Capital structure refers to the way a corporation finances its assets through some combination
of equity, debt, or hybrid securities. A firm's capital structure is then the composition or
'structure' of its liabilities. For example, a firm that sells $20bn dollars in equity and $80bn in
debt is said to be 20% equity financed and 80% debt financed. The firm's ratio of debt to total
financing, 80% in this example, is referred to as the firm's leverage.
The Modigliani-Miller theorem, proposed by Franco Modigliani and Merton Miller, forms the
basis for modern thinking on capital structure, though it is generally viewed as a purely
theoretical result since it assumes away many important factors in the capital structure
decision. The theorem states that, in a perfect market, the value of a firm is unaffected by how
that firm is financed. This result provides the base with which to examine real world reasons
why capital structure is relevant, that is, a company's value is affected by the capital structure
it employs. These other reasons include bankruptcy costs, agency costs and asymmetric
information. This analysis can then be extended to look at whether there is in fact an 'optimal'
capital structure: the one which maximizes the value of the firm.
Capital Structure in a Perfect Market
Assume a perfect capital market (no transaction or bankruptcy costs; perfect information);
firms and individuals can borrow at the same interest rate; no taxes; and investment decisions
aren't affected by financing decisions. Modigliani and Miller made two findings under these
conditions. Their first 'proposition' was that the value of a company is independent of its
capital structure. That is, you cannot change the size of a cake by cutting it into different sized
pieces. Their second 'proposition' stated that the cost of equity for a levered firm is equal to
the cost of equity for an unlevered firm, plus an added premium for financial risk. That is, as
leverage increases, while the burden of individual risks is shifted between different investor
classes, total risk is conserved and hence no extra value created.
Their analysis was extended to include the effect of taxes and risky debt. Under a classical tax
system, the tax deductibility of interest makes debt financing valuable; that is, the cost of
capital decreases as the proportion of debt in the capital structure increases. The optimal
structure, then would be to have virtually no equity at all.If capital structure is irrelevant in a
perfect market, then imperfections which exist in the real world must be the cause of its
relevance. The theories below try to address some of these imperfections, by relaxing
assumptions made in the M&M model.
Trade-off theory allows bankruptcy costs to exist. It states that there is an advantage to
financing with debt, the tax benefit of debt and there is a cost of financing with debt, the
bankruptcy costs of debt. The marginal benefit of further increases in debt declines as debt
increases, while the marginal cost increases, so that a firm that is optimizing its overall value
will focus on this trade-off when choosing how much debt and equity to use for financing.
Empirically, this theory may explain differences in D/E ratios between industries, however it
doesn't explain differences within the same industry.
Pecking Order theory tries to capture the costs of asymmetric information. It states that
companies prioritize their sources of financing (from internal financing to equity) according to
the law of least effort, or of least resistance, preferring to raise equity as a financing means
“of last resort”. Hence internal funds are used first, and when that is depleted debt is issued,
and when it is not sensible to issue any more debt, equity is issued. This theory maintains that
businesses adhere to a hierarchy of financing sources and prefer internal financing when
available, and debt is preferred over equity if external financing is required. Thus, the form of
debt a firm chooses can act as a signal of its need for external finance.
Asset substitution effect: As D/E increases, management has an increased incentive to
undertake risky (even negative NPV) projects. This is because if the project is successful,
share holders get all the upside, whereas if it is unsuccessful, debt holders get all the downside.
If the projects are undertaken, there is a chance of firm value decreasing and a wealth
transfer from debt holders to share holders. Underinvestment problem: If debt is risky (eg in a
growth company), the gain from the project will accrue to debtholders rather than
shareholders. Thus, management have an incentive to reject positive NPV projects, even
though they have the potential to increase firm value. Free cash flow: unless free cash flow is
given back to investors, management has an incentive to destroy firm value through empire
building and perks etc. Increasing leverage imposes financial discipline on management.
The difference between nominal price and relative or real price (as exchange ratio) is often
made. Nominal price is the price quoted in money while relative or real price is the exchange
ratio between real goods regardless of money. The distinction is made to make sense of
inflation. When all prices are quoted in terms of money units, and the prices in money units
change more or less proportionately, the ratio of exchange may not change much. In the
extreme case, if all prices quoted in money change in the same proportion, the relative price
remains the same.
In economics and finance, arbitrage is the practice of taking advantage of a price
differential between two or more markets: a combination of matching deals are struck that
capitalize upon the imbalance, the profit being the difference between the market prices. 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, a
risk-free profit. A person who engages in arbitrage is called an arbitrageur. The term is
mainly applied to trading in financial instruments, such as bonds, stocks, derivatives,
commodities and currencies.
If the market prices do not allow for profitable arbitrage, the prices are said to constitute an
arbitrage equilibrium or arbitrage-free market. An arbitrage equilibrium is a precondition for
a general economic equilibrium. The assumption that there is no arbitrage is used in
quantitative finance to calculate a unique risk neutral price for derivatives.Statistical arbitrage
is an imbalance in expected values. A casino has a statistical arbitrage in almost every game of
chance that it offers.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 only
possible with securities and financial products which can be traded electronically.
In the most simple 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 be 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.
