A time before which insiders would not undertake risk

TL;DR

This paper investigates how the overall minimum of the numeraire portfolio influences insider trading behavior, showing that risk-averse insiders would avoid risky investments before this point, highlighting its role as a market performance indicator.

Contribution

It introduces a novel link between the numeraire portfolio's minimum and insider trading timing, providing new insights into market behavior and risk aversion.

Findings

All wealth processes become local martingales when stopped at the minimum of the numeraire portfolio.

Insider traders would refrain from risky investments before the overall minimum of the numeraire portfolio.

The minimum point of the numeraire portfolio is uniquely significant in discouraging risky positions in complete markets.

Abstract

A continuous-path semimartingale market model with wealth processes discounted by a riskless asset is considered. The numeraire portfolio is the unique strictly positive wealth process that, when used as a benchmark to denominate all other wealth, makes all wealth processes local martingales. It is assumed that the numeraire portfolio exists and that its wealth increases to infinity as time goes to infinity. Under this setting, an initial enlargement of the filtration is performed, by including the overall minimum of the numeraire portfolio. It is established that all nonnegative wealth processes, when stopped at the time of the overall minimum of the numeraire portfolio, become local martingales in the enlarged filtration. This implies that risk-averse insider traders would refrain from investing in the risky assets before that time. A partial converse to the previous result is also established in the case of complete markets, showing that the time of the overall minimum of the numeraire portfolio is in a certain sense unique in rendering undesirable the act of undertaking risky positions before it. The aforementioned results shed light to the importance of the numeraire portfolio as an indicator of overall market performance.