Playing with fire: banks’ distressed sales under solvency and liquidity constraints

Caterina Lepore and Jamie Coen

Many commentators on the global financial crisis identified ‘fire sales’ as one of the key mechanisms by which shocks to banks were amplified and transmitted across the wider financial system. When firms in distress sell assets held by other institutions at discounted prices, losses can spread through the financial system as prices fall, amplifying the initial stress. In a working paper published last year, we explored this mechanism by presenting a new model of fire sales. In doing so, we answer the following questions: Which types of financial shocks combine to produce fire sales? How can banks optimally liquidate their portfolios when forced to do so? How big a risk are bank fire sales?

There are two key reasons for a bank to sell assets in a stress: to raise cash to repay withdrawing creditors and to de-risk its balance sheet (for instance to comply with regulatory requirements). Since the crisis, regulators have strengthened banking regulation, raising solvency requirements and introducing new liquidity requirements. These regulations have the potential to influence how and when banks undertake fire sales.

Our work seeks to understand how banks’ fire sales are triggered, how they play out and the risks they might pose. Two innovations help us do this. Firstly, we include funding shocks as well as solvency shocks as potential triggers of fire sales. Secondly, while most existing models of fire sales assume firms sell assets following mechanical rules of thumb, we derive banks’ optimal liquidation strategies.

What we can learn from looking at data on banks’ cross-holdings of assets?

A natural first step is to look at which assets banks hold and how these holdings overlap. Selling an illiquid asset can cause large price falls, which leads to losses for banks holding the asset. So we’d be particularly concerned about fire-sale spillovers if UK banks had large cross-holdings of illiquid assets.

Reassuringly, cross-holdings in the UK banking system appear limited to the most liquid assets. Figure 1 takes instrument-level data on the seven major UK banks and plots the extent of portfolio overlap by asset class. The bulk of overlaps are in highly liquid government bonds. Banks have large holdings of corporate bonds, but typically only one or two banks hold the same instrument.

Figure 1: Cross-holdings of securities by UK banks in 2016

Note: Negative values represent short positions.

Hence we can rest assured that there are no risks from fire sales in the UK banking system and this is the end of the post. Wait a second – what if the system was subject to a stress and banks were to sell assets in response? Which assets would they sell and what would be the resulting losses? To answer these questions we need a model.

A model of bank fire sales

Our model begins with a shock to banks, whereby they face losses on their assets and/or their creditors withdraw funds. This shock might leave a bank with a problem which it needs to fix. Banks can take a number of actions in response to stress, like cutting funding or raising new equity. Here we assume they can only sell assets.

If it’s a solvency shock, the bank might fall below its capital or leverage requirement, in which case it will sell assets to deleverage. If it’s a funding shock, the bank may sell assets to raise cash to repay withdrawing creditors, or to restore its liquidity coverage ratio (LCR) to the level it targets. The LCR ensures banks hold sufficient liquid assets to cover outflows for a severe but plausible 30-day stress. The liquid asset buffer is intended to be usable – banks can fall below 100% in a stress and hence avoid fire sales. Nevertheless, in certain circumstances banks may be reluctant to use up their liquid asset buffers and sell illiquid assets instead.

Distressed asset sales entail price impacts which impose losses on other asset holders, amplifying and transmitting shocks across the system. The size of these losses depends on which assets banks sell. Existing work typically assumes banks sell assets in proportion to their initial holdings. We find it more plausible that banks choose which assets to sell in order to minimise losses.

Figure 2: A model of bank fire sales

We show that banks’ optimal strategies depend on the constraints they face. If leverage is the binding constraint, all banks care about is minimizing liquidation losses. Hence they sell assets that are liquid and which they hold in small amounts. In contrast, a bank faced with a risk-weighted capital constraint or that targets a certain LCR level must balance the liquidity of an asset with its effect on these ratios. For the capital ratio, selling assets with higher risk weights is most effective, but these assets tend to be less liquid. As a result, a bank seeking to improve its risk-weighted capital ratio would generally choose to sell less liquid assets.

Armed with this model, we can now assess the risks from bank fire sales in the UK. To do this, we need to take a stand on correlations between asset prices during fire sales. Figure 1 treats every asset as separate, ignoring correlations between similar assets. In what follows, we group together assets with similar characteristics and assume a perfect correlation between the prices of assets within each group, and zero correlation between groups.

What if UK banks were subject to a solvency shock?

Assume banks are subject to the Bank of England 2017 annual cyclical stress scenario (and increased intensities of this scenario) and they sell assets to maintain their capital ratios above minimum requirements. How large could losses from fire sales be?

If banks only faced a leverage requirement the losses they incurred due to fire sales, on top of the losses from the scenario itself, would be small. Losses are larger when they’re constrained by the risk-weighted capital ratio. This is because under these shocks our banks are more constrained by their capital ratios, and so sell larger quantities. Moreover banks sell less liquid assets when constrained by the capital ratio relative to the leverage ratio. Nonetheless, fire-sale losses due to solvency shocks are moderate – even when banks face both constraints losses never exceed 10% of aggregate equity.

Figure 3: Fire-sale losses following shocks to banks’ solvency, by binding requirement

Note: Equity denotes common equity Tier 1 capital. ACS denotes the Bank’s annual cyclical stress scenario.

Now we can rest assured that there are no risks from bank fire sales in the UK and this is the end of the post. Wait a second…

What if UK banks were to face a funding shock instead?

We base this scenario on the outflows scenario embedded in banks’ LCR requirement. We scale these outflows up and down to see how losses change with the severity of the shock. While regulators have stressed that liquid assets buffers should be used in a stress, banks may be reluctant to exhaust their buffers in certain circumstances. We therefore consider cases where banks defend an LCR above 100%, and where they allow it to fall to various levels below this.

For small shocks losses are minimal (Figure 4). UK banks’ liquidity positions are currently healthy, so they can absorb these shocks without being forced into costly fire sales. As the shock grows, more banks are forced to sell assets, and losses from fire sales can exceed 30% of banks’ capital in extremis. Losses are smaller when banks use their cash reserves and most liquid assets first, rather than seeking to protect their liquid asset buffers by selling illiquid assets.

Figure 4: Fire-sale losses following funding withdrawals, by LCR targeted by banks

Note: Equity denotes common equity Tier 1 capital.

Comparing Figures 3 and 4, it’s striking how much larger losses can be following funding shocks than following solvency shocks. While it’s hard to compare shocks of different nature, our model highlights one feature of bank behaviour that contributes to making losses following funding shocks more severe: there are some assets banks will never sell to improve their solvency. If it’s sufficiently illiquid and they hold enough of it, selling an asset would lead to losses so large that their solvency ratios would actually get worse. If all they care about is raising cash due to funding outflows then they may be willing to sell such an asset, even if it worsens their solvency ratios. These highly illiquid assets can cause large losses to the banking system. As a result losses under the worst-case scenario following funding shocks are larger than under solvency shocks.


Our work seeks to provide a flexible way of studying fire sales when banks are subject to different shocks and both solvency and liquidity constraints. We hope it can prove useful to regulators and academics seeking to model amplification mechanisms in a stress. Applying it to our banking system taught us some valuable lessons that are not obvious from banks asset holdings data. Firstly, it’s important to consider liquidity shocks when thinking about fire sales – ignoring this could mean significantly underestimating the likelihood and extent of contagion via fire sales. Secondly, ensuring banks’ regulatory buffers are used in times stress can be an effective way of minimising losses from fire sales.

Caterina Lepore works in the Bank’s Stress Testing Strategy Division and Jamie Coen works in the Bank’s Stress Testing Strategy Division and London School of Economics.

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