Insider Information, Arbitrage and Optimal Portfolio and Consumption Policies

Abstract

This article extends the standard continuous time financial market model pioneered by Samuelson (1969) and Merton (1971) to allow for insider information. The paper derives necessary and sufficient conditions for arbitrage opportunities of insiders and presents optimal portfolio strategies for investors having anticipative information. We prove that if the investment horizon of an insider ends after his initial information advantage has disappeared, an insider has arbitrage opportunities if and only if the anticipative information is so informative that it contains zero-probability events given initial public information. When it ends before or when anticipative information does not contain such events we derive expressions for optimal consumption and portfolio policies and examine the effects of anticipative information on the optimal policies of an insider. Optimal insider policies are shown not to be fully revealing. Anticipative information is of no value and therefore does not affect the optimal behavior of insiders if and only if it is independent from public information. We show that arbitrage opportunities allow to replicate arbitrary consumption streams such that the insider's budget constraint is not binding. Consequently, Merton's consumption-investment problem has no solution whenever investment horizons are longer than resolution times of signals and insider information contains events whose occurrence is not believed. If the true signal is perturbed by independent noise this problem can be avoided. But since in this case investors never learn the true anticipative information we argue that this does not capture an important feature of insider information. We also show that the valuation of contingent claims measurable with respect to public information at maturity is invariant to insider information if the latter does not allow for arbitrage opportunities. In contrast contingent claims have no value for insiders with anticipative information generated by signals with continuous distribution.