Logistic function

**Legal Risks in M&A, How Do You Quantify Them?**

The AT&T, T-Mobile deal marked a great relief for consumers from a competition standpoint, but also a large quarterly loss for AT&T given the exorbitant break-up fee they agreed to pay in the event of that the deal falls through.

Last year in June, I wrote about the harmful effects to consumers from the proposed merger, however what I have also been interested in is quantifying the regulatory risk that companies may run into for either cross-border transactions or ones which may harm competition.

My original approach on working with large M&A data sets was to unsupervised learning techniques such as cluster analysis to cluster transactions into distinct groups, yet this technique gives no good method to make future predictions. Rather such a technique would only allow a primitive classification of the deal being analyzed with the historical transactions. Of course, building a classifier for a multi-categorical data set would be possible, but perhaps an easier method would be to utilize logistic regression.

**The Need for Numbers**

The issue historically has been the difficulty of placing a hard physical number of the likelihood of a deal facing legal scrutiny to go through. Surely, there must be associated patterns hidden in M&A data that may reveal whether one or another legal firm (Linklaters or Sullivan Cromwell) are better at such tricky issues.

The use of logistic regression is a viable method to estimate the probability of success. Given a data set of M&A transactions limited to within a specific time period, we can classify transactions as either having succeeded or failed and according to a range of variables (deal size, financial advisors, legal advisors).

The beauty of the logistic function is its range boundaries are between 0 and 1 for all x in R, which works well in the case of probability estimates. Thus we can define a Z to be a linear combination of selected variables which would have a domain in R. The linear coefficients in Z are regressed against the chosen variables and data. We would be able to make a prediction for the probability of success P(Success) based on the inputs of the variables we have chosen for our predictor equation.

This is a very early stage idea which arose out of the interest in quantifying risks in M&A and thus could provide a basis for event driven trading strategies or event driven M&A insurance underwriting.

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