Liquidity and Risk Management
This paper by Nicolae Garleanu and Lasse Heje Pedersen, formalizes the interaction between risk management and liquidity risk and especially the feedback loop from liquidity to tighter risk management.
The authors build on the over-the-counter (OTC) model from Duffie et al. (2005, 2007). In this model, two types of securities co-exist, a riskless security and an illiquid security. There are two types of agents, one with low tolerance for risk and one with high tolerance for risk. The type can change randomly according to a Markov chain.
Each agent has a risk management constraint that depends on his tolerance for risk and his holding of the risky security. A holding cost per share and per unit of time is imposed if this constraint is violated. In the “simple risk management” constraint, the risk of a position is calculated over a fixed period. In the “liquidity-adjusted risk management” constraint, the risk is over the time required for selling the security (the more illiquid a security is, the more binding is the constraint).
The trading is done OTC, meaning that it involves random searching of a counter party with some probability of success (the intensity reflects the liquidity). When two parties meet, the seller has a constant bargaining power. The seller will be an agent with low tolerance for risk.
In equilibrium, the asset price is equal to the present value of dividends minus a liquidity adjustment term. The more illiquid is the security the lower is the price. The liquidity discount increases with the share of low risk-tolerant agents.
Their main result is in Proposition 2: With high volatility of dividends, lower risk limit, lower switching intensity to high risk tolerance type, higher switching intensity to low risk tolerance type, the equilibrium position in the risky asset decreases, the search time increases and the price decreases. All these effects are larger with “liquidity-adjusted risk management”.
Intuitively, higher illiquidity increases search costs and imposes a tighter risk management that reduces positions and increases search costs and the illiquidity.
These results seem to be verified in practice (see for instance {ln:Limited Arbitrage in Equity Markets} or {ln:Slow Moving Capital}) and is rather worrisome for the risk management of our financial system.
References:
Duffie, D., N. Garleanu, and L.H. Pedersen (2005), “Over-the-Counter Markets”, Econometrica, 73, 1815-1847.
Duffie, D., N. Garleanu, and L.H. Pedersen (2007), “Valuation in Over-the-Counter Markets”, Review of Financial Studies.
Garleanu, Nicolae Bogdan and Pedersen, Lasse Heje, "Liquidity and Risk Management" (February 2007). NBER Working Paper No. W12887 Available at SSRN: http://ssrn.com/abstract=961808
