Rollover risk and credit risk under time-varying margin

Abstract

For a firm financed by a mixture of collateralized (short-term) debt and uncollateralized (long-term) debt, we show that fluctuations in margin requirements, reflecting funding liquidity shocks, lead to increasing the firm’s default risk and credit spreads. The severity with which a firm is hit by increasing margin requirements highly depends on both its financing structure and debt maturity structure. Our results imply that an additional premium should be added when evaluating debt in order to account for rollover risks, especially for short-matured bonds. In terms of policy implications, our results strongly indicate that regulators should intervene fast to curtail margins in crisis periods and maintain a reasonably low margin level in order to effectively prevent creditors’ run on debt.

Keywords:

• Funding liquidity
• Margin requirements
• Rollover risk
• Structural credit risk models

JEL Classification:

• G10
• G32
• G33

Acknowledgements

This work was jointly supported by the German Research Foundation through the project Modelling of market, credit- and liquidity risks in fixed income markets and the UTS Business School Research Funds. The financial support is gratefully acknowledged by the authors. We are grateful to Harry Scheule, Nan Chen, and Erik Schloegl for several helpful comments and suggestions. We also thank the participants at the IME 2014 in Shanghai and at the Financial Maths Symposium in Sanya, China, for several valuable remarks. Finally, we want to thank the editors and two anonymous referees for valuable comments and suggestions that helped to significantly improve our paper.

Notes

No potential conflict of interest was reported by the authors.

1 Margin, also called haircut, is a percentage cut from the value of assets that are used as collateral to borrow. For example, when a firm pledges assets worth 100 dollars as collateral but can only borrow 80 dollars, the margin rate is , meaning that 20% is sliced off from the assets’ value. Margin is dependent on both quality of collateral and moral hazard of creditors.

2 High-quality collateral such as high-rated bonds has small variation under normal market conditions. However, typical margins on asset-backed securities and structural products can be high as 20–25% even in normal times (see ‘The role of margin requirements and haircuts in procyclicality’, CGFS Papers, No. 36).

3 Former Federal Reserve Chair Ben Bernanke provided a definition in April 2012 at the 2012 Federal Reserve Bank of Atlanta Financial Markets Conference: ‘Shadow banking, as usually defined, comprises a diverse set of institutions and markets that, collectively, carry out traditional banking functions—but do so outside, or in ways only loosely linked to, the traditional system of regulated depository institutions. Examples of important components of the shadow banking system include securitization vehicles, ABCP conduits, money market mutual funds, markets for repurchase agreements (repos), investment banks, and mortgage companies’.

4 Our model investigates how a specific company can reduce its risk exposure to a funding liquidity shock and studies how the firm can benefit from a managed margin in distressed periods. The model, however, does not deal with the risky counterparty since we do not model the creditors that provide funding. Thus, our model cannot address quantitative easing and its implications in currency rate depreciation, inflation and many others. Taking these systemic effects into account is beyond the scope of this paper and is left for future work.

5 Our analysis can easily be extended towards a finer financing structure where a fraction of both short- and long-term debt is secured and the rest is unsecured. A finer debt financing structure would, however, only change the pay-off for both types of creditors. This would only shift the default probability as a funding liquidity default in our model is defined as an event where assets are not sufficient to collateralize short-term borrowing. Therefore, our main results, induced by an illiquidity default, would stay unchanged. Furthermore, we do not specify exactly the financing sources of the firm. Instead, we only assume that the short-term debt borrowing is colleteralized as is the case, e.g. in repos and commercial papers, which expose a firm to high funding liquidity risk.

6 The endogenized short-debt coupon incorporating liquidity risk has been studied in Lütkebohmert et al. (Forthcoming) and Schroth et al. (2014).

7 The reason is that in our setting a default due to extremely tight margin requirements occurs when the firm’s assets are not enough to sustain short-term financing profile. Hence, before defaulting, the firm would first use all available assets as collateral. If also a fraction of long-term debt is collateralized by some assets, the residual assets would be used as collateral for short-term debt resulting in a shift in the default probability.

8 If the firm’s expected mean return is a constant, denoted by , we can propose the market prices of risk to firm fundamental shock and margin shock as

respectively. The particular choice of market prices of risk maintains the geometric Brownian motion dynamics of the firm fundamental and the continuous GARCH(1,1) dynamics of the margin..

9 The countercyclical margin is motivated by the work of Adrian and Shin (2014) who show that leverage is procyclical and thus, margin as the reciprocal of leverage is countercyclical vs. the firm’s asset value.

10 Note that if some short-term creditors were to withdraw their funding for idiosyncratic reasons, the firm will always be able to find new creditors to replace them as long as there is no systematic funding liquidity shock.

11 See, e.g. ‘International banking and financial market developments’, BIS Quarterly Review December 2011, or ‘The role of margin requirements and haircuts in procyclicality’, CGFS Papers, No. 36.

12 The unconditional variance of is given by such that the unconditional standard deviation of margin is 9.6% (compare Barone-Adesi et al. 2005, equation (6) on p. 290, for reference).

13 Note that the expectation of is given by . Thus, the condition implies that or equivalently , where t is measured in units of years. Hence, the half-life can be computed as days.

14 Negative correlation means the firm fundamental value tends to be low when margin is high and vice versa. Total default probability, however, increases slightly in negative . This is because a default in our model is determined by both the firm fundamental value V and the collateral value . Further, the correlation between an illiquidity default and an insolvency default is determined by the correlation between V and .

15 There is no authoritative data on the use of haircuts/initial margins in the repo market in either Europe or the US. Table 1 in the research report published by Committee on the Global Financial System Study Group shows margin data in bilateral interviews in various financial centres with various market users, including banks, prime brokers, custodians, asset managers, pension funds and hedge funds. For reference see http://www.bis.org/publ/cgfs36.pdf.

16 Note that the difference in credit spreads across maturities in the baseline model is caused by simulation errors.

17 Based on TRACE bond transactions data, Bao (2009) finds evidence consistent with Huang and Huang (2003).

Additional information

Funding

This work was supported by Deutsche Forschungsgemeinschaft [grant number LU 1186/3-1]; UTS Business School Research Funds.