From Unexpected Loss to Capital As we noted early on, economic capital is not a question of how much we have but rather how much we need (i.e.,how much capital is needed to support a particular portfolio of assets). The more risky the assets, the more capital will be required to support them.The question is: How Much Is Enough? After all, if we attribute more economic capital to one transaction or business, we have less to use to support another transaction or business. To answer the question, it is necessary

to know the target insolvency rate for the financial institution.

The question of the target insolvency rate is one that must be answered by the board of directors of the institution. It turns out that many large commercial banks are using 0.03%—3 basis points—as the target insolvency rate. It appears that the way they came to this number was asking themselves the question: “What is important?” The answer to that question turned out to be their credit rating—in the case of these large commercial banks, AA. Looking at historical, one-year default rates, the probability of default for an entity rated AA is 3 basis points. Once the board of directors has specified the target insolvency rate, it is necessary to turn that into a capital number. It would be so much easier if everything in the world was normally distributed. Let’s suppose that the loss distribution is normally distributed.

■ If the target insolvency rate is 1%, the amount of economic capital needed to support the portfolio is the mean loss (the expected loss) plus 2.33 standard deviations. Where did we get the number 2.33? We got it out of the book you used in the statistics class you took as an undergraduate. In the back of that book was a Z table; and we looked up in that Z table how many standard deviations we would need to move away from the mean in order to isolate 1% of the area in the upper tail.

■ If the target insolvency rate is 1/10 of 1% (i.e., if the confidence level is 99.9%), the amount of economic capital needed to support the portfolio would be the expected loss plus 3.09 standard deviations. If the loss distribution was normally distributed, it would be simple to figure out the amount of economic capital necessary to support the portfolio.