.
This process can increase the overall riskiness of institutions under a risk insensitive regulatory regime, as described by Alan Greenspan in his October 1998 speech on .
The term "Regulatory Arbitrage" was used for the first time in 2005 when it was applied by Scott V. Simpson, a partner at law firm Skadden, Arps, to refer to a new defence tactic in hostile mergers and acquisitions where differing takeover regimes in deals involving multi-jurisdictions are exploited to the advantage of a target company under threat.
In economics, regulatory arbitrage may refer to situations when a company can choose a nominal place of business with a regulatory, legal or tax regime with lower costs. This can occur particularly where the business transaction has no obvious physical location. In the case of many financial products, it may be unclear "where" the transaction occurs.
Regulatory arbitrage can include restructuring a bank by outsourcing services such as IT. The outsourcing company takes over the installations, buying out the bank's assets and charges a periodic service fee back to the bank. This frees up cashflow usable for new lending by the bank. The bank will have higher IT costs, but counts on the multiplier effect of money creation and the interest rate spread to make it a profitable exercise.
Example:
Suppose the bank sells its IT installations for US$40 million. With a reserve ratio of 10%, the bank can create US$400 million in additional loans. The bank can often lend to the IT services company to cover the acquisition cost of the IT installations. This can be at preferential rates, as the sole client using the IT installation is the bank. If the bank can generate 5% interest margin on the 400 million of new loans, the bank will increase interest revenues by 20 million. The IT services company is free to leverage their balance sheet as aggressively as they and their banker agree to. This is the reason behind the trend towards outsourcing in the financial sector. Without this money creation benefit, it is actually more expensive to outsource the IT operations as the outsourcing adds a layer of management and increases overhead.
According to PBS Frontline's 2012 four-part documentary, "Money, Power, and Wall Street," regulatory arbitrage, along with asymmetric bank lobbying in Washington and abroad, allowed investment banks in the pre- and post-2008 period to continue to skirt laws and engage in the risky proprietary trading of opaque derivatives, swaps, and other credit-based instruments invented to circumvent legal restrictions at the expense of clients, government, and publics.
Due to the Affordable Care Act's expansion of Medicaid coverage, one form of Regulatory Arbitrage can now be found when businesses engage in “Medicaid Migration”, a maneuver by which qualifying employees who would typically be enrolled in company health plans elect to enroll in Medicaid instead. These programs that have similar characteristics as insurance products to the employee, but have radically different cost structures, resulting in significant expense reductions for employers.

Telecom arbitrage

Telecom arbitrage companies allow phone users to make international calls for free through certain access numbers. Such services are offered in the United Kingdom; the telecommunication arbitrage companies get paid an interconnect charge by the UK mobile networks and then buy international routes at a lower cost. The calls are seen as free by the UK contract mobile phone customers since they are using up their allocated monthly minutes rather than paying for additional calls.
Such services were previously offered in the United States by companies such as FuturePhone.com. These services would operate in rural telephone exchanges, primarily in small towns in the state of Iowa. In these areas, the local telephone carriers are allowed to charge a high "termination fee" to the caller's carrier in order to fund the cost of providing service to the small and sparsely populated areas that they serve. However, FuturePhone ceased operations upon legal challenges from AT&T and other service providers.

Statistical arbitrage

is an imbalance in expected nominal values. A casino has a statistical arbitrage in every game of chance that it offers, referred to as the house advantage, house edge, vigorish, or house vigorish.

The fall of Long-Term Capital Management

lost 4.6 billion U.S. dollars in fixed income arbitrage in September 1998. LTCM had attempted to make money on the price difference between different bonds. For example, it would sell U.S. Treasury securities and buy Italian bond futures. The concept was that because Italian bond futures had a less liquid market, in the short term Italian bond futures would have a higher return than U.S. bonds, but in the long term, the prices would converge. Because the difference was small, a large amount of money had to be borrowed to make the buying and selling profitable.
The downfall in this system began on August 17, 1998, when Russia defaulted on its ruble debt and domestic dollar debt. Because the markets were already nervous due to the 1997 Asian financial crisis, investors began selling non-U.S. treasury debt and buying U.S. treasuries, which were considered a safe investment. As a result, the price on US treasuries began to increase and the return began decreasing because there were many buyers, and the return on other bonds began to increase because there were many sellers. This caused the difference between the prices of U.S. treasuries and other bonds to increase, rather than to decrease as LTCM was expecting. Eventually this caused LTCM to fold, and their creditors had to arrange a bail-out. More controversially, officials of the Federal Reserve assisted in the negotiations that led to this bail-out, on the grounds that so many companies and deals were intertwined with LTCM that if LTCM actually failed, they would as well, causing a collapse in confidence in the economic system. Thus LTCM failed as a fixed income arbitrage fund, although it is unclear what sort of profit was realized by the banks that bailed LTCM out.

Types of financial arbitrage