John H. Cochrane1 Graduate School of Business, University of Chicago March 19, 2004
School of Business, University of Chicago, 1101 E. 58th St. Chicago IL 60637, 773 702 3059, firstname.lastname@example.org. I am grateful to Susan Woodward, who suggested the idea of a selection-bias correction for venture capital returns, and who also made many useful comments and suggestions. I gratefully acknowledge the contribution of Shawn Blosser, who assembled the venture capital data. I thank many seminar participants and two anonymous referees for important comments and suggestions. I gratefully acknowledge research support from NSF grants administered by the NBER and from CRSP. Data, programs, and an appendix describing data procedures and algebra can be found at http://gsbwww.uchicago.edu/fac/john.cochrane/research/Papers/. JEL code: G24. Keywords: Venture capital, Private equity, Selection bias.
Abstract This paper measures the mean, standard deviation, alpha and beta of venture capital investments, using a maximum likelihood estimate that corrects for selection bias. We can only measure a return when a ﬁrm goes public, is acquired, or gets a new ﬁnancing round. These events are more likely when the ﬁrm has achieved a good return, so estimates that do not correct for selection bias are optimistic. The bias-corrected estimate neatly accounts for log returns. It reduces the estimate of mean log return from 108% to 15%, and of the log market model intercept from 92% to -7%. However, log returns are very volatile, with an 89% standard deviation. Therefore, arithmetic average returns and intercepts are much higher than geometric averages. The selection bias correction dramatically attenuates but does not eliminate high arithmetic average returns: it reduces the mean arithmetic return from 698% to 59%, and it reduces the arithmetic alpha from 462% to 32%. I check the robustness of the estimates in a variety of ways. The estimates reproduce and are driven by clear stylized facts in the data, in particular the pattern of returns and exits as a function of project age. They are conﬁrmed in subsamples and across industries, and they are robust to several ways of handling measurement errors. I ﬁnd little diﬀerence between estimates that emphasize round-to-round returns and estimates based on round-toIPO returns, where we might see an illiquidity premium lifted. I also ﬁnd that the smallest Nasdaq stocks have similar large means, volatilities, and arithmetic alphas in this time period, conﬁrming that even the puzzles are not special to venture capital.
This paper measures the expected return, standard deviation, alpha, and beta of venture capital investments. Overcoming selection bias is the central hurdle in evaluating these investments, and it is the focus of this paper. We only observe a valuation when a ﬁrm goes public, receives new ﬁnancing, or is acquired. These events are more likely when the ﬁrm has experienced a good return. I overcome this bias with a maximum-likelihood estimate. I identify and measure the increasing probability of observing a return as value increases, the parameters of the underlying return distribution, and the point at which ﬁrms go out of business. I base the analysis on measured returns from investment to IPO, acquisition, or additional ﬁnancing. I do not attempt to ﬁll in valuations at intermediate dates. I examine individual venture capital projects. Since venture funds often take 2-3% annual fees and 20-30% of proﬁts at IPO, returns to investors in venture capital funds are often lower. Fund returns also reﬂect some diversiﬁcation across projects. Issues The central question is whether venture capital investments behave the same way as publicly traded securities. Do venture capital investments yield larger risk-adjusted average returns than traded securities? In addition, which kind of traded securities do they resemble?...