Ce chapitre reprend Funding Liquidity Risk from a Regulatory Perspective1 co- écrit avec Christian Gouriéroux.
Résumé. Dans la régulation bâloise, seule l’incertitude sur la valeur des actifs ou sur
le défaut des emprunteurs est prise-en-compte alors que l’incertitude sur le compor- tement des déposants ou des investisseurs au passif est négligée. Au contraire, nous considérons les risques à l’actif et au passif. Nous adaptons les mesures de risque usuelles, Value-at-Risk ou probabilité de défaut, pour distinguer les pertes dues à un besoin de liquidité des pertes dues à une difficulté de solvabilité. Appliqués à des données américaines, ces termes additionnels sont significatifs lorsque les chocs sur les prix et sur les volumes sont corrélés. Par conséquent, les réserves réglementaires pour le risque de solvabilité ne peuvent être établies indépendemment des réserves pour le risque de liquidité. Nous montrons comment fixer et gérer conjointement deux comptes de reserves pour limiter les différents risques.
Mots-clefs : régulation, risque de financement, besoin de trésorerie, solvabilité 2,
valeur-à-risque, gestion actif-passif.
Code JEL : G18, G01, E58, C58.
1. Nous remercions S. Darolles, C.P. Georg, A. Monfort and D. Shakourzadeh pour leurs com- mentaires et suggestions avisés.
This chapter is based on Funding Liquidity Risk from a Regulatory Perspective2
co-authored with Christian Gouriéroux.
Abstract. In the Basel regulation, only the uncertainty on the asset price or on
the default of borrowers is considered while the uncertainty about depositors’ or investors’ behaviors on the liability side is neglected. In contrast, we consider risks on both the asset and liability sides. We adapt usual risk measures, such as Value- at-Risk or Probability of Default, to disentangle the losses due to liquidity shortage from the losses due to a lack of solvency. Applied to US data, these additional terms are significant when shocks on prices and volumes are correlated. Consequently, the regulatory reserves for solvency risk cannot be set independently of the reserves for liquidity risk. We show how to set and manage jointly two reserve accounts to con- trol the different risks.
Key words: Regulation, Funding Liquidity Risk, Liquidity Shortage, Solvency 2,
Value-at-Risk, Asset/Liability Management.
JEL Code: G18, G01, E58, C58.
2. We thanks S. Darolles, C.P. Georg, A. Monfort and D. Shakourzadeh for insightful comments and suggestions.
IV.1
Introduction
In Basel 2 regulation the computation of the required capital is based on condi- tional measures of risk of a future portfolio value, such as the Value-at-Risk (VaR), or the Expected Shortfall (ES). This future value is defined on a crystallized portfo- lio: the portfolio allocation it kept fixed, whereas prices are uncertain. This practice accounts for the uncertainty on market prices (i.e. the market risk) as well as for the counterparty risk (i.e. the default risk). However, the assumption of crystal- lized portfolio has to be discussed more carefully, because volume changes are very different on the asset and on the liability sides. On the asset side, volume changes result from portfolio re-allocation managed by the financial institution according to the expected price movements. This first reason, that affects the asset side, is endogenous. On the liability side, volume changes result from modifications in the behaviors of customers and investors. This second source of variations in volume, which concerns the liability component of the balance sheet, does not depend on the management of the firm: the liability variations are exogenous. Therefore, a financial institution is exposed to shocks on price on its asset side and to shocks on volumes on its liability side. In this paper we focus on these exogenous shocks to show how they should be taken into account jointly with the shocks on prices. We explicitly consider the need for cash, that is the funding liquidity risk. Thus, from a regulatory perspective, we are going from a Basel 2 approach to a Basel 3/Solvency 2 approach common to banks and insurance companies.
