Statistical arbitrage of coherent risk measures
John Armstrong and
Papers from arXiv.org
We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability if the market admits statistical arbitrage opportunities which we term $\rho$-arbitrage for a risk measure $\rho$. We show how to determine analytically whether such portfolios exist in complete markets and in the Markowitz model. We also consider realistic numerical examples of incomplete markets and determine whether expected shortfall constraints are ineffective in these markets. We find that the answer depends heavily upon the probability model selected by the risk manager but that it is certainly possible for expected shortfall constraints to be ineffective in realistic markets. Since value at risk constraints are weaker than expected shortfall constraints, our results can be applied to value at risk.
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