Comparing value-at-risk and tail conditional expectation in shortfall-constrained portfolio selection

摘要

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 same limiting effect.