CHAPTER 6Estimating the Probability of a Transaction's Occurrence

It is very helpful for an arbitrageur to have estimates of both return and risk, but having these two elements does not give the arbitrageur a complete picture. The third and hardest element of the risk arbitrage decision process involves estimating the probability of a transaction's occurrence.

By taking several examples, an arbitrageur can estimate both return and risk on separate proposed transactions. As Exhibit 6.1 illustrates, each transaction has its own return and risk. The dollar amounts vary from deal to deal. If we look at the two columns that show return and risk estimates, we realize that it is very difficult for an arbitrageur to determine which deal, if any, is worth an investment. Is it wise to invest in Deal ABC and earn $1.00 per share, or does it make more sense to invest in Deal GHI for a spread of only $0.188 per share? The amount of dollars at risk in these deals is almost the same. Why invest capital to earn only $0.188 per share?

Deal Return ($) Risk ($)
ABC 1.000 4.000
DEF 1.500 7.000
GHI 0.750 2.950
JKL 2.650 12.500

EXHIBIT 6.1 Risk and Return on Selected Deals (in terms of dollars)

In Exhibit 6.2, we express return and risk in percentages. The return incorporates the required capital investment. Because percentage calculations incorporate the element of timing, they are usually more useful than return and risk expressed in terms of absolute dollars. We can ...

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