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Algorithmic trade execution has become a standard technique
for institutional market players in recent years,
particularly in the equity market where electronic
trading is most prevalent. A trade execution algorithm
typically seeks to execute a trade decision optimally
upon receiving inputs from a human trader.
A common form of optimality criterion seeks to
strike a balance between minimizing pricing impact and
minimizing timing risk. For example, in the case of
selling a large number of shares, a fast liquidation will
cause the share price to drop, whereas a slow liquidation
will expose the seller to timing risk due to the
stochastic nature of the share price.
We compare optimal liquidation policies in continuous time in
the presence of trading impact using numerical solutions of
Hamilton Jacobi Bellman (HJB)partial differential equations
(PDE). In particular, we compare the time-consistent
mean-quadratic-variation strategy (Almgren and Chriss) with the
time-inconsistent (pre-commitment) mean-variance strategy.
The Almgren and Chriss strategy should be viewed as the
industry standard.
We show that the two different risk measures lead to very different
strategies and liquidation profiles.
In terms of the mean variance efficient frontier, the
original Almgren/Chriss strategy is signficently sub-optimal
compared to the (pre-commitment) mean-variance strategy.
This is joint work with Stephen Tse, Heath Windcliff and
Shannon Kennedy.