Private Equity Valuation under Model Uncertainty

The study incorporates model uncertainty into the private equity (PE) valuation model (SWY model) (Sorensen et al., 2014) to evaluate how model uncertainty distorts the leverage and valuations of PE funds. This study applies a continuous-time model to PE project valuation, modeling the LPs’ goal as multiplier preferences provided by Anderson et al. (2003), and assuming that LPs’ aversion to model uncertainty causes endogenous belief distortions with entropy as a measure of model discrepancies. Concerns regarding model uncertainty, according to the theoretical model, have an unclear effect on LPs’ risk attitude and GPs’ decision, which is based on the value of the PE asset. It also demonstrates that model uncertainty lowers the certainty-equivalent valuation of the LPs. Finally, we compare the outcomes of the Full-spanning risk model with the Non-spanned risk model, and they match the intuitive economic reasoning. The most important implication is that model uncertainty will have negative effects on the LPs’ certainty-equivalent valuation but has ambiguous effects on the portfolio allocation choice of liquid wealth. Our works contribute to two literature streams. The first is the literature that models the PE funds. The second is the literature introduces model uncertainty into standard finance models.