Asset Prices and Trading Volume Under Fixed Transactions Costs

Motivation(s)

There is a consensus among researchers that transaction costs in asset markets affect the trading behavior of market participants. However, how it affects market liquidity and asset prices in equilibrium are still in debate. Existing equilibrium models assume agents trade infrequently. This contradicts empirical HFT evidence and may underestimate the effect transaction costs on asset prices.

Proposed Solution(s)

The authors investigate the impact of fixed transaction costs on asset prices and trading behavior in a continuous-time equilibrium model in which two agents trade with each other to hedge their exposure to non-traded risk.

The notion of equilibrium in the stock market consists of

  • an equilibrium price process for the risky asset,

  • an allocation of the fixed transaction costs between buyer and seller, and

  • trading policies for both agents that consist of optimal quantities and optimal trade times for each agent that coincide with the other’s.

The proposed model serves as a bridge between the market microstructure literature (in which market making facilitates trading) and the equilibrium asset-pricing literature (in which risk sharing promotes trading). The agents must wish to trade the same quantities with each other at a certain price, and they must want to do so at the same time. One agent can bear a larger share of the cost to induce the other agent to trade earlier.

Evaluation(s)

The authors assume the agents and economy follow Brownian motion. They calibrate their model using historical data from CRSP and TAQ.

Their analysis shows that investors follow an optimal policy of not trading until their risk level reaches either a lower or upper boundary, at which point they incur the fixed cost and trade back to an optimal level of risk exposure. The expected time-between-trades is proportional to the fourth root of the fixed transaction costs. This implies a square root power law between trading volume and inter-arrival times.

While fixed costs do imply less-than-continuous trading and finite trading volume, the experiments found that an increase in such costs has only a slight effect on volume at the margin. However, the size of the illiquidity discount increases with the agent’s trading needs at high frequencies and is very sensitive to their risk aversion. As the agents’ endowment uncertainty increases, their “no-trade” region increases as well. This reduction in the agents’ asset demand leads to a decrease in the equilibrium price. The price decrease is approximately proportional to the square root of the fixed cost.

Note that the model assumes a perfect correlation between the dividend and endowment flows, which is likely to exaggerate the hedging motive. The fixed transaction costs do not differ across agents, and the model does not allow for an aggregate endowment component. The persistence of the endowment shocks in the proposed economy may increase both the illiquidity discount and the desire to trade.

Future Direction(s)

  • Instead of using Brownian motion to simulate the economy, would using the tick or minute orders to estimate the expected successful execution of a trade be equivalent or more accurate?

Question(s)

  • Are agents individual traders or firms? Does it matter?

  • The authors focus on continuous-time stochastic processes, but how much more effective is it compared to discrete stochastic processes?

  • Would backtesting with a set of agents parameterized by their risk aversion yield similar results?

Analysis

Small fixed transaction costs have a profound effect on volume, frequency of trades, and illiquidity premiums. Yet increasing it further does not compound that effect.

While it is good that the paper expanded upon the effects transaction costs induce, wouldn’t optimizing for execution costs already account for the effects of the fixed costs?

The analysis and derivations should be useful for future work, but the rest of the paper could be more succinct. The experiments would have formed a stronger argument if the authors focused on analyzing historical data instead of simulations. For example, the authors assume a fixed economy interest rate and justify that it will largely not affect the overall result. There are a lot of other simplifications that fail to make economy simulation preferable to historical order book data.

References

LMW01

Andrew W Lo, Harry Mamaysky, and Jiang Wang. Asset prices and trading volume under fixed transactions costs. Technical Report, National Bureau of Economic Research, 2001.