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Review of Quantitative Finance and Accounting

Erschienen in:

01.05.2011 | Original Research

A flow-based corporate credit model

verfasst von: Tsung-Kang Chen, Hsien-Hsing Liao, Chia-Wu Lu

Erschienen in: Review of Quantitative Finance and Accounting | Ausgabe 4/2011

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Abstract

The main purpose of this paper is to develop a flow-based corporate credit model. This model can concurrently and endogenously generate a firm’s multi-period probabilities of liquidity crunch and expected liquidity shortfalls. This study builds a state-dependent internal liquidity model that incorporates both systematic and idiosyncratic shocks into corporate internal liquidity dynamics. The flow-based credit model differs from structural form credit models in that it considers a flow-based insolvency rather than a stock-based one, and has a potential to capture short-term credit information. Additionally, it differs from both reduced form and traditional accounting-based bankruptcy prediction models in that it is able to provide multi-period expected liquidity shortfalls endogenously.

Vorheriger Artikel The advantages of using quarterly returns for long-term event studies

Nächster Artikel The reputation effect of venture capital

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Different from trading liquidity, internal liquidity is an indicator of a firm’s funding liquidity that describes the relationship between a firm’s available liquidity and obligation payments.

Kane (2006) mentioned that flow-based proxies (earnings and operating accruals), compared with book value-based proxies (normal earnings and abandonment value), should be relatively more useful in assessing the likelihood of emergence from distress.

The probability of liquidity crunch and the expected liquidity shortfall are analogous to the probability of default and loss given default in credit risk literature. However, liquidity crunch does not indicate a default event as defined in credit literature and the liquidity shortfall does not indicate an estimate of the loss when the liquidity crunch finally evolves into to a default event.

This line of study includes Black and Cox (1976), Geske (1977), Jones et al. (1984), Kim et al.(1993), Hull and White (1995), Longstaff and Schwartz (1995), Leland and Toft (1996), Collin-Dufresne and Goldstein (2001), Duffie et al. (2007) and Wang and Yang (2007).

These models include Jarrow and Turnbull (1995), Lando (1998), Duffie and Singleton (1999), Duffee (1999) and Unal et al. (2003), McQuown (1997) and so on.

Recently, many new modeling techniques applying artificial intelligence have been developed. Since they heavily rely upon computer programming, we do not include them in the classic models.

The classical statistical models also include Turetsky and McEwen (2001), Hillegeist et al. (2004), Butera and Faff (2006) and so on.

It can be referred to the representative interest rate equilibrium models, such as Vasicek (1977).

Idiosyncratic shocks relate to firm-specific characteristics and a firm’s policies of operating, financing, and investing activities.

The assumption is supported by the empirical examinations of Chen et al. (2009). They implemented goodness-of-fit tests on this internal liquidity indicator for publicly traded companies listed in NYSE/AMEX/NASADQ exchanges. Their results show that around 90% of the 656 sample firms each year do not reject the null hypothesis of normality at a significance level of 0.05.

This study assumes their dynamics as lognormal according to the non-negative characteristics.

Equation 2 is a general form for a mean-reverting Gaussian process. By the definition of Eq. 1, the expected value of a factor’s long-term mean (\( b_{{F_{jt} }} \)) in Eq. 2 is zero. However, when doing empirical analyses, because the estimated parameter of a factor’s long-tern average level is the joint-estimated result with the other two parameters (\( a_{{F_{jt} }} \)and \( \sigma_{{F_{jt} }} \)), the estimated result may diverge from the theoretical value in Eq. 1.

According to Sklar’s Theorem, if \( F( \cdot ) \) is a n-dimension cumulative distribution function with continuous margins F ₁, …, F _n, it has the following unique copula representation: \( F(x_{1} , \ldots ,x_{n} ) = C(F_{1} (x_{1} ), \ldots ,F_{n} (x_{n} )) \).

