Investment, consumption and hedging under incomplete markets

Entrepreneurs often face undiversifiable idiosyncratic risks from their business investments. Motivated by this observation, we extend the standard real options approach to investment to an incomplete markets environment and analyze the joint decisions of business investments, consumption-saving and portfolio selection. We show that precautionary saving motive affects the investment timing decision in an important way. When the investment payoffs are given in lump sum, risk aversion accelerates investment. Moreover, when the agent's precautionary motive is strong enough, an increase in volatility may accelerate investment, opposite to the standard real options analysis. When the agent can trade the market portfolio to partially hedge against his investment risk, the systematic volatility is compensated via the standard CAPM argument, and the idiosyncratic volatility generates a private equity premium. When the investment payoffs are given in flows, the agent's idiosyncratic risk exposure alters both the implied option value and the implied project value, causing the reversal of the results in the lump sum payoff case.