Valuing Real Options without a Perfect Spanning Asset
Professor Vicky Henderson, Bendheim Center for Finance, Princeton University

Abstract:
The real options approach to corporate investment decision making recognizes a firm can delay an investment decision and wait for more information concerning project cashflows. The classic model of McDonald and Siegel (1986) (see also Dixit and Pindyck (1994)) values the investment decision as a perpetual American option and in doing so, essentially assumes the real asset underlying the option is traded, or that there is a perfect spanning asset available. Most real projects however can only be partially hedged by traded securities. Our model relaxes this assumption and assumes only a partial spanning asset can be found.

In this model, we obtain in closed form the value of the option to invest and the optimal investment trigger level, above which investment takes place. These both depend on the correlation between project cashflows and the spanning asset, risk aversion of the firm's shareholders, and volatilities of project cashflows and the partial spanning asset. We observe that the value of the option to invest and the trigger level are both lowered when the spanning asset is less than perfect. This implies the firm should invest earlier than the classic models suggest.

Although the partial spanning model contains the classic model as a special case, it is much richer. In particular, there are situations where the classic model recommends the firm always postpones investment, whereas if a highly (but not perfectly) correlated spanning asset were assumed, the firm should invest at a certain trigger level.