Strategic Informed Trading and the Value of Private Information

Abstract: We consider a market of risky financial assets whose participants are an informed trader, a representative uninformed trader, and noisy liquidity providers. We prove the existence of a market-clearing equilibrium when the insider internalizes her power to impact prices, but the uninformed trader takes prices as given. Compared to the associated competitive economy, in equilibrium the insider strategically reveals a noisier signal, and prices are less reactive to publicly available information. Additionally, and in direct contrast to the related literature, in equilibrium the insider's indirect utility monotonically increases in the signal precision. Therefore, the insider is motivated not only to obtain, but also to refine, her signal. Lastly, we show that compared to the competitive economy, the insider's internalization of price impact is utility improving for the uninformed trader, but somewhat surprisingly may be utility decreasing for the insider herself. This utility reduction occurs provided the insider is sufficiently risk averse compared to the uninformed trader, and provided the signal is of sufficiently low quality.