Long Horizons, High Risk Aversion, and Endogeneous Spreads

Details Long Horizons, High Risk Aversion, and Endogeneous Spreads Long Horizons, High Risk Aversion, and Endogeneous Spreads

2011-10-06

arxiv.org/abs/1110.1214v1

Economy

Quantitative Finance

Portfolio Management

27 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1108.1167

Scientific paper

For an investor with constant absolute risk aversion and a long horizon, who trades in a market with constant investment opportunities and small proportional transaction costs, we obtain explicitly the optimal investment policy, its implied welfare, liquidity premium, and trading volume. We identify these quantities as the limits of their isoelastic counterparts for high levels of risk aversion. The results are robust with respect to finite horizons, and extend to multiple uncorrelated risky assets. In this setting, we study a Stackelberg equilibrium, led by a risk-neutral, monopolistic market maker who sets the spread as to maximize profits. The resulting endogenous spread depends on investment opportunities only, and is of the order of a few percentage points for realistic parameter values.

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