Destabilizing properties of a VaR or probability-of-ruin constraint when variances may be infinite
Despite the use of VaR as a means to control risk, regulations that constrain VaR can have an effect opposite of their intent: to increase risk taking by firms that are doing poorly. Hence VaR constraint regulations can have a destabilizing effect on the financial system. A VaR constraint on the probability that future firm equity value will be less than a floor is a constraint on the probability-of-ruin when the floor is zero. The marginal price of risk with this constraint is coherent and also additive. For a wide class of distributions, the firm--when it is doing poorly--may pay a premium for a lottery that will increase the risk of its portfolio and the opposite when the firm is doing well.
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