Risk Arbitrage

Conventional arbitrage is most succinctly defined as creating a portfolio with zero cost that has no possibility of a negative future value, and at least some possibility of a positive future value. There would be no reason that an investor would not create as much of this portfolio as possible -- it costs zero -- and maximize his possible future value.

Conventional arbitrage is riskless: there is no possibility of any loss. There are sometimes references to "risk arbitrage," which is (vaguely) taking a position that has a better return than its risk profile would suggest.

I have developed a more precise definition of risk arbitrage, based on the ability to short a portfolio with very little likelihood of loss. In particular, if for any positive x, positive or negative y, and positive z, a portfolio can be created to short for which the probability of any future positive value at all is less than x, the expected rate of return is less than y, and the maximum future value is less than z, then an opportunity for risk arbitrage exists.

This definition relies on the fact that prices are set at the margin: if any investor is willing to entertain the possibility of additional risk, then regardless of how small z is set (which will tend to diminish the size of the short position taken), the price paradigm will be broken.

Basically, the choice of z sets the maximum loss from shorting the portfolio, and then x and y can be selected to make arbitrarily remote the probability of any loss and arbitrarily small the expected loss: if no one is interested in selling short a portfolio that has 1% chance of having any positive future value at all at a given future point in time and that has -50% expected rate of return, how about a portfolio with 0.5% chance of having any positive future value and that has -75% expected rate of return? And the probability of future value, and the expected future value, can be continually reduced until a reasonable investor would not be able to resist at least a taste.