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Optimal Execution of Portfolio Transactions

Summary: Optimal Execution
of Portfolio Transactions
Robert Almgren
and Neil Chriss
December 2000
We consider the execution of portfolio transactions with the aim of
minimizing a combination of volatility risk and transaction costs aris-
ing from permanent and temporary market impact. For a simple lin-
ear cost model, we explicitly construct the efficient frontier in the
space of time-dependent liquidation strategies, which have minimum
expected cost for a given level of uncertainty. We may then select op-
timal strategies either by minimizing a quadratic utility function, or
by minimizing Value at Risk. The latter choice leads to the concept of
Liquidity-adjusted VAR, or L-VaR, that explicitly considers the best
tradeoff between volatility risk and liquidation costs.

We thank Andrew Alford, Alix Baudin, Mark Carhart, Ray Iwanowski, and Giorgio
De Santis (Goldman Sachs Asset Management), Robert Ferstenberg (ITG), Michael Weber
(Merrill Lynch), Andrew Lo (Sloan School, MIT), and George Constaninides (Graduate


Source: Almgren, Robert F. - Courant Institute of Mathematical Sciences, New York University


Collections: Mathematics