A bank has assets of $100M, liabilities of $95M, and $5M of equity capital, and the banks profit over a given period equals the change in assets minus the change in liabilities. In other words, if

A = A^End - A^Beginning , etc., then Profit =A L.

1. Show that this profit definition is the same as the change in capital (C).
2. Assume asset and liability annual returns are normally distributed with respective means of 0.05 and 0.02, respective standard deviations of 0.15 and 0.04, and that these returns have a correlation of 0.20. What is the mean and standard deviation of annual profit?
3. Regulators want to be 99.9% confident that the banks equity capital is adequate for potential losses. Does the bank have enough capital with $5 million? If not, how much additional equity capital should regulators require?

NOTE: If $5M is not enough and you have to increase it, then A also increases so you have changed the risk and need another calculation.