Michael Ewens

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.

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			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.

Tomorrow I will discuss the motivation — theoretical and statistical — for the mixture model and parameterization of the mixing probabilities.

Warning: Preliminary Dissertation Results Below

My work on VC risk and return currently focuses on fitting a mixture model to the selection-corrected round-to-round returns data. This model can incorporate non-normality, skewness, kurtosis and outliers. Recently, I introduced lagged capital stock into the mixing probabilities through a multinomial logit model because analysis of the full model on “small” and “large” firms illustrated significant differences in results across firm size. With a continuous variable like capital stock, I can produce the estimated mixture pdf for a wide range of entrepreneurial firm sizes. The video below shows the progression of the selection and endogeneity-corrected (they are different!) mixture pdf.

[vimeo]http://www.vimeo.com/6393464[/vimeo]

The most dramatic change as firm size increases is in the right tail: larger firms have significantly more mass in the middle of the distribution. The underlying regimes match a world of “Losers,” “Winners” and “Break Even” as seen in the figure below.

3-regime VC returns

I have discovered that incorporating lagged capital stock into the mixing probability helps to separate the individual regimes. I will be posting some more information about my results later in the week.

Since March 2008, the S&P 500 is down 36%, the Nasdaq is down 32% and the Dow is down 35%.  Venture capital returns — proxied by exit rates — are down significantly more:

-There were just 68 M&A deals, the lowest total for a quarter since at least 1999. That’s 35% fewer deals than in the year-ago period.

-Liquidity – the amount of money generated in M&A deals and IPOs, if there were any - fell for the fifth straight quarter, plumetting 65% from a year ago to $3.2 billion. That is the lowest quarterly amount since the first quarter of 2003.

I am slightly more confident in the beta of 2.4 that I find in my VC returns paper.

Fred Wilson of Union Square Ventures asks:

But is 3x a good venture return? It depends entirely on the stage you invest in and your “batting average”.

As an economist, I also think it matters how long it took to earn this return.  Ignoring that, Fred explains his terms:

In VC parlance, the batting average is the number of times you make a successful investment divided by the total number of investments you make.

Depending on what types of investments you make — late stage (less risky) or early stage (more risky) — the expected batting average will be different.  In order to earn a respectable final return then, a low batting average has to include at least a couple of home runs to “make the fund”:

[I]f you are an early stage investor (like our firm Union Square Ventures), then it is a different story. I’ve said many times [...] that our target batting average is “1/3, 1/3, 1/3″ which means that we expect to lose our entire investment on 1/3 of our investments, we expect to get our money back (or maybe make a small return) on 1/3 of our investments, and we expect to generate the bulk of our returns on 1/3 of our investments.

Surprisingly, this division of returns looks very similar to the empirical results of the mixture model in my venture capital returns paper.  Some 1/3 of investments earn a positive mean return, while the remain earn a negative annualized return. The large positive alphas in the bottom 1/3 regimes have a negative expected return and significant systematic risk. Fred confirms that at least for early stage investors, outliers generate the bulk of the returns:

I’ve also said on this blog a bunch of times that we look for one investment to return the entire fund. In the case of our 2004 fund, that would be a $125mm return on one single investment.

Fred suggests that late-stage investors typically hit “100%” but have lower average returns. How can I reconcile these anecdotal facts with my paper’s results?  First, what Fred states are goals, not actual results.  Next, the final weights and returns look much like those earned by early-stage VCs rather than late-stage investors.  My model effectively averages across all VC investments, so the final mixture weights are across all stages and industries.   The model says something about the full population of VC investment opportunities that the average VC faces.

Ignoring investment skill or sorting, suppose that a VC simply draws from one of the three “bins” in the final mixture distribution.  My last draft suggests these are the possible outcomes:

66% of the time the investment will have a negative expected return (in an annualized sense).  However, once a VC chooses a bad “bin” they face an enormous amount of idiosyncratic risk, so they could earn a large return with a small probability.  I ran the mixture model separately for early and late-stage investments:

Here, the mixture weights suggest that again, 66% of investments have a negative expected return. Probability has shifted from the very low return state to the low return state. The last table shows the distribution of returns for late-stage investments:

Note: the low volatility and probability of the first stage may suggest a two-state, rather than three-state model.

For late-stage investments, only 38% have a negative expected return, while 52% “break-even.” The expected return to all late-stage investments is -%5 versus -15% for early-stage investments.  Late-stage investors earn higher average returns, face much less risk, but don’t have the same opportunities for outliers.  It is not immediately clear whether the late-stage estimates confirm the “100%” batting average , as the model’s final predict 50% of both late and early-stage investment lose money.  The implied cdfs of each sub-sample show that early-stage investments have much more left-tail risk:

The cdf for early and late stage investments

Do late-stage investors bat “100%”?  The data suggests the have less left-tail risk, a near zero expected return and low volatility.  Although presented for early-stage investors, the full population of VC returns looks much like the “1/3,1/3,1/3″ model proposed by Fred Wilson.