Risk Arbitrage

An arbitrage opportunity arises when an investor can earn riskless profits without making a net investment. for example, if shares of a stock sold for different prices on two different exchanges. The las of one price states that if two assets are equivalent in all economically relevant respects, then they should have the same market price. This law is enforced by arbitrageurs: if they observe a violation of the law, they will engage in arbitrage activity---simultaneously buying the asset where it is cheap and selling where it is expenseive. in the process, they will bid up the price until the arbitrage opportunity is eliminated.

the idea that market prices willmove to rule out arbitrage opporunties is perhaps the most fundmental concept in capital market theory. the critial property of a risk free arbitrage portfolio is that any investor, regardless of its reisk aversion or wealth, will want to take an infinte position in it. becuase those large postitions will quickly force prices up or down until the opportunities vanishes, security prices should satisfy a-no arbitrage condition-, a condition that rules our the existence of arbitrage.

there is an important difference between arbitrage and risk-return dominance arguments. a dominance argument hold that when an equilibrium price relationship is violated, many investors will make limited portfolio changes, depending on their degree of riskaversion. by contrast, when arbitrage opportunies exist each investor wants to take as large a position as possible, hence it will not take many investor to bring about the price pressure necessary to restore equilibrium.

the CAPM is an example of a dominance argument, implying that all investors hold mean-variance efficient proftolios. if a security is mispriced, then ivnestor will tilt their portfolio toward the underpriced and away from the overpriced. the consumption that a large number of investor are mean-variance sensitive is critical. in contrast, the implication of a no-arbitrage condition is that a few investors who identify an arbitrage opportunity will mobilize large dollar amounts and quickly restore equilibrium.

 For derivative securiteis, strict arbitrage is practical possible and the condition of no-arbitrage leads to exact pricing. For stocks, no-arbitrage conditions must be obtained by applealing to diversification arguments.