Looking under the hood – The IRB formula

This post is irredeemably technical so stop here if that is not your interest. If you need to understand some of the mechanics of the formula used to calculate credit risk weighted assets under the advanced Internal Ratings Based (IRB) approach then the BCBS published a paper in 2005 which offers an explanation:

  • describing the economic foundations
  • as well as the underlying mathematical model and its input parameters.

While a lot has changed as a result of Basel III, the models underlying the calculation of Internal Rating Based Capital (IRB) requirements are still based on the core principles agreed under Basel II that are explained in this BCBS paper.

The notes in the linked page below mostly summarise the July 2005 paper with some emphasis (bolded text) and comments (in italics) that I have added. The paper is a bit technical but worth reading if you want to understand the original thinking behind the Basel II risk weights for credit risk.

I initially found the paper useful for revisiting the foundation assumptions of the IRB framework as background to considering the regulatory treatment of Expected Loss as banks transition to IFRS9. The background on how the RW was initially intended to cover both Expected and Unexpected Loss, but was revised such that capital was only required to cover Unexpected Loss, is especially useful when considering the interaction of loan loss provisioning with capital requirements.

Reading the BCBS paper has also been useful for thinking through a range of related issues including:

  • The rationale for, and impact of, prudential conservatism in setting the risk parameters used in the IRB formula
  • The cyclicality of a risk sensitive capital requirement (and potential for pro cyclicality) and what might be done to mitigate the risk of pro-cyclical impacts on the economy

If you have read this far then my summary of the BCBS paper and my comments /observations can be found here (and thank you).

I am not a credit risk model expert, so the summary of the paper and my comments must be read with that in mind. I did this to help me think through some of the issues with bank capital adequacy. Hopefully others will find the notes useful. If you see something wrong or something you disagree with then let me know.

“The End of Alchemy” by Mervyn King

Anyone interested in the conceptual foundations of money and banking will I think find this book interesting. King argues that the significant enhancements to capital and liquidity requirements implemented since the GFC are not sufficient because of what he deems to be fundamental design flaws in the modern system of money and banking.

King is concerned with the process by which bank lending creates money in the form of bank deposits and with the process of maturity transformation in banking under which long term, illiquid assets are funded to varying degrees by short term liabilities including deposits. King applies the term “alchemy” to these processes to convey the sense that the value created is not real on a risk adjusted basis.

He concedes that there will be a price to pay in foregoing the “efficiency benefits of financial intermediation” but argues that these benefits come at the cost of a system that:

  • is inherently prone to banking crises because, even post Basel III, it is supported by too little equity and too little liquidity, and
  • can only be sustained in the long run by the willingness of the official sector to provide Lender of Last Resort liquidity support.

King’s radical solution is that all deposits must be 100% backed by liquid reserves which would be limited to safe assets such as government securities or reserves held with the central bank. King argues that this removes the risk/incentive for bank runs and for those with an interest in Economic History he acknowledges that this idea originated with “many of the most distinguished economists of the first half the twentieth century” who proposed an end to fractional reserve banking under a proposal that was known as the “Chicago Plan”. Since deposits are backed by safe assets, it follows that all other assets (i.e. loans to the private sector) must be financed by equity or long term debt

The intended result is to separate

  • safe, liquid “narrow” banks issuing deposits and carrying out payment services
  • from risky, illiquid “wide” banks performing all other activities.

At this point, King notes that the government could in theory simply stand back and allow the risk of unexpected events to impact the value of the equity and liabilities of the banks but he does not advocate this. This is partly because volatility of this nature can undermine consumer confidence but also because banks may be forced to reduce their lending in ways that have a negative impact on economic activity. So some form of central bank liquidity support remains necessary.

King’s proposed approach to central bank liquidity support is what he colloquially refers to as a “pawnbroker for all seasons” under which the  central bank agrees up front how much it will lend each bank against the collateral the bank can offer;

King argues that

“almost all existing prudential capital and liquidity regulation, other than a limit on leverage, could be replaced by this one simple rule”.

which “… would act as a form of mandatory insurance so that in the event of a crisis a central bank would be free to lend on terms already agreed and without the necessity of a penalty rate on its loans. The penalty, or price of the insurance, would be encapsulated by the haircuts required by the central bank on different forms of collateral”

leaving banks “… free to decide on the composition of their assets and liabilities… all subject to the constraint that alchemy in the private sector is eliminated”

Underpinning King’s thesis are four concepts that appear repeatedly

  • Disequilibrium; King explores ways in which economic disequilibrium repeatedly builds up followed by disruptive change as the economy rebalances
  • Radical uncertainty; this is the term he applies to Knight’s concept of uncertainty as distinct from risk. He uses this to argue that any risk based approach to capital adequacy is not built on sound foundations because it will not capture the uncertain dimension of unexpected loss that we should be really concerned with
  • The “prisoner’s dilemma” to illustrate the difficulty of achieving the best outcome when there are obstacles to cooperation
  • Trust; he sees trust as the key ingredient that makes a market economy work but also highlights how fragile that trust can be.

My thoughts on King’s observations and arguments

Given that King headed the Bank of England during the GFC, and was directly involved in the revised capital and liquidity rules (Basel III) that were created in response, his opinions should be taken seriously. It is particularly interesting that, notwithstanding his role in the creation of Basel III, he argues that a much more radical solution is required.

I think King is right in pointing out that the banking system ultimately relies on trust and that this reliance in part explains why the system is fragile. Trust can and does disappear, sometimes for valid reasons but sometimes because fear simply takes over even when there is no real foundation for doubting the solvency of the banking system. I think he is also correct in pointing out that a banking system based on maturity transformation is inherently illiquid and the only way to achieve 100% certainty of liquidity is to have one class of safe, liquid “narrow” banks issuing deposits and another class of risky, illiquid institution he labels “wide” banks providing funding on a maturity match funded basis. This second class of funding institution would arguably not be a bank if we reserve that term for institutions which have the right to issue “bank deposits”.

King’s explanation of the way bank lending under the fractional reserve banking system creates money covers a very important aspect of how the modern banking and finance system operates. This is a bit technical but I think it is worth understanding because of the way it underpins and shapes so much of the operation of the economy. In particular, it challenges the conventional thinking that banks simply mobilise deposits. King explains how banks do more than just mobilise a fixed pool of deposits, the process of lending in fact creates new deposits which add to the money supply. For those interested in understanding this in more depth, the Bank of England published a short article in its Quarterly Bulletin (Q1 2014) that you can find at the following link

He is also correct, I think, in highlighting the limits of what risk based capital can achieve in the face of “radical uncertainty” but I don’t buy his proposal that the leverage ratio is the solution. He claims that his “pawnbroker for all seasons” approach is different from the standardised approach to capital adequacy but I must confess I can’t see that the approaches are that different. So even if you accept his argument that internal models are not a sound basis for regulatory capital, I would still argue that a revised and well calibrated standardised approach will always be better than a leverage ratio.

King’s treatment of the “Prisoner’s Dilemma” in money and banking is particularly interesting because it sets out a conceptual rationale for why markets will not always produce optimal outcomes when there are obstacles to cooperation. This brings to mind Chuck Prince’s infamous statement about being forced to “keep dancing while the music is playing” and offers a rationale for the role of regulation in helping institutions avoid situations in which competition impedes the ability of institutions to avoid taking excessive risk. This challenges the view that market discipline would be sufficient to keep risk taking in check. It also offers a different perspective on the role of competition in banking which is sometimes seen by economists as a panacea for all ills.

I have also attached a link to a review of King’s book by Paul Krugman