12. (Change h") Suppose that a bank has position X that has a normal probability density. The value at risk is known to be V at the loss tolerance h. The bank plans to take some capital out of reserve, which would increase the VaR. The bank argues that the change would be acceptable if the required confidence level were only slightly increased. (a) Develop a formula that expresses implicitly, in terms of the inverse standard normal distribution function F, the amount that the loss tolerance must change to com- pensate for a change A in capital. [Hint: Express the result as the difference of two quantities.] 12. (Change h") Suppose that a bank has position X that has a normal probability density. The value at risk is known to be V at the loss tolerance h. The bank plans to take some capital out of reserve, which would increase the VaR. The bank argues that the change would be acceptable if the required confidence level were only slightly increased. (a) Develop a formula that expresses implicitly, in terms of the inverse standard normal distribution function F, the amount that the loss tolerance must change to com- pensate for a change A in capital. [Hint: Express the result as the difference of two quantities.]