Journal of Risk

Optimal execution of portfolio transactions

Robert Almgren, Neil Chriss


The authors consider the execution of portfolio transactions with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. In the space of time-dependent liquidation strategies, the efficient frontier consists of strategies having the lowest expected execution cost for a given level of uncertainty; with a linear cost model this frontier can be explicitly constructed. It is then possible to select particular optimal strategies either by minimizing a quadratic utility function or by minimizing value-at-risk (VaR). The latter choice leads to the concept of liquidity-adjusted VaR, or L-VAR, which explicitly considers the best tradeoff between volatility risk and liquidation costs.

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