Abstract
We analyze the result of allowing a risk averse trader to split his order among risk averse market makers. We find that the market makers’ aggregate expected utility of profit can increase with the number of market markers and that the aggregate liquidity always increases with it. Despite this latter finding, we show that the cost of trading for the traders increases with the number of market makers as measured by their aggregate expected utility of profit. The larger the market makers’ risk aversion, the bigger that cost is. We also find that when the number of market makers tends to infinity, their aggregate expected utility of profit tends to zero. We also obtain that the market makers’ individual and aggregate expected utility of profit can increase with their risk aversion and that the trader’s expected utility of profit can increase or decrease with the market makers’ risk aversion. We offer a potential answer to the ongoing debate concerning the dealers’ competitiveness. Indeed, risk aversion reduces competition between market makers as it acts as a commitment for market makers to set higher prices. This commitment is higher the higher the risk aversion.
Highlights
The competition between markets and the result of that competition has received much attention in Finance
We find a counter-intuitive result that increasing the number of market makers, N, with whom the trader exchanges, can adversely affect the trader’s welfare and this despite the fact that the aggregate liquidity increases with N
This paper looks at the case where traders can split their orders among different market makers
Summary
The competition between markets and the result of that competition has received much attention in Finance. As a result of the first and second assumptions, risk neutral market makers set a price equal to the expected value of the asset given the market maker’s information and aggregate order flow This implies that market makers earn zero expected profit. Despite a higher price, the trader is willing to exchange on that market, as by splitting his order he reduces its overall impact on the price This implies that, due to their risk aversion, all market makers have an incentive to set less competitive price schedules. Their setting is similar to [2] with market makers setting price schedules as a function of the aggregate order flow before traders submit their orders They show that in equilibrium market makers cannot earn zero expected profits.
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