The Risk Capital Bank Lending Multiplier

Measuring bang-for-buck is crucial in cost-benefit analysis of government programmes. We need a reasonable bang-for-buck metric to evaluate the cost-benefit of NAMA and alternatives.

As I have argued in an earlier post, the main objective of NAMA is to increase risky lending to Irish businesses. This leads to an obvious cost-benefit metric for NAMA and alternatives: Euros of additional commercial lending by banks generated per Euro of risk capital provided to the banks by the government.  I will call this the risk capital bank lending multiplier.

How big is the risk capital bank lending multiplier of the NAMA plan? It should be substantially higher than the banks’ normal equity leverage ratio to justify government intervention. If the multiplier is less than 10, then some alternative, perhaps do-nothing as a cautiously sensible choice, is preferable.

The multiplier is not a comprehensive measure since the type of induced lending also matters.  If an injection of risk capital can induce the banks to change the composition of their loan books, with more high-risk entrepreneurial loans and fewer safety-first mortgages, this could be employment and growth-enhancing even if total loans do not increase.  The multiplier does not capture this but it is still a useful, partial measure of policy effectiveness.

Risk capital is not identical to equity capital, although providing new equity capital is one method of risk capital provision. When NAMA purchases risky loans from banks for cash, it is injecting risk capital into the banks. The government’s blanket guarantee on bank borrowing is also a type of risk capital injection into the banking system.

Different types of risk capital can be standardized by scaling them using a reward-to-variability ratio. So if NAMA purchases a portfolio of risky loans with annual volatility of 20 billion Euros and we assume an equity risk-to-variability ratio of 0.20 than this is equivalent to 4 billion Euros of equity capital. This is only a rough guide since volatility is not a uniformly reliable measure of risk.

NAMA, NTMA acting on behalf of NAMA, or a government agency should provide a credible case that the risk capital bank lending multiplier for the NAMA programme is large enough to justify the trouble and expense.



3 replies on “The Risk Capital Bank Lending Multiplier”

By volatility I mean the standard deviation of return. The reward-to-variability ratio (also called the Sharpe Ratio) is the annual expected return minus the riskfree return divided by annual standard deviation of return. William Sharpe is the one who used the informal term variability rather than standard deviation or volatility in his terminology. Most people call it the Sharpe Ratio. Obviously with a loan book especially a book of troubled loans the concept of the standard deviation of annual return is a bit difficult to measure. It would be necessary to get current market value of the loans, and consider the uncertainty about end of year market value after whatever happens during the year in terms of value discovery, add in the random cash flows during the year, to get realized return and hypothesize about how much uncertainty there is in that random return. It is important to consider that “thought experiment” to get a sense of how much risk the Irish state is taking on in this NAMA programme. When the Irish state takes on a large risky asset in exchange for cash, in uncertain times such as these, it is providing risk capital even if the NAMA exchange is “fair” in terms of cash value. Reward-to-variability ratio times standard deviation of return is one hypothetical way of measuring the “amount” of risk capital provided in such a transaction. Admittedly, this does not work that well for the blanket guarantee of bank borrowing since empirically reward-to-variability ratios tend to undervalue insurance-type instruments.

I suggest considering the following quantity for the ‘reward-variability’ ratio: annualized maximal Sharpe Ratio of the economy (say 0.7) x correlation between the risk taken (by NAMA/taxpayer) and the kernel that prices assets held by Irish taxpayers (this needs to be estimated or reflected upon).
This would give you the amount of equity-equivalent risk capital you are comitting per annum. If, as you suggest, you use 0.2 as the ‘reward-variability’ ratio in this calculation, you are implicitly assuming that NAMA risk exposure has a correlation of ca. 0.29 (= 0.2/0.7) with the kernel, which to me seems too low (if things go wrong, i.e. in real bad states of the world, the irish economy would be so hooked up to NAMA that correlation would be close to one, I think). So, your estimate of risk capital ‘absorption’ of NAMA (Eur 4 billion) might be a bit on the low side. Does it sound right?

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