Now that we've explored how the arbitrageur estimates the possible returns and risks, and the probability of any particular transaction's occurring, we will use these estimates to form a decision framework for the arbitrage investment process.
In Chapter 6, we saw that the arbitrageur had estimates of return and risk on four separate deals (see Exhibits 6.1 and 6.2). The probabilities of those deals, expressed as percentages, are shown in Exhibits 7.1 and 7.2.
|Deal||Return ($)||Risk ($)||Probability (%)|
EXHIBIT 7.1 Risk Arbitrage: Returns, Risks, and Probability (in dollars)
|Deal||Return (%)||Risk (%)||Probability (%)|
EXHIBIT 7.2 Risk Arbitrage: Returns, Risks, and Probability (in percentages)
We can now use the three estimates in each deal to calculate the risk‐adjusted expected return on each transaction, as follows:
|where RAR||=||risk‐adjusted return|
|P1||=||probability of deal closing|
|EP||=||expected profit (net spread)|
|P2||=||probability of deal's breaking up = 1 − P1|
|EL||=||expected loss (total risk)|
|P||=||estimated investment period|
All the returns we have used in the previous calculations are unleveraged returns. ...