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Comparing Value-at-Risk and Tail Conditional Expectation in Shortfall-Constrained Portfolio Selection

Daniel A. Akume


We compare Value-at-Risk (VaR) and Tail Conditional Expectation (TCE) as risk bounds in determining optimal portfolio strategies, in a Black-Scholes market. Our numerical procedure leads to an approximate solution to the problem, which enables us to verify that, be it Tail Conditional Expectation or Value-at-Risk, the imposition of the constraint curbs investment in risky assets in much the same way, despite TCE being a coherent risk measure
and Value-at-Risk not being coherent. Our numerical simulation also enables us to confirm that TCE takes a bigger numerical value than VaR to produce the the same limiting effect.


portfolio optimization, Value-at-Risk, quadratic utility, Tail Conditional Expectation.

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