CHAPTER 7The Risk Arbitrage Decision Process

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 (%)
ABC 1.000 4.000 85
DEF 1.500 7.000 90
GHI 0.750 2.950 80
JKL 2.650 12.500 70

EXHIBIT 7.1 Risk Arbitrage: Returns, Risks, and Probability (in dollars)

Deal Return (%) Risk (%) Probability (%)
ABC 6 24 85
DEF 7 32 90
GHI 9 35 80
JKL 11 51 70

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:

images
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)
I = total investment
P = estimated investment period

All the returns we have used in the previous calculations are unleveraged returns. ...

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