Our analysis highlights funding and market liquidity risks as new factors for pre- dicting the default of financial institutions, in top of the usual market and credit risks. These factors have been identified by observers during the last crisis. For instance, in the mid-March 2008, Bear Stearns had an exposure to funding liquidity risk (through rollover mechanisms) of about $ 85 billions on the overnight market [Cohan (2010)]. Similarly in the months before its bankruptcy, Lehman-Brothers was rolling 25% of its debt every day through overnight repos. These heavy posi- tions on short-term debt generate a high funding liquidity risk [see the discussions in Brunnermeier (2009), Krishnamurthy (2010)]. Usually, these risks were man- aged by different divisions in the firms. For instance, VaR models accounting for the riskiness of trading portfolios are independent of liquidity analysis made by the Asset-Liability Management (ALM) department. Our first contribution to the risk management literature is to propose a flexible framework encompassing three classes of risks: market/credit risk (risk of losses on the asset side), funding liquidity risk (risk of losing creditors) and market liquidity risk (risk of losing value in selling illiquid asset). In that framework, we show how to decompose currently used risk measures into the usual term, that considers only solvency risk, and additional terms accounting for funding liquidity risk and market liquidity risk. This decomposition takes into account the interactions between these risks.
Our framework has to be compared with the standard literature on the link be- tween rollover risk and default risk for instance, which assumes that a unique simple default boundary is given [see e.g. Black and Cox (1976), Leland (1994), Leland and Toft (1996), He and Xiong (2012b), He and Xiong (2012a)]. Such an assumption is compatible with the basic analysis of solvency risk [Merton (1974)], but does not
IV.2. THE BALANCE SHEETS AND THEIR RESPONSES TO EXOGENOUS SHOCKS ON LIABILITY
capture the specificity of liquidity risks. We distance ourselves from this strand of literature by describing the different possible joint regimes of liquidity and solvency for a given firm. Loosely speaking, each regime is associated with a joint rating of the firm. The first rating accounts for the degree of liquidity distress while the second one accounts for solvency situation. Mapping these regimes leads us to dis- tinguish in the total risk what comes from a lack of solvency from a liquidity need. Therefore, we introduce a composite boundary of default which structure depends intrinsically on the exposures to the various classes of risk.
In this respect, we also complement the current Basel 3 approach that consider two independent default boundaries: a solvency boundary considering only market and credit risks, and a liquidity boundary dealing with funding and market liquidity risks (the so-called "Liquidity Coverage Ratio"). Since there are two major sources of risks, two regulatory reserve accounts have indeed to be introduced. Our second contribution is to discuss how to jointly manage these accounts and how to set the associated required capitals in a comprehensive approach.
The plan of the paper is as follows. In Section IV.2, we consider the impacts of the exogenous shocks on volumes on a simplified balance sheet and investigate how the balance sheet is quickly adjusted to avoid a short-term default due to a funding liquidity shortage. We first analyze a financial institution with an unlimited line of credit. In this framework, a lack of cash after the shocks on volumes requires the use of the credit line with an additional cost. When the credit line is of limited size, the financial institution can be forced to sell in a hurry illiquid assets, generating fire-sale phenomena. Selling in a hurry has a negative impact on value since illiquid asset are converted into cash with an haircut. In other words, the funding liquidity risk can generate a market liquidity risk and this effect may be reinforced by the liquidity spiral highlighted in Brunnermeier and Pedersen (2009). Sections IV.3 and IV.4 focus on the adaptation of risk measures to account consistently for the various risks. We first decompose the standard Value-at-Risk (VaR) to highlight the effect of the funding and market liquidity risks. We also introduce specific measures of the probability of using the credit line and of the magnitude of this use as well as measures of the probability of selling illiquid assets and the size of these sales. Application of these decomposition on US data shows that the liquidity terms are significant when shock on prices (asset side) and on volume (liability side) are corre- lated. Section IV.5 discusses the definition and the design of regulatory reserves. We derive the levels of required capital associated with these reserve accounts. In other words, we provide the bidimensional Probability of Default appropriate to a joint monitoring of solvency and liquidity. Section IV.6 concludes. Proofs are gathered in appendices.