\( \begin{aligned} f^{p} \left( {L_{t}^{1} , \ldots ,L_{t}^{n} \left| {\tilde{F}} \right.} \right) & = {\frac{{\partial^{n} F^{p} \left( {L_{t}^{1} , \ldots ,L_{t}^{n} \left| {\tilde{F}} \right.} \right)}}{{\partial (L_{t}^{1} ) \ldots \partial (L_{t}^{n} )}}} = {\frac{{\partial^{n} C\left( {F_{1} (L_{t}^{1} \left| {\tilde{F}} \right., \ldots ,F_{n} (L_{t}^{n} \left| {\tilde{F}} \right.)} \right)}}{{\partial \left( {L_{t}^{1} } \right) \ldots \partial \left( {L_{t}^{n} } \right)}}} \\ & = {\frac{{\partial^{n} C\left( {F_{1} (L_{t}^{1} \left| {\tilde{F}} \right., \ldots ,F_{n} (L_{t}^{n} \left| {\tilde{F}} \right.)} \right)}}{{\partial F_{1} \left( {L_{t}^{1} |\tilde{F} = F_{t}^{k} } \right) \ldots \partial F_{n} (L_{t}^{n} \left| {\tilde{F}} \right. = F_{t}^{k} )}}}\prod\limits_{i}^{n} {{\frac{{\partial F_{i} \left( {L_{t}^{j} \left| {\tilde{F} = F_{t}^{k} } \right.} \right)}}{{\partial L_{t}^{i} }}}} \\ & = {\frac{{\partial^{n} \left( {\int {\prod\limits_{i = 1}^{n} {F_{i} \left( {L_{t}^{1} \left| {\tilde{F}} \right. = F_{t}^{k} } \right)\int {f\left( {\tilde{F}} \right){\text{d}}\tilde{F}} } } } \right)}}{{\partial F_{1} (L_{t}^{1} \left| {\tilde{F}} \right. = F_{t}^{k} ) \ldots \partial F_{n} \left( {L_{t}^{n} \left| {\tilde{F}} \right. = F_{t}^{k} } \right)}}}\prod\limits_{i}^{n} {{\frac{{\partial F_{i} \left( {L_{t}^{i} \left| {\tilde{F} = F_{t}^{k} } \right.} \right)}}{{\partial L_{t}^{i} }}}} \\ & = \int {f\left( {\tilde{F}} \right){\text{d}}\tilde{F}} \prod\limits_{i}^{n} {f_{i} \left( {L_{t}^{i} \left| {\tilde{F}} \right.} \right)}. \\ \end{aligned}\)

Regarding investing cash inflows, they primarily include disposals of long-term investments and assets. They are not liquid and do not frequently happen. On the contrary, investing cash outflows are mainly capital expenditures. Since capital expenditures are necessary for maintaining stable growth, investing net cash flows are mostly negative. As a result, they have little influence on the cash inflow items.

Because that corporate financial (accounting) information on the financial industry is very different from that on non-financial industries, the current internal liquidity model is not able to be applied to financial firms. However, the current model should be applicable to financial firms after a redefining on the solvency ratio for financial firms.

The number of sample firms both with long-term and short-term S&P credit ratings is 54 and the number of sample firms only with long-term credit rating is 69.

The exception includes the three companies MDT, WY, CPB whose available complete data are only in the periods 1996–2004Q1, 1994–2002Q1, and 1994–2001Q1, respectively.

The estimation results are available from the authors upon request.

By the corresponding table of credit rating and cumulative default rates for each maturity, we can reasonably assign an appropriate credit rating according to a firm’s estimated PLC and the table.

The reason why this study divides the full sample firms into these four groups is that each range can correspond to its short-term credit rating. In other words, the firms with the above AA−, A ~ A+, BBB+ ~ A−, and below BBB rating have the same their corresponding short-term credit ratings, respectively.

For the first two groups, above AA− and A ~ A+, their lower bounds of one-year default rates are 0.03 and 0.06% based on the S&P corresponding table, respectively.

Due to PLC and ELSR are highly-correlated in our sample, we then create a new factor, called flow-based factor by factor analysis and it can explain 99.851% of the sample variances.

That is, for four group scenario, the result of multinomial logit model 59.3% falls between the interval of correction classification rates of previous best and worst choice situation results 51.85 and 74.07%.; while similarly 77.8% is between 64.81 and 87.04% for three group scenario.

The variables include the Betas (4 proxies of interest coverage, operating margin, LT debt leverage, Total debt leverage, Market value, market model beta, standard error); Year dummy, Variance of MV; and the lower boundary for rating category.

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Titel: A flow-based corporate credit model
verfasst von: Tsung-Kang Chen
Hsien-Hsing Liao
Chia-Wu Lu
Publikationsdatum: 01.05.2011
Verlag: Springer US
Erschienen in: Review of Quantitative Finance and Accounting / Ausgabe 4/2011
Print ISSN: 0924-865X
Elektronische ISSN: 1573-7179
DOI: https://doi.org/10.1007/s11156-010-0186-z

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