Our empirical study comprises of two parts, the first of which involves the analysis of the predictive ability of the BSM and DOC structural mode\s. We estimate the probability of fmns defaulting using the two models
,
and then use three validation methods to assess their respective predictive capabi\i句 In addition to providing an17 As noted earli缸" a total often explanatory variables are selected
18 A description ofthe variables is provided in Section 2.
124 Predicting the Default Risk of Firms:A Model with Safety Covenants
explanation of the results on the assessment of predictive performance, we also compare their performance on da旭 fordifferent forecast periods. In the second p甜。f our analysis, we provide an explanation of the reasons for the variances in the predictive capabilities of the two models through the variables relating to defaults by our sample firms.
4.1
Comparison of the PredictiveAbility
of the ModelsSince 吐le purpose of credit risk models is to predict 吐le fu仙repossibility of firms defaulting, we examine the predictive capabilities of the BSM and DOC models on our sample of firms during the two-ye訂 period prior to defaults by referring to their AUC, AR and KS vaIu賊"的 to determine whether the models can accurately predict these actuai defa叫ts.A comparison of the variances in the predictive ability of the two s仕uctural models for the different forecast periods is provided in Table 2 (Table 3) for one-year- (two-ye語)ailead default predictions. We find 由atthe cIoser
吐ledefault tin1e，世le better 也ediscriminant capability of the two s仕ucturalmodels in
de記ctingdefault ris
k,
and 也at 世le emphasis in the structural models is on real-time detection.GeneraIIy speaking, the AUC values ofthe BSM and DOC models both exceed 0.7, whilst the AR values are above 0.5 and 出eKS valu的 exceed0.4; these values show that the two s甘ucturaI modeIs have a certain degree of default prediction ability.19 The use of historical
da胞， stock price information or financi
aI statements that are too remote 企omthe debt ma切ritymay undermine the predictive abili妙。f也Gmodels because such data lack timeliness. 百le main advantage of the s的蛇肉ral
models is their ability to assess real-time stock market price da但 to de紀ct 也echanges
in the defauIt risk of firm月 thus，the above results demonstrate that s的lcturalmodels are more suitable for the measurement of default risk over shorter horizons.
According to the assumption of the traditional BSM modeI, defaults only
19 Hosmer 阻d Lemeshow (2000) note that in the relationship between the AUC value and the discriminant capability of the models, good discriminant capabi1ity is demonstrated by the models when the AUC value ranges between 0.7 and 0.8. Furthermore, according to Engelmann, Hayden, and Tasche (2003), AUC and AR have a linear conversion relationship;
that is, AR ~乞4UC-1 ， wi自由emodel being regarded 晶 havinggood discriminant capabi1ity when AR ranges between 0.4 and 0.6.
Chiao Da Management Review 均l.29 No. 1, 2009 125
occur at debt maturity. However
,
in the real wor1d,
many firms will often default long before the maturity of the debt; thus,
the barrier option model should be more consistent with the actual process of defaulting. By relaxing the assumption of the BSM model on the setting of 也e default point,
it is possible to observe defaults prior to the maturity of the 4ebt. Using the DOC model,
which treats company equity as a down-and-out call option on the firm's assets with a s甘ikeprice which is equal to 甘le face value of the debt, it is possible to derive a more general outcome.
In order to determine whether 也is general model is more effective 也an the BSM model in terms of detecting defaul怨， using the same ful1 samples, we compare the predictive capabilities of the two models with the predictive capability values listed in Tables 2 and 3. As the tables show，吐leDOC model has higher AUC, AR and KS values 由仙也e BSM model; thus, our study shows that the general DOC model has superior predictive ability to that of the 仕aditional BSM model, a resu1t which may be attributable to the fact that the structural models reflect the short-term situations in firms based upon real-time stock price data.
τbe BSM model assumes that the default time is at debt maωrity， which eliminates any possibility of e訂Iy defaults; as a result
,
there can be no early detection of companies with problems. In∞n甘ast，世le DOC model consid巴rs the default situation in the real world,
allowing defaults to 0ω，ur prior to debt maturity.τbus， in cases where there is a discernible excessive fal1 in the asset value of a fi訂n
over a certain period of time, there may be a greater likelihood of 甘æfi口n
defaulting prior to the maturity of由edebt; henc巴，the DOC model exhibits superior predictive ability to that of the BSM model.
