Valuing Real Options without a Perfect Spanning Asset

The real options approach to corporate investment decision making recognizes a firm can delay an investment decision and wait for more information concerning project cash-flows. The well known models of McDonald and Siegel (1986) and Dixit and Pindyck (1994) value the investment decision as a perpetual American call option on the project value. The former specifies the equilibrium return via CAPM, whilst the latter, along with much of the literature, uses a replicating portfolio argument. This involves identifying a perfect spanning asset for the project value, often called a " twin security ". In this paper, we instead assume only a partial spanning asset can be found which is imperfectly correlated with project value. This is more realistic, as most real projects can only be partially hedged by traded securities and private risks are common. We find the value of the option to invest and the trigger level are both lowered (compared to the complete model) when the spanning asset is less than perfect, although the option to invest still has value even when there is no spanning asset at all. This implies the firm should wait to invest, but invest earlier than the complete real options model suggests. Investment should also take place earlier under our partial spanning model than under the model of McDonald and Siegel (1986). Both the McDonald and Siegel (1986) and complete models are special cases of our model, obtained when risk aversion tends to zero and when correlation approaches one, respectively. Despite this, we conclude that approximating via these classic models when correlation is high (or risk aversion is low), may lead to an incorrect investment decision. Thus, by taking private risks into account, the partial spanning model gives a much richer model of corporate investment decisions.