Series FF stock and the Friedman-Savage Model for Risk Profiles

The Friedman-Savage model was developed to explain an economic paradox: assuming rationality, why would the same person buy both insurance and lottery tickets?  The answer that Friedman and Savage proposed is a double inflection utility curve:

The x-axis here corresponds to the size of the payout for a particular activity, the y-axis to the utility actually gained from the payout.  (Click on the graph for a larger version.)  Imagine that right now you have wealth = zB, and thus have utility = B.  The uncertain future forces you to take two different gambles: one with a payout somewhere between A and B and another with a payout between B and C.  The expected value of the payout is shown by the chords E and E'.  Although the expected value is everywhere lower than the actual utility gained from the payout between points A and B, a risk-averse person will prefer the certain result of E.  Thus, a risk-averse person would choose paying an insurance premium costing E over an uncertain result between A and B.  Likewise, a risk-preferring person would prefer the certain result of E' (which might be obtained, for example, by squandering income on lottery tickets) to the uncertain result between B and C.

The need for Series FF stock, which was pioneered at The Founders Fund where I work, can be explained by assuming that entrepreneurs (in particular, company founders) bear a similar risk profile.  Series FF stock can be issued to founders in place of common stock when the company is founded.  But unlike common stock, at later rounds of financing, a portion of the Series FF stock can be sold (subject to board of directors approval) to a later-round investor, and converted into whatever series of preferred stock is being issued at that round of financing.  For example, if a company founder held a 25% stake in the company through Series FF stock at formation, that company founder could one or two years later choose to sell 10% of that stake (or 2.5% of the company) to a Series A investor.  The company founder would get cash equivalent to the 2.5% stake at the Series A valuation.  The investor would get a 2.5% stake in the company in Series A stock.  Why should this be preferred to the status quo, in which company founders (usually) keep their common stock until the company is either acquired or goes public?

Entrepreneurs are extremely leveraged in their startups, and take a relatively small salary for the amount of value they create.  What they get in exchange is the payout on their equity when the company hits liquidity.  Although the timeline from seed stage to liquidity is shortening in some areas, the period is still on the order of 10 years.  This presents a problem from the point of view of maximizing the value of a company when, 5 years in, the entrepreneur is under pressure from personal creditors at the same time she is entertaining acquisition offers from a larger company.  In that situation, the entrepreneur has a strong personal incentive to sell the company at a low (but certain) price now, rather than holding out for a better offer in the uncertain future.

Referring to the curve, if the average person (including the average entrepreneur) tends to be risk-averse at lower payouts and risk-preferring at higher payouts, then it makes sense for investors to compensate for that by (1) monitoring management through board seats, thereby avoiding the excessive risk-taking between points B and C that is probably more common at later-stage companies, and (2) offering some liquidity, thereby avoiding the excessive risk-aversion that is probably more common at early-stage companies.

Most venture capital investors are already doing (1).  Series FF is the first formal, concerted effort that I know of to do (2).

Update: From the hypothesis of periodicity, we can get a new insight into the Friedman-Savage curve.  Most often, I believe the concavity and convexity obatain over different temporal ranges.  What you get is a two-dimension surface, with time along the y-axis and utility along the x-axis.  What you're looking at a above is a cross-section in that curve at the inflection point.