What is the relationship between a markets-based measure of leverage and banks’ funding costs?

Kieran Dent, Sinem Hacioglu Hoke and Apostolos Panagiotopoulos

The Great Financial Crisis demonstrated an important feedback loop between banks’ capitalisation and funding costs. As banks’ capitalisation declined, banks’ wholesale creditors responded by demanding higher interest rates to lend to them. In turn, higher funding costs dented banks’ profitability, further weakening their capitalisation. Quantifying the relationship between funding costs and market-based measures of leverage – a proxy for bank solvency – is key to understand how banks might fare in a future stress situation – for instance as part of regulatory stress tests.

In a working paper, we show that modelling the relationship between banks’ market-based leverage and funding costs in a stress requires a non-linear econometric model. Our motivation is summed up in Chart 1 below. The horizontal axis shows the weekly ‘Market-Based Leverage Ratio’ (market value of equity over book value of assets – MBLR) of four major UK financial institutions between 2007 and 2016. We use MBLR as a proxy for market’s perception of banks’ solvency. The vertical axis shows these banks’ Credit Default Swap (CDS) spreads. Since CDS insure against banks defaulting on their unsecured debt, CDS spreads provide a useful proxy for banks’ marginal unsecured cost of funding.

It is immediately obvious that the relationship between the MBLR and funding costs is highly nonlinear. To see this, let’s first concentrate on the right end of the chart. At this point, banks are relatively well capitalised. And as the MBLR deteriorates – that is, as we move slightly to the left on the horizontal axis – CDS spreads increase only moderately. This suggests that bank creditors are not very sensitive to a bank’s capitalisation as long as it is high enough to make a default sufficiently remote.

Now let’s focus on the left end of the chart. Here, a small deterioration in the MBLR goes along with a much higher increase in CDS spreads. In other words, bank creditors are very responsive to a drop in banks’ market capitalisation if it enters at a low level.

Chart 1: Weekly CDS spreads (vertical axis) and Market-Based Leverage Ratio (horizontal axis) for four UK banks between 2007 and 2016

Despite this evidence, most existing empirical studies in this area have assumed a linear relationship between bank solvency and funding costs. Our paper adds to an emerging literature (for others see eg Aymanns et al (2016) and Korsgaard (2017)) that seeks to do justice to the apparent nonlinearity of this relationship.

In order to capture this potential non-linear relationship, we have estimated a smooth-transition panel model (introduced by Gonzalez et al (2017)) for the four major UK banks included in Chart 1. In this model, the relationship between two variables is not uniform. Instead, it depends on the level of a ‘transition’ variable. Here, given the evidence from Chart 1, we assume that the relationship between banks’ solvency and funding costs depends on the level of banks’ solvency. We estimate the model while controlling for other potential determinants of funding costs such as the risk-free rate, equity-price volatility and stock market volatility, and the bid-ask spreads of the CDS quotes to account for the liquidity premium component of CDS spreads. 

Table A and Chart 2 illustrate the key findings of the model. To highlight the benefit of our non-linear model, we start by estimating a traditional linear model of the relationship between solvency and funding costs. The result of the linear model is illustrated by the dashed orange line in the chart. We find that when a bank’s MBLR deteriorates by 100bps, its CDS spread increases by approximately 8bps. By construction, this relationship is independent of the level of MBLR and thus does not change over time and across banks. Moreover the linear model implies that the relationship between MBLR and funding costs is not very material.

Table A: The change in CDS spread conditional on different levels of Market-Based Leverage Ratio

MBLR levelChange in CDS
Point AMBLR > 4.7%8bps
Point BMBLR = 3%17bps
Point CMBLR = 2%43bps

Chart 2: The change in CDS spread as a response to a 100bps change in Market-Based Leverage Ratio

The easiest way to make sense of the non-linear results is to compare the points A, B and C in Chart 2. Table A summarises the change in CDS spread associated with a 100bps change in MBLR for each of these points. Starting on the right of Chart 2, point A shows that for a bank whose MBLR is 4.7%, a 100bps change in MBLR implies only an 8bps change in its CDS spread. This same relationship holds for banks with MBLR levels higher than 4.7%. At point B, however, where MBLR level is 3%, a 100bps change in MBLR implies a 17bps change in CDS spread. And as we move further to the left in the chart, the relationship between MBLR and CDS spread becomes steeper. At point C, where MBLR is 2%, CDS spread changes by 43bps with a 100bps change in MBLR.

This analysis, in combination with the visual evidence in Chart 1 indicates clear nonlinearities in the relationship between CDS spread and MBLR. Our interpretation of this evidence is that a small decline in the solvency of a highly capitalised bank is less likely to cause concerns about that bank’s solvency. However, if the solvency level of a bank decreases further, investors will increase the interest they demand to make their funds available to this bank. This will be reflected as higher CDS spread for that bank.

Looking at the results from another perspective, an improvement in the capitalisation of a highly solvent firm does not reduce its funding costs much. But if a bank starts with a low level of equity, an increase in its capitalisation implies a bigger reduction in their CDS spread. Linear models fall short of identifying such a relationship and underestimate the effect on market’s view of solvency on funding costs.

The non-linear approach we use provides an intuitive explanation for what banks experienced during the Great Financial Crisis and European debt crisis. The resulting model provides policymakers with a tool for considering how the funding costs faced by banks might respond to solvency shocks. Our results could also inform the debate about the appropriate level of minimum capital requirements, by identifying the solvency levels at which deteriorations in capitalisation and funding costs start to amplify each other.

Kieran Dent works in the Bank’s Monetary Analysis Division, Sinem Hacioglu Hoke works in the Bank’s Financial Stability Strategy and Risk Division and Apostolos Panagiotopoulos works for the International Monetary Fund.

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