A conflict resolution strategy for capital allocation?

Ten years ago, a bank exiting a business because of regulatory capital constraints would have been unheard of. Today, it’s a different story. Since 2008, many banks have closed down or cut back businesses that were too expensive to keep on their balance sheet. Prominent examples of this include UBS’s decision to retreat from fixed income, and Deutsche Bank’s sale of a large portion of its credit default swap business.

Post-crisis reforms such as Basel III have significantly increased capital requirements in recent years, so it has become more important for banks to allocate the cost of regulatory capital to trading desks in a way that encourages them to minimise it.

This is no exact science, though. Nearly six years after the Basel Committee on Banking Supervision issued Basel III, capital allocation within banks is still an evolving area, with different types of capital charge often allocated in different ways.

“I believe this is the case for most banks; there is no coherent methodology to allocate different types of capital charges across the board,” says Yadong Li, head of trading book risk modelling in the quantitative analytics group at Barclays. “For example, a bank may be using standalone allocation for value-at-risk, Euler allocation for counterparty credit risk capital, and some other ad hoc allocation for standardised rules.”

Due to the lack of a consistent method of allocation, some businesses and trading desks argue for more favourable models that allocate lesser capital costs to them.

Lower capital requirements

Diversification effects mean the overall capital requirement for a bank should, in theory, be lower than the sum of individual capital charges across desks. Commonly used methods for capital allocation don’t take into account the organisational structure of banks, which distribute diversification effects between desks. Individual desks might be more interested in their own return on capital, because that number determines their own compensation and growth opportunities. That makes conflicts over capital allocation more likely.

“When a bank tries to decide what allocation methodology to use, every business unit or trading desk naturally enters that discussion with a strong incentive to tweak the allocation to their own favour, so their return on capital becomes better than the others,” says Li. “We have had experiences in the past where individual traders knew certain trades would reduce the overall bank’s risk-weighted assets, but they had no incentive to take on such a risk-reducing trade, because most of the benefit goes to the other desks.”

In a technical paper published recently on Risk.net, Organising the allocation, Li and his co-authors – Marco Naldi, Jeffrey Nisen and Yixi Shi – propose a capital allocation method that tries to tackle the problem by factoring in the organisational structure of a bank.

The authors do so by extending a common technique called the Shapley allocation, in which each business unit’s allocation is based on an average of incremental contributions to risk capital over all possible permutations of trades. Unfortunately, the Shapley allocation requires a high level of computational resources, because a large number of permutations of trades needs to be sampled – and big banks have millions of trades.

As a result, the authors propose their own modification called the constrained Aumann-Shapley method, which samples only book-level instead of trade-level permutations, making the calculations faster by three orders of magnitude. Because desk structure is one of the inputs to the process, the organisation of a bank’s business units is taken into account, which eliminates inconsistencies across different desks.

The method is superior to the Shapley allocation, believes one regulator who spoke with Risk.net. “This approach to capital and risk allocation avoids the counterintuitive results and numerical problems observed for the established approaches like Shapley value,” he says.

The consistency that can be achieved across desks has the potential to avoid conflicts and offers an easier way of understanding where the numbers come from. Barclays rolled out the technique earlier this year on selected risk capital metrics, says Li, and disputes between desks over capital allocation based on those metrics have stopped.

“If we find one methodology that is theoretically sound and works well for all capital metrics so that people have nothing to debate on, then the burden of proof is on anyone who wants to argue for a departure from the established method,” he explains. “They have to explain why they are not going for the standard method.”

In general, post-crisis rules are driving individual business units towards making decisions based less on their own self-interest and more on the overall impact on the bank. It’s not surprising there remain conflicts between business units and trading desks that want to try to swing things in their favour. But when it comes to capital allocation, the uniform standard approach outlined by Li and his co-authors looks like a good way to tackle such conflicts.