Estimating the risk–return profile of new venture investments using a risk-neutral framework and ‘thick’ models

Abstract

This study proposes cascade neural networks to estimate the model parameters of the Cox–Ross–Rubinstein risk-neutral approach, which, in turn, explain the risk–return profile of firms at venture capital and initial public offering (IPO)financing rounds. Combining the two methods provides better estimation accuracy than risk-adjusted valuation approaches, conventional neural networks, and linear benchmark models. The findings are persistent across in-sample and out-of-sample tests using 3926 venture capital and 1360 US IPO financing rounds between January 1989 and December 2008. More accurate estimates of the risk–return profile are due to less heterogeneous risk-free rates of return from the risk-neutral framework. Cascade neural networks nest both the linear and nonlinear functional estimation form in addition to taking account of variable interaction effects. Better estimation accuracy of the risk–return profile is desirable for investors so they can make a more informed judgement before committing capital at different stages of development and various financing rounds.

• risk-neutral framework
• risk–return profile
• financing rounds
• neural networks

• C13
• C31
• C45
• C53
• G17
• G11
• G24

Notes

1. Sahlman (1993) identifies three options for venture capital firms: the option to re-value an investment, the option to inject additional capital, and the option to abandon an investment.

2. Estimates of the risk-adjusted rates of return in Ruhnka and Young (1987, 1991) are: 54.8% for early stage, 42.2% for expansion stage, 35.0% for later stage of development of venture capital investments.

3. The following example illustrates the two approaches. Say there is an equal probability that cash flow payouts of a firm are $ 1 or $ 0 after one period. Assume that these cash flow payouts are risky. If the risk-adjusted discount rate is 20% the expected firm value is . This is the risk-adjusted expected firm value in present dollars. We can also obtain the $ 0.41 from the same original payouts, but risk-adjusting the probabilities of occurrence of each payout which we then discount at the risk-free rate. Suppose that the risk-free rate is 2.5%. We can calculate the expected $ 0.41 by solving the risk-neutral probability p in which is 42%.

4. See, for example, Hornik, Stinchcombe, and White (1989) and Cooper (1999) for details on the neural network methodology. Zhang, Patuwo, and Hu (1998) provide a survey of the literature on artificial neural networks.

5. See, for example, Billio, Sartore, and Toffano (2000), Dunis, Laws, and Evans (2008), and Franses and van Dijk (2000) for descriptions of this methodology.

6. Their sample consists of 597 observations of which 421 are venture capital financing rounds and 176 represent IPO financing rounds. The sample period only covers 1998 and 1999.

7. The sample distribution across industries is unclear in Seppä and Laamanen (2001) and could cast doubt on the generalizability and validity of their findings.

8. I thank Jai Ritter for making this data publicly available on http://bear. warrington.ufl.edu/ritter/ipodata.htm.

9. The sample firms show a decrease in firm value in 170 out of 3926 (4.3%) venture capital financing rounds, and 60 out of 1360 (4.4%) IPO financing rounds.

10. For applications see, for example, AlFuhaid and El-Sayed (1997) and McNelis and Yoshino (2004).

11. For a detailed discussion of the bootstrap method see, for example, Efron and Tibshirani (1993) or Hall (1995). Studies applying bootstrapping include, for example, Brock, Lakonishok, and LeBaron (1992), Kosowski, Naik, and Teo (2007), Kothari and Shanken (1997), Kothari and Warner (1997), etc.

12. They report a coefficient of determination of 0.22 to explain the risk-neutral probabilities.