VAR, Probability-of-Ruin and their Consequences for Normal or Lognormal Risks

Despite the use of VaR as a means to control risk, using VaR can have the opposite effect. VaR is used by bank and insurance regulators more than any other risk measure. A value-at-risk (VaR) constraint on the probability that future firm equity value will be less than a floor, when the floor is zero, is also a constraint on the probability of ruin. A manager who maximizes his firm's expected equity value subject to a VaR constraint, when the firm is in bad financial health, may pay a premium for financial instruments that increase his firm's volatility and does the opposite when the firm is in good financial healths, so it's use may increase banks' volatility in bad economic conditions. Hence the use of VaR may increase the instability of the global banking network when the banking system when it is more vulnerable. This paper examines the cases where risks are multivariate normal or lognormal.