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«A Capital Adequacy Buffer Model David Allen1 Michael McAleer2 Robert Powell3 Abhay Singh3 University of South Australia, and University of Sydney, ...»

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TI 2013-168/III

Tinbergen Institute Discussion Paper

A Capital Adequacy Buffer Model

David Allen1

Michael McAleer2

Robert Powell3

Abhay Singh3

University of South Australia, and University of Sydney, Australia;


National Tsing Hua University, Taiwan; Econometric Institute, Erasmus School of Economics,


Erasmus University Rotterdam, and Tinbergen Institute, The Netherlands, and Complutense

University of Madrid, Spain;

3 Edith Cowan University, Australia.

Tinbergen Institute is the graduate school and research institute in economics of Erasmus University Rotterdam, the University of Amsterdam and VU University Amsterdam.

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DSF research papers can be downloaded at: http://www.dsf.nl/ Duisenberg school of finance Gustav Mahlerplein 117 1082 MS Amsterdam The Netherlands Tel.: +31(0)20 525 8579 A Capital Adequacy Buffer Model* David Allen Centre for Applied Financial Studies University of South Australia and School of Mathematics and Statistics University of Sydney Michael McAleer Department of Quantitative Finance National Tsing Hua University Taiwan and Econometric Institute Erasmus School of Economics Erasmus University Rotterdam and Tinbergen Institute The Netherlands and Department of Quantitative Economics Complutense University of Madrid Robert Powell School of Accounting, Finance & Economics Edith Cowan University Abhay Singh School of Accounting, Finance & Economics Edith Cowan University October 2013 * The authors wish to thank the Australian Research Council, Edith Cowan University Faculty of Business and Law Strategic Research Fund, and the National Science Council, Taiwan, for financial support.

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In this paper, we develop a new capital adequacy buffer model (CABM) which is sensitive to dynamic economic circumstances. The model, which measures additional bank capital required to compensate for fluctuating credit risk, is a novel combination of the Merton structural model which measures distance to default and the timeless capital asset pricing model (CAPM) which measures additional returns to compensate for additional share price risk.

Keywords: Credit risk, Capital buffer, Distance to default, Conditional value at risk, Capital adequacy buffer model.

JEL Classification: G01, G21, G28

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Extreme credit risk had a devastating impact on global economic stability during the Global Financial Crisis (GFC). Unable to withstand the sheer weight of credit losses, the global banking sector was beset by capital shortages, and large numbers of bank failures. The Basel capital adequacy framework could not cope. Although Basel III has subsequently introduced stricter requirements, the standardized model which is used by the majority of US banks (Federal Reserve Bank, 2012) is still based on fairly static criteria such as credit ratings, which do not change with dynamic economic circumstances. In addition, Basel only provides minimum requirements and banks and regulators need to ensure that their capital buffers and regulation can withstand extreme economic circumstances. Wide calls have been made for capital models to be improved on aspects such as less complexity, greater standardization, better alignment to dynamic economic conditions, and less reliance on static credit ratings (see Kretzschmar, McNeil, and Kirchner (2010), Weber (2010) and Woo (2012)).

In this paper, we propose a novel Capital Adequacy Buffer Model (CABM), which meets all these needs, combining simplicity with high market responsiveness. It is based on a combination of the Capital Asset Pricing Model (CAPM) (Sharpe, 1964) and the Merton (1974) Distance to Default (DD) Model. CAPM is soundly entrenched in financial theory, estimating the additional share price return required to compensate for additional risk, as measured by the share’s Beta (β). CAPM’s beauty lies in its simplicity and effectiveness in pricing risk, and in its wide global acceptance. The Merton model, as modified by Moody’s KMV, is also widely accepted, with Moody's Analytics (2013) reporting use by more than 2,000 firms in over 80 countries including most of the world’s 100 largest financial institutions.

The beauty of the Merton model lies in its rapid response to market conditions, whereby market asset values can be measured even daily if required. CABM combines the benefits of both these models to provide a dynamic, highly responsive model which introduces a credit β to estimate capital buffers required for extreme credit risk. CABM captures CAPM’s strengths in its simplicity, and in in CABM’s application of the widely understood CAPM pricing techniques to capital measurement. From Merton, CABM derives its dynamic ability 3 to measure credit risk, which permits capital adequacy to be re-assessed daily. We compare CABM outcomes to actual impaired assets and defaults and find it to be highly accurate and very responsive to changing conditions. A sound, uncomplicated model like CABM, which can accurately estimate capital adequacy over a range of economic circumstances, is critically important to financial and economic stability.

The importance of the link between the volatility of market asset values of banks (measured by models like the Merton DD) and capital adequacy, has been emphasized several prominent bodies, including BOE (Bank of England, 2008), ECB (European Central Bank, 2005), and the IMF (International Monetary Fund (Chan-Lau & Sy, 2006)). BOE report that as bank probabilities of default (PDs) increase with deteriorating market conditions, so too does the chance of the assets needing to be liquidated at market prices. Therefore as PDs rose during the GFC, market participants changed the way they assessed underlying bank assets, placing a greater weight on mark to market asset values, implying lower asset values and higher capital needs for banks. Thus BOE sees the mark to market approach of a bank’s assets as a measure of how much capital needs to be raised to restore market confidence in the bank’s capitalization.

The ECB see a reducing DD as a useful measure of bank distress, and the IMF see DD in a bank context as “Distance to Capital” (DC), which indicates when capital has been eroded and needs to be restored. In line with this thinking by the BOE, ECB and IMF, our CABM shows what capital buffers are required to restore market confidence in volatile times. The link between volatility and credit risk is also highlighted by Bucher, Diemo, and Hauck (2013), who argue that economic volatility can drive the dynamics and stability of credit. The focus on capital buffers through our CABM is consistent with Basel III (Bank for International Settlements, 2011), which requires banks to hold countercyclical capital buffers.