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 to the same prices, in all markets, in each category. The
speed at which prices converge 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, as long as the buyers are not prohibited from reselling and the
transaction costs of buying, holding and reselling are small relative to the difference in prices
in the different markets.
Arbitrage moves different currencies toward purchasing power parity. As an example, 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, and 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 for the exported cars. Both actions would
increase demand for US Dollars, and supply of Canadian Dollars, and as a result, there would
be an appreciation of the US Dollar. Eventually, if unchecked, this would make US cars more
expensive for all buyers, and Canadian cars cheaper, until there is no longer an incentive to
buy cars in the US and sell them in Canada. More generally, international arbitrage
opportunities in commodities, goods, securities and currencies, on a grand scale, tend to
change exchange rates until the purchasing power is equal.
In reality, of course, one must consider taxes and the costs of travelling back and forth
between the US and Canada. Also, the features built into the cars sold in the US are not
exactly the same as the features built into the cars for sale in Canada, due, among other
things, to the different emissions and other auto regulations in the two countries. In addition,
our example assumes that no duties have to be paid on importing or exporting cars from the
USA to Canada. Similarly, most assets exhibit (small) differences between countries,
transaction costs, taxes, and other costs provide an impediment to this kind of arbitrage.
Arbitrage transactions in modern securities markets involve fairly low risks. 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. There is also counter-party risk, that the other party to
one of the deals fails to deliver as agreed; though unlikely, this hazard is serious because of the
large quantities one must trade in order to make a profit on small price differences. These
risks become magnified when leverage or borrowed money is used.
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 correla ted or predictable. In
the extreme case this is risk arbitrage, described below. In comparison to the classical quick
arbitrage transaction, such an operation can produce disastrous losses.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
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 by events. 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 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 (that is, before the other arbitrageurs act). 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 the risk is through the illegal use
of inside information, and in fact risk arbitrage with regard to leveraged buyouts was
associated with some of the famous financial scandals of the 1980s such as those involving
Michael Milken and Ivan Boesky.
Types of arbitrage
Also called risk arbitrage, merger arbitrage generally consists of buying 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.
Also called municipal bond relative value arbitrage, municipal arbitrage, or just muni arb,
this hedge fund strategy involves one of two approaches.
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 (in the case of revenue bonds). Managers aim to capture the inefficiencies arising
from the heavy participation of non-economic investors (i.e., high income "buy and hold"
investors seeking tax-exempt income) as well as the "crossover buying" arising from
corporations' or individuals' changing income tax situations (i.e., insurers switching their
munis for corporates after a large loss as they can capture a higher after-tax yield by
offsetting the taxable corporate income with underwriting losses). 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
BMA (short for Bond Market Association ). 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
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 U.S. dollars.
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.
A depository 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 (American Depositary Receipt) or GDRs (Global
Depositary Receipt) depending on where they are issued, are typically considered "foreign"
and therefore trade at a lower value when first released. However, they are exchangeable into
the original security (known as fungibility) and actually have the same value. In this case there
is a spread between the perceived value and real value, which can be extracted. 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 you can hedge that risk
Regulatory arbitrage is where a regulated institution takes advantage of the difference
between its real (or economic) 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.
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 Role
of Capital in Optimal Banking Supervision and Regulation. In economics, regulatory arbitrage
(sometimes, tax arbitrage) may be used to refer to situations when a company can choose a
nominal place of business with a regulatory, legal or tax regime with lower costs. For
example, an insurance company may choose to locate in Bermuda due to preferential tax rates
and policies for insurance companies. 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.
Telecom arbitrage companies like Action Telecom UK allow mobile phone users to make
international calls for free through certain access numbers. 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. The end effect is telecom arbitrage. This is usually marketed as "free
international calls". The profit margins are usually very small. However, with enough volume,
enough money is made from the cost difference to turn a profit. This is very similar to Future
Phone in the US.
The debacle of Long-Term Capital
Long-Term Capital Management (LTCM) 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 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 return on U.S. treasuries 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 returns 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.
Many current U.S. ETFs are based on some index; for example, SPDRs (Standard & Poor's
Depository Receipts, or "Spiders") (AMEX: SPY) are based on the S&P 500 index. The index
is generally determined by an independent company; for example, Spiders are run by State
Street, while the S&P 500 is calculated by Standard & Poor's. Sometimes, a proprietary index
is used.Although the SEC states that an ETF is "a type of investment company whose
investment objective is to achieve the same return as a particular market index," this is no
longer reality. The development of investment structures has progressed more quickly than the
A series of ETFs introduced by ProShares in 2006 - 2007 no longer follow the traditional
definition. These funds, while correlating to the performance of the S&P 500, NASDAQ 100,
DJIA, and S&P 400 Midcap, do not attempt to merely achieve the same return as the
underlying index. These forty funds attempt to either achieve the daily performance of the
designated benchmark times two, times negative one, or times negative two. They are ETFs
with integrated leverage.Another example of an innovative ETF that has broken the classic
mold is the oil futures ETF: USO. This ETF tracks the performance of the Western Texas
Intermediate light sweet crude. This is not a benchmark, but a traded commodity.Rydex has
taken a different direction and worked with S&P to create new, equal-weight benchmarks for
their proprietary benchmarks. These "benchmarks" are rebalanced quarterly.