The Determinants of the Riskiness of Banks

Abstract

The authors argue that settling the issue of what reforms are required must be based on empirical evidence. They first set out the key bank risks, including those associated with collateralised agreements at the heart of complexity and interdependence problems. They point out that in normal times these risk positions mostly cancel out (one’s loss being another’s gain), but when risk is mispriced these positions become pro-cyclical, correlated and concentrated activities involving chains of counterparties that create interconnectedness risk. The authors choose bank distance-to-default (DTD) data as their dependent variable and show that 4 business model features have a much stronger impact on risk than any capital rule: the size of (un-netted) derivatives, the extent wholesale securities financing, the availability of liquid assets and a measure of interdependence.

Appendices

Appendix to Chapter 6: Modelling the Distance-to-Default

(for the technically interested)

The formula to calculate the DTD is derived from the option pricing model of Black and Scholes (1973) and is set out as follows:

$${\text{DTD}}_{t} = \frac{{\log \left( {\frac{{V_{t} }}{{D_{t} }}} \right) + \left( {r_{f} - \frac{{\sigma_{t}^{2} }}{2}} \right)\,.\,T}}{\sigma_{t} \sqrt T }$$

Where $V_{t}$ is the market value of bank’s assets at time t; $r_{f}$ is the risk-free interest rate; $D_{t }$, is the book value of the debt at time t; $\sigma_{t}$ is the volatility of the bank’s assets at time t; and $T$ is the maturity of the debt.

However, the market value of assets (V_t) and its volatility ($\sigma_{t}$) have to be estimated. Equity holders have the residual claim on a firm’s assets and have limited liability. Equity can be modelled as a call option on the underlying assets of the bank, with a strike price equal to the total book value of the bank’s debt. Thus, option-pricing theory can be used to derive the market value and volatility of bank’s underlying assets from equity’s market value (VE) and volatility ($\sigma_{E}$), by solving:

$$V_{t} = \frac{{{\text{VE}}_{t} \, + \, D_{t} {\text{e}}^{{ - r_{f} T}} N\left( {d2} \right)}}{{N\left( {d1} \right)}}$$

$$\sigma_{t} = \frac{{{\text{VE}}_{t} }}{{V_{t} }}\frac{{\sigma_{E,\,t} }}{{N\left( {d1} \right)}}$$

where

$$d1 = \frac{{\log \left( {\frac{{V_{t} }}{{D_{t} }}} \right) + \left( {r_{f} + \frac{{\sigma_{t}^{2} }}{2}} \right)\,.\,T}}{{\upsigma_{t} \sqrt T }}$$

$$d2 = d1\, - \,\sigma_{t} \sqrt T$$

VE: value of bank’s equity; N: the cumulative normal distribution; and $\sigma_{E}$: equity’s volatility.

A bank defaults (or is bankrupt) when DD_t equals to 0 (or is negative). All data are extracted from Bloomberg. The total annual debt liabilities (i.e. the difference between annual total assets and annual total equity) are interpolated using a cubic spline to yield daily observations (D_t). The volatility of equity $\left( {\sigma_{E} } \right)$ is the standard deviation of daily return multiplied by $\sqrt {252}$ (i.e. 252 trading days by year). The expiry date of the option (T) equals the maturity of the debt. A common assumption is to set it to 1. The risk-free interest rate $(r_{f} )$ is the 12-month interbank rate.

Model of GSIB Banks’ DTD

A panel regression approach is used to explain the differences in DTDs across banks over the period 2005–2011 (to the crisis) and updating to 2016 (see Table 6.1). The sample consists of GSIB commercial and broker-dealer banks. Six banks that failed in the crisis, but which can be considered as systemically important: HBOS, Merrill Lynch, Lehman Brothers, Washington Mutual, Wachovia and Bear Stearns are included. Japanese and Chinese banks are excluded as not involved in the 2007–2008 crisis. An OLS panel estimator with cross-sectional fixed effects is used. The DTD model is estimated with two alternatives for leverage: the simple leverage ratio and the Basel RWA concept (positive sign expected). Trading securities are the sum of the trading book and available-for-sale securities and are expected to have a positive sign (a liquidity buffer). Wholesale funding (liabilities other than deposits and long-term debt) is expected to have a negative sign. The gross market value of derivatives as a share of the banks’ total assets, but converting all US banks and one Swiss bank to the IFRS concept for consistency (a negative sign). Total assets of the bank are harmonised to IFRS concepts for all banks (a negative sign). Beta is the covariance of the firm’s stock price with the national stock market, using daily data to calculate annual observations, divided by the variance of the national stock index (a negative sign). The house price index refers to the annual percentage change in the national house price index (a positive sign as loan-to-value ratios fall with higher house prices).

Table 6.1 Model estimates: GSIBs