hard · Market Microstructure
An Almgren-Chriss optimizer is calibrated for a trader with risk-aversion parameter lambda = 0.001 (in units of cost per share-squared). The optimizer determines that trading 500,000 shares over 5 days minimizes the sum of expected market impact and timing risk.
If the trader's risk aversion doubles to lambda = 0.002 while the stock's volatility and liquidity parameters remain unchanged, what is the most likely change to the optimal execution schedule?
- The trader slows execution, spreading shares over 10 days to reduce temporary market impact per period.
- The trader accelerates execution, concentrating more shares in earlier periods to reduce exposure to price-volatility risk, accepting higher temporary impact costs.
- The optimal schedule is unchanged because risk aversion affects the cost function's intercept, not the slope of the optimal trajectory.
- The trader switches to a TWAP schedule because the Almgren-Chriss framework no longer applies at higher risk aversion.
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