# Credit risk for a living

All is well when credit risk is under control. A bank is surely supposed to know how to lend to creditworthy borrowers because it has all the bells and whistles the trade may require. And it certainly expects that some borrowers may stumble and fall on their timely debt service routines though a certain amount of optimism is a spicy seasoning to all businesses. Risk can come in all shapes and colors and a suitable coverage is needed.

Supervisors have agreed that capital is the primary means to financial stability being vitally linked to individual bank’s balance sheet resilience and the Basel group, an authoritative think-tank, has come up with prudential tools to ensure that banks hoards capital to withstand losses on loans and securities on their books. Internal rating systems – at least for the banks that use them – can lower capital requirements by opportunistically rigging – up to a certain extent, of course – certain parameters and the Basel based group has since long established well defined constraints to prop up balance sheet strength vis-a-vis credit risk.

Risk managers employed by banks love formulas and what they can hide behind them. Nevertheless, supervisors – enlightened by the Swiss based group – know their trade as well: in the formula below, where $UL$ is the unexpected loss component and where optimism works most – banks must apply a magnifying scalar ($\sigma$, now equal to 1.06) to their capital ratios so that they set aside enough capital to melt away concerns about their credit resilience.

$UL=\sigma \cdot b\left(LGD\cdot N\left(\frac{N^{-1}\left(PD\right)-w\cdot N^{-1}\left(0.001\right)}{\sqrt{1-w^2}}\right)-PD\cdot LGD\right)$

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