Today is the 10th anniversary of Lloyds TSB acquiring HBOS. An awful lot has been written about this, but there has been comparatively little about why a regulatory approach that was implemented in early 2008, and which was meant to protect the bank from losing its capital with a probability of 1 in 1,000 years, failed so spectacularly only 9 months later. What went wrong?
The regulatory approach was the ‘Basel Advanced Internal Ratings Based’ (AIRB) regulatory capital model, the brainchild of a Federal Reserve Board official called Michael Gordy. Gordy adapted the credit default model originally devised by Oldrich Vasicek, a gifted Czech mathematician and probability theorist who had worked with the legendary Fischer Black and Myron Scholes at Wells Fargo Bank. At the time, the Federal Reserve Board was the leading voice for capital model reform, and Gordy’s paper supported their contribution to the Basel II consultative process. Here is the Vasicek formula as modified by Gordy:
K = LGD . [probability of unexpected default – probability of expected default ]
= LGD. [Φ(sqrt(1/(1- R)) . Φ-1(pd) + sqrt(R/(1-R)) . Φ-1(0.999)) – pd]
where K is the capital requirement for an individual credit, LGD the loss given default, Φ the cumulative normal distribution function, Φ-1 its inverse, pd is the probability of default and R is the ‘dependence on the economy in general’, as Vasicek called it. The hard-wired number 0.999 represents the 1 in 1,000 year probability. The appeal to regulators was that the capital requirement for each credit (or book of similar credits) could be aggregated to give an overall capital requirement for an entire credit book, not to forget the benefit of preventing the financial system from collapse for the greater part of a millenium.
There are too many problems with this approach to cover in one post. For example, the formula subtracts the expected loss based on the assumption that the expected loss has already been incorporated by the accountants into reserves so that capital already incorporates expected losses, in theory. But we don’t know whether the accountants have done this, even though they are required to: the accountancy operation of a bank is typically miles away from its capital management function, moreover it is run by accountants. So we already have a nonsensical distinction between the regulatory balance sheet assumed by the model and populated by the risk people, and the statutory balance sheet manned by the accountants. This is a fundamental flaw of Solvency II that we have discussed elsewhere.
Another problem is the assumption about the dependence R on the ‘economy in general’. What is this R? How do we measure it? How do we know that the dependence we have measured in the past, typically through a period of low defaults, is going to resemble the dependence realised during a period of catastrophe?
I shall discuss these problems later. The problem I shall focus on today is the probability of default. The whole capital management system of the world depends on it. If it is small, then capital available will be large. By the same token, the unexpected loss will also be small, so the capital required will be small. The solvency ratio (capital available divided by capital required) will then look healthy. But if the probability of default goes up, this drives the available capital down, and the required capital up, reinforcing the impact of pd on the solvency ratio.
Probability of default therefore has a leveraged effect on the capital system, yet it is notoriously hard to measure. Vasicek assumed that the effect of newly available information on asset value could be modelled by a geometric random walk. This is a standard assumption of modern financial theory. If so, the valuation of a credit portfolio does not depend on the judgment of some internal credit committee or skilled person, which was the way it had been done up until then (and still is). This is not because such a judgment is not important – it certainly is – but the judgment has already been made by the market, based on all currently available information about the company’s assets, and is already reflected in the company’s market value. This fact does not mean that the judgment is accurate in the sense that its implicit forecasts of default will be realised, but rather that no judgment by any person, committee or institution is likely to be superior. 1 This is a classic formulation of the so-called efficient markets hypothesis that emerged in the 1960s and 1970s.
However, it is far from certain that markets do reflect available information in this way. As I argued here, there can be information in the public domain (e.g. a regulatory report) that investors and analysts simply haven’t noticed. There can also be information in the private domain which could have an important impact on the company’s share price but which has not reached the public.
In the case of HBOS, one such secret was a book of Irish loans by the oddly named Bank of Scotland (Ireland). Not only was the risk of this book hidden from the market and the regulators, it was hidden even from the bank’s own head of credit risk.
An urgent meeting was called on the morning of Sunday 5 October 2008 attended by the Corporate Risk function and representatives of both Corporate and Group senior management to go through the impairment forecasts on a loan by loan basis. There are no minutes for this meeting and the Head of Group Credit Risk at HBOS has told this Review that he was ‘completely excluded’ from all decisions about Corporate impairments because of the concerns he had previously raised. 2
It was loan books like the Irish book that sunk HBOS. There was limited recovery of HBOS’s impairment losses. Up to 2013, 86% of losses totalling £39.6bn were written off as irrecoverable.3
So, returning to the exam question of why a model intended to prevent a bank from collapsing with the probability of in a thousand years failed in the same year it was implemented, it seems that it wasn’t the model itself, but rather the data fed into the model, primarily the estimated probability of default. This assumption depends entirely on the information available to the market, and is based on theories about free flows of information such as assumed by Vasicek. The problem with any such theory is the way that vested interests (and regulators) like to keep things secret. Information may want to be free, but it is often a hostage locked up a high security block. What is the probability, over one thousand years, that there won’t be a similar event such as HBOS, at any bank or insurance company, where information about potential losses is carefully protected from the market by those who have a commercial interest in doing do?
Quite low, wouldn’t you think? Yet the Gordy/Vasicek formula is still with us, buried under a pile of other trifling adjustments introduced by a succession of subsequent regulators. The Pillars of Basel are built on feet of clay.
References
Gordy, M. B. ‘A risk-factor model foundation for ratings-based bank capital rules’. Journal of Financial Intermediation 12, 3 (July 2003), 199–232.
PRA (2015a) ‘The failure of HBOS plc: A report by the Financial Conduct Authority and the Prudential Regulatory Authority, UK’, Published by PRA and FCA, November.
Vasicek, O. The distribution of loan portfolio value. Risk 15, 12 (2002), 160–162.