The remainder of the paper is organized as follows. Section 2 describes our data and methodology. Section 3 examines applications of the CABM model and provides some policy prescriptions. Section 4 concludes.

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In order to demonstrate the model, we provide an example of a single loan asset as well as a portfolio of loan assets. Our portfolio consists of entities comprising the S&P400 mid-cap index, which provide a better mix of higher and lower credit ratings than a high-cap or small cap-index. We use only entities with external ratings from Moody’s Default & Recovery Database (so we can compare our outcomes to Basel as well as to actual defaults for each rating). This yields 177 entities across several industries, including aerospace & defense, banking, business services, consumer goods, capital equipment, chemicals, food & beverage, healthcare, insurance, leisure, media, metals & mining, real estate, retail, technology, transportation and utilities. Our period spans 10 years (2003 - 2012), encompassing a range of economic circumstances including pre-GFC, GFC and post-GFC years. We use the year end Moody’s rating for each entity and year. The assets, liabilities and daily equity information required to calculate DD are obtained for each entity from Datastream. To ascertain the accuracy of our model, we compare outcomes to Moody’s actual default data and to corporate delinquent loan percentages obtained from the U.S. Federal Reserve Bank (2013).

2.2 Our Capital Asset Buffer Model

In a stock market context beta (β) measures the systematic risk of an individual security with CAPM predicting what an asset or portfolio’s expected return should be relative to its risk and the market return. As CAPM is a widely used model, we will not explain it in detail, other than a brief summary and an explanation of our modifications. Within CAPM is the Capital Market line (CML), where additional volatility (σ) above a benchmark σ or market σ, needs to be compensated for by additional return above the risk free rate (Rf). This is shown

in Figure 1. For CML, E(Ri) is the expected asset return and E(Rm) is the market return:

E(Ri)=Rf+βi(E(Rm)-Rf) (1)

5 CABM follows a similar thought process to CAPM, but instead of extra returns compensating for share price volatility above a risk-free rate, we measure additional capital required to compensate for additional volatility in market asset values (measured by the Merton DD model) above a specified benchmark. There are some important differences between CAPM and CABM. It measures capital as opposed to returns, it incorporates the Merton model to measure volatility in market asset values as opposed to share price volatility and it uses a capital benchmark as opposed to a risk free rate. A further feature is that it also a default measurement model, as DD (see sections 2.3 and 3) can be measured from the CBL as Ki / σi.

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(2) CAPM’s CML is re-defined as the Capital Buffer Line (CBL) as shown in Figure 1, which

shows additional capital required for risky loan assets. Capital required (Ki) for asset i:


Additional capital required for asset i (Kai) to compensate for risk above the benchmark rate:


2.3 The Merton DD Model Volatility in our model is based on market asset value volatility as per the Merton (1974) Distance to default (DD) model. As the model is well documented, we only provide a brief summary of its key features to assist the reader. Key components of the model are equity (E), market asset values of the firm (V), debt (F) and fluctuations in market asset values (σV). The firm defaults when liabilities exceed assets. This equals the payoff of a call option on the firm’s value with strike price F. If, at time T, loans exceed assets, then the option will expire unexercised and the owners default. The call option is in the money where VT - F 0, and out the money where VT - F 0. As V-F is a measure of the firm’s capital, in our model V = F is the point where the lender has run out of capital. An increase in σV indicates capital erosion, which needs to be restored, as noted by BOE and IMF (see our introduction). Merton assumes that asset values are log normally distributed, and calculates DD (with µ being the

drift in asset values) as:

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There are different ways in which this “capital” numerator can be defined. Basel III has a risk-weighted capital calculation. Capital in an accounting sense is measured as book value of debts minus liabilities. Moody’s KMV (Crosbie & Bohn, 2003), find that in general firms do not default when asset values reach total liability book values, due to the breathing space given by long term liabilities. Thus KMV use current debt plus half of long term debt as the default point (so do we, when applying equation 5 in this paper). Gapen, Gray, Lim, and Xiao (2004) from the IMF, refer to “Distance to Distress” where the capital numerator is measured as market value of assets minus a specified distress barrier. Crosbie and Bohn (2003), provide

the following simplified equation:

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where K is the capital held as a percentage of the relevant asset or portfolio. If for example capital is 4% and σV is 2%, then DD is 2 standard deviations away from default. In our model, it is immaterial which formula is used to measure K, as long as the denominator is σV. This is because we are interested in the relative capital changes brought about by changes in σV, rather than absolute capital measures. Our benchmark capital (Kb) is the minimum capital which a bank is required to maintain, and any increase in the σV denominator requires a proportionately equal increase in the capital numerator to restore the DD.

To derive σV, we obtain daily equity returns per entity, and calculate the standard deviation of the logarithm of price relatives. Following the estimation, iteration and convergence procedure outlined by KMV (Crosbie & Bohn, 2003) and Bharath and Shumway (2008), we 8 derive asset value returns, allowing for correlation between returns as described by KMV’s Kealhofer and Bohn (1993). These figures are then applied to the DD calculation (equation 5). We measure µ as the mean of the change in lnV as per Vassalou & Xing (2004).

3. Applications of CABM

We commence our illustration with a single asset portfolio, using an entity from our dataset, Con-way, a transport company. Con-way was hard hit during the GFC through a combination of factors. This included volatility in energy prices and a meltdown of core industries that the company was reliant on such as housing, construction and automotive industries. Prices and margins came under severe pressure. Profits plunged from $147m in 2007 to $67m in 2008, and then to a huge loss of $111m in 2009. Although a small profit was achieved in 2010, which has been steadily climbing since, profits have never returned to pre-GFC levels.

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