Joseph Noss and David Murphy
For some years, financial regulations have been becoming more complex. This has led some prominent commentators, regulators and regulatory bodies, to set out the case for simplicity, including Adrian Blundell–Wignall, Andy Haldane, Basel Committee and Dan Tarullo. In his contribution, Haldane illustrates how simple rules can achieve complex tasks: by simply adjusting its speed to keep its angle of gaze fixed, a dog can manage the complex task of catching a Frisbee. In this post, however, we argue that some financial risks are hard to catch with simple rules – they are more like a boomerang’s flight path than that of a Frisbee. Complex rules can sometimes do a better job at catching risk; and simple rules can be less prudent.
Simple rules have several advantages of course. They can be easier to draft, carry less risk of getting parameters wrong and have greater ability to withstand market adaptions, compared to their more complex counterparts. And complex rules sometimes encourage the regulated to manage to the rule rather than managing their risk. Moreover there is convincing evidence that prior to the crisis, some complex bank regulation – in particular, some aspects of the Basel II accord – had been implemented in ways that had loop-holes. When it became clear that these were being exploited investors lost confidence in the veracity of some banks’ risk weight calculations.
But just because some complex rules were flawed, it does not follow that all are.
When simplicity fails
To illustrate, we take a simple example of a problem faced by regulators a few years ago. In 2012, the Basel Committee sought to agree the appropriate capital treatment for exposures to cleared derivatives portfolios (and the CCPs clearing them). An example – in the case of a hypothetical portfolio – is given in Chart 1. Some of these positions are designed to profit from increases in interest rates of a given maturity, some from decreases (ie. they have either positive or negative exposures to a given directional move in rates). Notice that, in common with many such cleared portfolios, these exposures are ‘well hedged’ – that is, they consist of a large number of exposures to interest rates, of different – yet similar – maturities, with opposite signs. Providing interest rates of all maturities change to a similar degree, the overall change in the value of the portfolios will be far less than the sum of the absolute value of individual exposures.
Chart 1: A hypothetical swap portfolio
(1) Sensitivity of portfolio to a change in interest rates of a given maturity.
Basel’s regulators chose at the time to try applying a simple heuristic in calculating banks’ capital charges against such portfolios. They used a simple rule which had been designed for small directional portfolios, and applied it to the much larger, better hedged cleared exposures. The chosen approach was the Current Exposure Method, or ‘CEM’, a regulatory rule that calculated capital requirements using a simple fixed percentage of their total notional value.
This raised a problem. Whilst the risk of each individual derivative – that is, their sensitivity to changes in interest rates – was potentially large; put together, the risk of the hedged portfolio was, in aggregate, fairly small. But, in applying its simple methodology, the CEM cried wolf – and mistook the comparatively safe for the highly risky. Suddenly many portfolios that had never suffered material losses were subject to an enormous capital charge – so large in fact that it raised concerns that banks might be disincentivised from transacting such portfolios via a central counterparty all together.
But perhaps this was just a price worth paying for simplicity?
This might have been the case were simple rules always more prudent; but this is not the case.
To see why, consider what a better representation of the risk of such a large and ‘well hedged’ derivatives portfolio might look like. A key choice that a regulator need make is to what degree derivatives that profit from increases in one interest rate (say the two year rate) should be allowed to ‘cancel out’ or offset – risk from those that profit from a decrease in an interest rate of a similar – but not identical – tenor (say the three year).
Chart 2: Risk can be represented by different schemes of risk factors that differ in their granularity
At one extreme, the exposure of all derivatives could be totalled up in its entirety. Positive and negative exposures would be allowed to cancel out. This would result in a simple representation of risk by a single parameter or ‘risk factor’, as it is known, represented by the far-left bracket on Chart 2. This is a world of utmost simplicity. It also results in a lower risk measure: by allowing exposures of differing signs to cancel out fully, whatever their maturity, the regulator in effect assumes that any increase in interest rates will occur at all maturities simultaneously. In such a scenario, because positive exposures to rising rates would gain – and negative exposures lose – money to an equal degree, the overall change in the value of our hypothetical portfolio would be relatively small.
At the other extreme, the risk of every derivative could be considered separately, with the risk of the portfolio set equal to the sum of their absolute exposure, whether positive or negative. This, in effect, would be akin to a regulator ignoring the degree to which these, in reality, are likely to cancel out. This treatment is more complex, involving a far larger number of risk factors, as indicated by the bracket to the far right of Chart 2. All else being equal, this would result in a larger estimate of risk, though the calculation is also #more complex. It captures the possibility of how, at least in theory, two interest rates of very similar – but not identical – maturities could move by different amounts or even in opposite directions, meaning that the loss/gain seen on interest rates of one maturity would not be cancelled out by that on another.
Between these two extremes lies a continuum of possibilities of bucketing and offsetting. These can be organised using a taxonomy of different representations of risk. Different approaches can differ markedly in their measures of risk for the same portfolio, and, potentially, capital requirements. All else being equal a finer representation of risk, reliant on more risk factors, and a more realistic treatment of offsets leads to a more risk appropriate capital charge, but entails a more complex calculation.
This is of course just one example. But in principle what it reveals applies to the way risk is calculated on any portfolio. Rather like the flight path of the boomerang, the risk of the portfolio can be quite complex, and rather unintuitive. A more complex representation of risk can actually lead to a more prudent outcome.
This discussion highlights the key role of the parameters in regulatory rules. Regulators do not just have to make decisions about how to measure individual risks, they also need to decide how much to let different risks offset each other, and how much capital to prescribe banks to hold against the net amount. The complexity of a rule isn’t just the length of its text: it also relates to the number of parameters it contains. A good example here is the rules which are replacing the CEM. These use three buckets to represent interest rate risk in each currency: exposures to rates less than one year; from one to five years; and over five years. Some benefit is given for offsets between buckets, and the overall framework was calibrated using data including a period of stress. These rules are appropriately complex, capturing essential features of the problem at hand, but not having so many parameters that it is impossible to calibrate.
The question of what the ‘right’ measure of risk is, in situations such as this is a difficult one, requiring judgement. But it’s a judgement that requires a relatively complex view of the world, and one that accounts for the complexity of real portfolios with offsetting exposures.
Joseph Noss works in the Bank’s Capital Markets Division and David Murphy works in the Bank’s Financial Market Infrastructure Division.
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Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.