Optimal Stopping Algorithms And Venture Investing
Eric Benhamou BGV Founder and General Partner shares his perspective on how “optimal stopping” computer algorithms may inform venture capital investment decisions. What does “optimal stopping” have to do with venture capital investing? More than you may think at first blush. “Optimal stopping” refers to the classical computer science problem of deciding when to stop looking for the optimal thing you are searching for and take the leap to pick the next available one that comes along the way. We all experience this problem in everyday life choices, most typically when we look for a parking space as close as possible to our ultimate destination. Instinctively, we tend to not take the first one that presents itself. We wait a little until we feel we are close enough, then we take the plunge: the next one open is the one we choose. When do we cross that threshold? Most of us don’t even think about it. We simply act by instinct. The more conservative ones among us will pick the first one available from within the range of acceptable parking spots (i.e. within acceptable walking range from our destination). At the other extreme, the ones who seek the very best parking spot and aren’t afraid to pass on (and most likely forego) the ones that are far away may exhaust the entire search within the range of acceptable distance and may still find themselves without a spot. Most of us will exhibit a behavior between these two extremes. It turns out this problem has an optimal solution: the answer is 37% (see “The Secretary Problem and its Extensions: A Review”, by P.R. Freeman, published by International Statistical Institute (ISI) in 1983 – http://www.jstor.org/stable/1402748)). In other words, in our parking example, if we intend to consider 100 possible parking spots near our optimal destination, the threshold beyond which we should stop looking and decide to pick the next one available is after we have scanned the 37th spot. I came across a helpful refresher of this classical computer science problem as I was reading the very insightful book by Brian Christian and Tom Griffiths titled “Algorithms to Live By”. It occurred to me that the situation he was describing was very analogous to one that all venture capitalist investors know all too well: as they process their deal flow, they must identify the optimal deal within a given period (they must maintain a reasonable predictable investment pace based upon the commitments they made to their limited partners) and continually reassess whether or not the opportunity they are looking at in any given moment is worth the leap of an investment. Should they take the leap, or instead should they wait a bit more to come across a better one? In our firm (BGV – www.benhamouglobalventures.com), it would be fairly typical that we review about 100 opportunities per quarter. We operate on a pace of about 4 investments per year (i.e. 1 per quarter). Our task is therefore to pick the best possible investment out of 100 new possibilities in any given quarter. If we were to use the “optimal stopping” algorithm of the parking problem, we therefore should plan to review 37 opportunities without acting upon them, then wait for the next one that comes along and meets our investment criteria and leap upon it. While this may sound a bit overly programmatic, re-reading the theory that underlie the optimal stopping problem has the merit of reducing the effect of emotions such as fear and greed and the impact of other cognitive biases on our investment choices. To be sure, the analogy has its limits. The parking problem is one of the simplest form of “optimal stopping” problems in that all the parking spots are equivalent and are in one of two binary states: available or occupied. It is also assumed that your time has no value: taking another 5 minutes to explore the next block bears no cost and does not enter into the equation. It also assumes that if you pass on an available parking spot, it will be taken by another motorist and will no longer be available to you if you decide to take another go around the block. The reality of venture capital investing is far more complex and nuanced. Often times, investment opportunities remain open for longer. Pausing on a deal is not exactly the same as passing on it. Deals exist in more than two states (good or bad). Many firms define several more complex methods to classify deals as they engage in portfolio construction. Further, waiting another month to add an investment to a venture portfolio has a cost in partner bandwidth, and potentially a penalty in the time value of capital (assuming the investment capital is sitting idle on a deposit account). More refined versions of the optimal stopping computer algorithm have been derived that take into account some of the more complex variations I listed. They would tend to suggest that 37% is probably the upper limit of what one should wait before crossing the threshold and taking the investment leap. 30% may be a more practical rule of thumb. As much as we would like decision making to become more data driven and objective, part of it remains an art. However, understanding the “optimal stopping” class of algorithms helps us correct the behaviors of our investing partners who tend to fall in the love with the 1st deal they see in a quarter, and those who procrastinate in full ambiguity until the very end of the quarter. At BGV we believe that sound venture investment decision-making requires a combination of analysis, patience and discernment — competencies that are often a function of deep experience in company building.