Home runs, singles and strike outs in venture capital returns
Yesterday I posted a graph of the implied distribution of returns as an entrepreneurial firm increases its capital stock. Today I present one important piece of that picture: the probabilities of return “regimes.” First, the mixture model with mixing probabilities as a function of capital stock results in the following set of returns pdfs.
- Individual return regimes and full pdf
It is clear from the figure that the return regimes separate nicely into the outcomes “high,” “medium” and “low.” Venture capitalists like to call the outcomes in their portfolios “home runs,” “singles” or “strikeouts” and they typically set goals for proportions of each in their portfolio. The mean log returns and volatilities for each regime show extreme separation between the two tails.
Distribution of Returns by Regime
| Regime | ![E[\ln R]](http://s.wordpress.com/latex.php?latex=E%5B%5Cln%20R%5D&bg=ffffff&fg=000000&s=0 "E[\ln R]") |
 |
Probability |
|---|---|---|---|
| Home run | 231% | 123% | 20% |
| Break-even | -1% | 80% | 60% |
| Bankruptcy | -273% | 137% | 20% |
| Full Model | -9% | 112% | N/A |
Includes all returns observations. Estimated with sample selection and endogeneity corrections.
The mixing probabilities are a function of lagged capital stock, so I can plot the probability of each outcome for a range of dollars invested. Figure 2 below shows that the bankruptcy risk is constant across capital stock while the probability of a home-run is highest for small firms. Similarly, as firms raise more capital (and thus avoid bankruptcy) the most likely outcome becomes the “break-even” state with a 0% return.
- The probability of each regime as a function of capital stock
Tomorrow I will discuss the motivation — theoretical and statistical — for the mixture model and parameterization of the mixing probabilities.