Secretary Problem Applied to Search Funds?

February 11, 2020

by a searcher from The University of Chicago - Booth School of Business in Chicago, IL, USA

TLDR: Math problem about optimal strategy for hiring job applicants has similar (but not same) assumptions to searching for a company. Does anyone have a set # of deals they want to seriously evaluate before pulling the trigger on an LOI?

The secretary problem (https://en.wikipedia.org/wiki/Secretary_problem) is a scenario in optimal stopping theory that derives an optimal policy for selecting a job applicant. The formulation assumes there is one position to fill, a known number of applicants (n) interviewed in random order, and that each applicant must be accepted/rejected immediately after the interview. The mathematically optimal approach is to reject the first n / e applicants (where e is approx###-###-#### and to then accept the first applicant that is better than all prior applicants. This is supposed to balance the risk of committing too early against waiting too long and missing your best chance.

Replace "applicant" with "company", and this sounds a little bit like a search fund. Assume you can seriously diligence/evaluate one business per week or 104 during a two-year search. If the secretary problem assumptions hold, you should theoretically evaluate ~38 companies before making an investment.

The secretary problem assumptions aren't exactly applicable (the company must also "accept" you, companies cannot be unambiguously ranked, LP experience can help you avoid the risk of committing too early, search can be extended, etc.).

However, does anyone have a set # of deals they plan to seriously diligence before committing to an LOI?

Reply by a searcher
from Yale University in Moscow, Russia

Clifford, I feel there are a couple of assumptions that make in inapplicable to search funds :

1) Interviewing event definition. Serious due dill happens after LOI. Before it, you screen companies. I believe that interviewing a candidate is a bit more similar to screening, than due dulling.
Number of companies you can screen during you search process and the quality of screening really depends on your GEO.
For example, in Russia I can see all of the private companies balance sheets and income statements for the past 10 years (if someone lies on them, they go to jail for 7 years). W.Europe has a similar situation. Of course, there are ways to obfuscate the data, but it's still of a good quality.
On the other hand as far as I know in Mexico, it takes a lot more creativity to get to approximate revenue. So, definitions of screening events in different GEOs would be different.

2) Assumption of rejection. Secretary problem assumes that you can never return to the rejected candidate (or the candidate that rejected you) which is not a process in a search process.
Company owners might change their mind and decide to sell. Similarly, unless you offend a company owner, you can always re-connect with them and have a conversation.

3) LOI rejections. It really depends on a lot of things, but most of the LOIs you submit would be rejected. And then you yourself will reject some companies you due dill.

4) Company quality knowledge. Secretary problem assumes you can't understand how good is the company unless you reject it and interview a certain "n" number of companies, because you don't know the market. That's not the case in search . If you got good investors to advice you and read good literature (HBR guide to buying a small business might be a good place to start) you won't have this problem.
I mean, if you find CAPEX light company in Mid-West USA with EBITDA of $3M, revenue of $9M, recurring revenue of 90%, historical&projected YoY growth of 8% that is willing to accept an EBITDA multiple of 3 with 25% sellers note you know you got an amazing deal. You don't need to look for "x" number of companies to understand that. (Though you probably won't find such a deal.)

Overall, I believe that the secretary problem is cool and all for mathematicians, but you can't use it that much in search funds.

Reply by an intermediary
from Wake Forest University in Winston-Salem, NC, USA

A couple thoughts -- first a disclaimer -- I'm an analytical person by nature so the concept is appealing. But, buying and owning a company is as much about the people and your relationships/connections (staff, customers, other stakeholders) as it is the numbers and the analytics. So be sure to mix in a lot of art in with the science. You should know in your gut if you come across the right one (none are ever perfect), whether it is one of the first you look at or one of the last (hopefully it is the last one you look at and you don't let the one that was a good fit slip away). Conversely, if you are trying to force yourself to like a company or talk yourself into it, it probably isn't the right fit.

Also, as Georgyi mentioned, pre-LOI you are mostly screening, not really doing due diligence on the company. Hopefully have a thorough CIM to review. However, if the seller and/or their broker/M&A Advisor found out you had seriously looked at 38 companies and were planning on looking at still many more, that would send up serious red flags, and plays into some of the concern and misconceptions that the seller's side has about searchers. The seller's side wants to limit the number of potential buyers they divulge confidential information to in order to reduce the chance of a confidentiality breach, not to mention time spent away from running the business. So, spend some serious diligence time on the industry, geography, and external factors. That way you are focused on what you are after and can limit the number of companies you actually dig into. And if you get to the LOI stage, you should definitely be ready to pull the trigger if due diligence confirms all is on the up and up.

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