To summarize, the structural models use stock price data to predict fi口n defaults.τbe c\oser the default time, the greater the information 血的 is factored into the stock pric旭 data; therefore, the s甘uctural models are better suited to short-term forecasting. Although the BSM model also exhibits good predictive ability, it remains necessary to strive to improve predictive accuracy，的sential1y
because firm defaults are detrimental to society as a whole
,
and any improvement in predictive accuracy can reduce such losses to society. The improved predictive ability of the DOC model constructed in this study could serve as the foundation126 Predicting the Dφult Risk of Firms:A Model with Safety Covenants
for ex-ante prevention of firm defaults by reducing the potential for huge losses resulting from such defaults
Table 2
Comparative Performance ofthe Two Structural Models for OnecYear Ahead Default Predictions
MHM 位
ctiBS扎4
0.7534 0.5069 0.4424
DOC 0.7799 0.5597 0.4591
Table 3
Comparative Performance of the Two Structural Models for Two-Y ear Ahead DefauIt Predictions
BSM DOC
AUC 0.6581 0.6692
AR 0.3162 0.3384
KS 0.3021 0.3118
4.2 Differences in the Predictive Ability of the Models
According to our previous analyses, the DOC model constructed in this study has superior predictive ability to that ofthe traditional BSM model. In order to gain a clear understanding of whether the variations in the predictive ability of these two structural models are statistically significant, w巳 goon to apply a paired sample test. As the results show, with regard to the measurement of default risk, the variations between the two models are statistically significant at the 5%
significance level.
We also caπY out a Tobit regression, exploring the factors relevant to fiπn
defaults and their inf1uence on such defaults, so as to observe the variations in the
Chiao Da Management Review Vol. 29 No. 1, 2009 127
predictive ability of the two models..20 u Prior to our analysis of the variations in the performance of the models, we first conduct a multicollinearity test on the explanatory variables used in 也e Tobit regression model. In accordance with the variance inflation factor (VIF) test, any variable with a VIF value of greater than 10 is gradually deleted until all ofthe VIF values in the model are below 10. After deleting all of the variables within the model with serious multicollinearity, eight explanatory variables are selected; these are: CACL, WCTA, CLTA, EBITOR,
SCAI
,
MVETL,
LLTA and VOL. We then carry out the Tobit regression analysis on these variables, with the results forming the input for the first regression equation in Tables 4 and 5.CLTA has statistical significance at the 1% level (with a positive coe伍cient)
in both the BSM and DOC models in the first regression equation, which indicates that firms with greater current liabilities have a higher probabili句 ofdefaulting.
MVETL has statistical significance at the 1% level (with a negative coefficient) in both the BSM and DOC models, which indicates that fi口ns with greater owned
capl個1 have better levels of protection for creditors' rights; thus the probability of defaulting is lower.
VOL also has statistical significance at the 1% level (with a positive coefficient) in both the BSM and DOC models
,
which indicates that greater stock price volatility will lead to greater uncertainty in investo詣， expec泊位ons of the firm's performance in fu個時，出的 theprobability of defaulting will be higher. LLTA has statistical significance at the 5% level (wi也 apositive coefficient) but only in the BSM model. Since LLTA in the DOC model does not have statisticalsignificanc巴， this indicates that the BSM model performs better than the DOC model in the measurement of non-current liabiliti的. If a firm has a higher ratio of long-term liabilities to total assets, this indicates that the capital structure of the firm is unstab 1巴，thus the probability of default will be higher.
EBITOR has statistical significance at the 1% level (with a negative
20 Referring to the previous section, defaul阻 canbe deterrnined based upon the predictive ability of the two structural models at one- and two-year-祉lead periods, with the perforrnance of the forrner proving to be superior; thus, we analyze the differences in the predictive ability of the models for one-year-ahead defàult probabili句 and the financial and market infonnation variables for one-year prior to the default.
128 Predicting the Dφult Risk of Firms:A 蛤del with Safety Covenants
coefficient) but only in the DOC model. Since EBITOR in the BSM model does not have statistical significanc巴，this indicates 出at the DOC model takes into account the profit-making characteristics ofthe finn when predicting its default risk. In other words, wh巳n the net profit m位gin is higher，也e con剖bution to profit is 趾gher for every doIlar of sales; thus
,
the profitωpability of 也E 祉m is higher and its default probability wiIl therefore be lower.To summarizc旱， when constructing the BSM model, only the liquidity variable (CLTA), solvency variables (MVETL and LLTA) and market information variable (VOL) 的 considered; when cons仕的ting 也eDOC model, in addition to considering the CLTA, MVETL and VOL variables，也e profitability index (EBITOR) is also considered. Based upon the differential analysis of the predictive ability of the BSM and DOC s仕uctural models examined in this study, along with the use of the Tobit regression model, we demonstrate that the variable constructs affecting the BSM model incIude the solvency variables and the
liq凶dity variable in the financial statements construct
,
as weIl as the market information variable in the stock priωcons仕uct.四levariable constructs affecting the DOC model include the solvency, liquidity and profitability variables in the financial statements construct,
and 址le market information variable in the stock price construct.Thus
,
during the construction of 甘le DOC model,
this study considers not only solvency factors, such as the matured debts and liquidity debts, and market information factors, such as stock price volatili臥 butalso the probability of default prior to the ma仙rityof the debts arising from a faIl in profitability; hen∞，世leDOCmodel may weIl demons甘ate improvements on the shortcomings of the traditional BSM model, which considers only the solvency and market information factors.
