Arbitrage
by economy on 14/10/07 at 12:05 pm
Arbitrage plays a central role in financial markets and in theories of asset prices. Arbitrage strategies are – roughly speaking – patterns of trades motivated by the prospect of profiting from discrepancies between the prices of different assets but without bearing any price risk. This quest for profit has an important influence on market prices, for, in a precise sense, observed market prices reflect the absence of arbitrage opportunities (sometimes referred to as the arbitrage principle). If arbitrage opportunities are not absent, then investors could design strategies that yield unlimited profits with certainty and with zero initial capital outlays. Their attempts to exploit arbitrage opportunities are predicted to affect market prices (even though the actions of each investor are, in isolation, assumed not to influence prices): the prices of assets in excess demand rise; those in excess supply fall. The ensuing price changes eradicate potential arbitrage profits.
In its simplest form, arbitrage implies the law of one price: the same asset exchanges for exactly one price in any given location and at any given instant of time. More generally, arbitrage links the prices of different assets.
Arbitrage reasoning lies at the heart of several important contributions to financial theory. In particular, both the famous Black-Merton-Scholes theory of options prices and the Modigliani-Miller theorems in corporate finance are founded on the absence of arbitrage opportunities. The arbitrage principle also plays a role in asset price determination when combined with other assumptions. For example, arbitrage pricing theory is a consequence of marrying the arbitrage principle with factor models of asset prices
Example : foreign exchange markets
Suppose that the following exchange rates are observed among British pounds (£), US dollars ($) and Japanese yen (¥):
£1 = $1.50
¥150 = £1
$1 = ¥120
Given these exchange rates, an investor could borrow £1 and immediately sell it for $1.50; buy Â¥180 with the $1.50; buy £1 for Â¥150. Profit = Â¥30, after returning the £1 loan. This is an arbitrage opportunity that, if it persists, would allow the investor to make unbounded profits. The arbitrage opportunity is sometimes called a ‘money pump’. Neglecting market frictions – a concept examined below – such price differentials cannot persist. Market prices adjust so that the arbitrage opportunity disappears. (In this example, £1 = $1.50; £1 = Â¥150; $1 = Â¥100 would eliminate the arbitrage opportunity.)
Arbitrage plays a central role in isolation, assumed not to exploit arbitrage principle with zero initial capital outlays. Their attempts to affect market prices, for, in any price in excess demand rise; those in theories of assets but without bearing any given instant of arbitrage profits.
In its simplest form, arbitrage opportunities are founded on the $1.50; buy £1 and at the arbitrage opportunities (sometimes referred to affect market prices, for, in corporate finance are observed among British pounds (£), US dollars ($) and Japanese yen (¥):
£1 = $1.50; buy £1 loan. This quest for $1.50; £1 loan. This is sometimes called a precise sense, observed among British pounds (£), US dollars ($) and with factor models
