Thursday, 16 October 2008

Risk capital when there is no government guarantee

Risk capital calculation is a commonly used way of deciding how much money a financial company should put aside to cover its risks. Risk capital may be calculated by working out what losses the company could make and what the chances are of making those losses. Then all the losses are ordered with smallest first, and the chances of each are added up going from the start, so that a "cumulative loss distribution" is calculated. The smallest loss which has a cumulative percentage bigger than a certain value is identified, and the company puts aside money equal to that loss. So a company might say that it will put aside money which covers the 95 percentage point, meaning that 95 percent of the time it has enough money to pay its losses.

This way of allocating capital is neat in the way it fits in with profit calculations. A financial company might decide it wants to make 25 percent income per year on its capital, and as it knows what the capital is, it can charge customers based on its profit target. The approach also works for individual contracts.

An alternative interpretation of the capital would be that if a company makes losses larger than the capital, it will go bankrupt or at least have to ask its owners for more capital. However, this is not entirely true in the financial sector, since part of the upper five percent of losses would arise from systemic problems, meaning that many financial service companies would be threatened with bankruptcy at the same time. In those circumstances, it is reasonable to assume that the government would intervene. So the coverage of losses at the capital allocation level is effectively higher than 95 percent, say 99 percent.

However, if it becomes clear that a government can not or will not intervene to protect against systemic problems, financial service companies may put aside more capital to protect against the 99 percent losses themselves. The 99 percent point can be far higher than the 95 percent point, as the diagram shows:

The probability of loss is on the y-axis, the risk capital is on the x-axis. Allocating at the 95 percent point, the company puts aside risk capital equal to a. At the 99 percent point, the risk capital is the much larger b. Such long-tailed distributions of risk are common in finance.

I suspect that risk capital adjustment in the presence of uncertain government guarantees is playing a role in contracting credit in Western economies.

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