As compared to the traditional BSM model, the DOC modeI constructed in this study could he崢 in the timely identification of potential default situations within firms resulting from a reduction in profitabili旬 thus， it might have superior default prediction capabilities to 也at ofthe traditional BSM model. Not only does the DOC model offer the possibiIity of real-time detection over the traditional BSM model, but it also considers a wide range of financial situations.
The selection of the explanatory variables in the abovementioned Tobit
Chiao Da Management Revi，帥肘. 29 No. 1, 2009 129
regression equations is based upon the variables used in the literature on defau1t
predicti冊， as well as the analysis of the eight basic variables selected through the VIF process. Following on 企om our previous analyses, we adopt a robustness analysis to observe whether the explanatory power of the basic variables remains robust, incorporating the liquidity variable CASHTA, operating capability variable
ORA間， solvency variable E凹， scale variable SIZE and corporate governance variable CG, along with the non-financial AGE variable as the con仕01 variables.
1n order to observe whether the factors influencing default risk in the two
s仕uctural models remain stable, these control variables are inc1uded in the Tobit regression eq閥.tion constructed using the abovementioned basic variables. The
secondωthe seven也 regression equations in Tables 4 and 5 inc1ude the con仕01
variables in the regression results ofthe BSM and DOC models.
According to the results of 曲的eregression equations, current liabilities/total assets (CLTA), market value of equity/totalliabilities (MVETL), long-term liabi1ity ratio (LLTA) and stock pri.∞ volatility (VOL) 缸自由e variables respectively representing liquidity, solvency and marketability 扭曲e BSM model; these variables are found to have important explanatory power on thedefault risks estimated by the BSM model. Current liabilities/total assets (CLTA), net profit margin (EBITOR)
,
market value of equity/totalliabilities (M陀TL)and stock price volatility (VOL) are the variables respectively representing liquidi紗" profi個bili旬，solvency and marketability in the DOC mode1; these variables are also found to have important explanatory power on the default risks estimated by the DOC model.
In other words, following the inc1usion of也econ甘01 v訂iables，世lesignificance levels of the variables of the 趴ro S仕ucturalmodels are found to be largely consistent
wl也 theregression results of the equations containing only the basic variables in the frrst regre鉤的nequation in Tables 4 and 5.τnerefore， based upon the second-stage analysis undertaken in this paper
,
since the DOC model takes into aω:ount a wid巴rrange of factors than the BSM mode1 within the mode1 cons甘uctlOn process, we could conc1ude that the DOC model has superior predictive ability to that of the BSM model.
130 Predicting the D~伽lt Risk of Firms:A Model with Safety Covenants
5. Conclusions
To theωonomic system as a whole
,
it is important to have advance wamings of firm defaults; however, since the traditional market-based BSM s甘ucturalmodelassumes 也at defaults occur only at 也e maturity of the debt, thereby oversimplifying the process of defauItin皂， there is a discrepancy between this model and the actual process of defaulting in the real world. Accordingly, in this study, we use barrier option theory to consider a defauIt waming model that may better refl的t
the process of defaulting within the economic system. Our results show that as compared ωthe 甘aditional BSM s甘uctural model, which is based upon stock market prices, the DOC model constructed in this study has improved default waming capability. Thus, we propose the application of the DOC model to the measurement of default probability, under the intemal rating-based approaches of Basel II Accord
,
to establish a firm credit risk quantification index.This study not only evaluates the predictive ability of the two structural models, but also uses the censored Tobit regression model to examine the related factors expressed by the two models. The results reveal that the traditional BSM model considers only firm solvency and market information factors
,
whereas the DOC model places greater emphasis on profitability factors, thereby providing potentially be仕er forecasting of defaults. In the advance detection of defaulting firms, the BSM model considers only defaults resulting 企om debts not to be repaid on the maturity date; this method of risk assessment is too conservative and has predictive errors. In contrast,
with the DOC model established in this study serving as a market-based BSM model, it represents an effective default waming tool for determining default risk.As discussed in the preceding sections
,
this study presents important resul的that are worthy of further study. In terms of the research methodology, our relaxation of the settings of the BSM model provides the potential for the early detection of defaulting firms under safety covenants by setting up an exogenous barrier level that changes with time. Future studies could further discuss whether there is an endogenous barrier level in the duration period of the debt, and compare the results with those reported in this study. In the construction of the default
Chiao Da Management Review Vol. 29 No. 1, 2009 131
waming model, this study demonstrates that the DOC model has better default predictive ability; thus