Registro de provisión de cuentas incobrables

As early as the study of Beaver (1968), the stock market has been recognized as a poten-

tial alternative to provide a superior source of information regarding bankruptcy probabil-

ity prediction. Shumway (2001) includes three market-driven variables: market size, past

stock returns, and idiosyncratic standard deviation of stock returns in his estimation model

Option-pricing models based on Black and Scholes (1973) and Merton (1974) (BSM) pro-

vide a natural starting point in extracting bankruptcy probability related information from

market prices. Equity can be viewed as a call option on the value of the firm’s future assets.

Equity holders are residual claimants of firm’s assets and determine when the firm declares

bankrupt. Under BSM framework, the strike price of the call option is equal to the face value

of the firm’s debt and option expires when debt matures. At maturity time, equity holders

will exercise the call option and pay off the debt holders if the firm’s assets value is greater

than the face value of debt, or let the option expire and declare bankruptcy if the value of the

firm’s assets is below the face value of debt. If the firm files for bankruptcy, the ownership is

transferred costlessly to debt holders. The payoff for equity holders is either the difference

between the value of firm’s assets and the face value of firm’s debt or zero otherwise. The

probability of each outcome is embedded in the BSM model. DenoteVE is the value of eq-

uity,VAis the value of firm’s assets,X is the face value of firm’s debt maturing intperiods,ris

the continuously compounded risk-free discount rate. Then the BSM European call option

formula, stated in terms of equity on a firm’s assets is

VE =VAN(d1)−X e−r tN(d2), (2.1) where d1= l nVA X +(r+0.5σ2A)t σA p t , (2.2) and d2= l nVA X +(r−0.5σ2A)t σA p t =d1−σA p t, (2.3)

N(d1) and N(d2) are standard cumulative normal probabilities ofd1 andd2, andσA is the

volatility of the value of assets. The probability that the option expires in-the-money at matu-

out-of-the-money, that is, the firm goes bankrupt. Equation (2.3) shows that the risk-neutral

probability of bankruptcy is a function of the distance between firm’s assetsVAand the face

value of the debt X, relative to the volatility of firm’s assets σA, which is referred to as the

distance-to-default.

Merton’s model is considered the first structural model3in assessing credit risk. Several

commercial vendors provide default probabilities based on option pricing models, KMV4

being the most famous. While the basic approach is similar to standard BSM model, the

implementation differs in several ways. KMV implemented a model developed by Vasicek-

Kealhofer (see Kealhofer (2003)) known as KV model. The model is a generalisation of BSM

framework and allows for various classes and maturities of debt. It assumes that the firm’s

equity is a perpetual option with the default point acting as the absorbing barrier for the

firm’s assets value. Bankruptcy occurs when the value of assets hits the default point. In-

stead of using the cumulative normal distribution to convert distance-to-default into default

probabilities, KMV uses an empirical distribution of actual defaults based on its large, pro-

prietary database. KMV also make proprietary adjustments to accounting information that

they use to calculate the value of debt. Other option-related studies include Cheung (1991),

Kealhofer et al. (1998), and Core and Schrand (1999).

The Merton model, however, is fairly parsimonious due to its rather restrictive assump-

tions, one being that default can only occur at the maturity of the zero-coupon bond. Subse-

quent studies have explored more appropriate default boundaries within structural frame-

work. Black and Cox (1976) introduced another approach that takes into account early de-

3_{In credit risk literature there are two main types of models that describe default processes: structural mod-}

els and reduced-form models. Structural models use the evolution of firm’s structural variables to determine time of default which is endogenously generated within the model; whereas in reduced-form models, default is exogenously determined. Reduced-form models do not consider the relation between default and firm’s eco- nomic and financial conditions. For the relevance of the purpose of this study, structural models are described in detail; for a review of reduced form models, see Elizalde (2006).

4_{KMV was acquired by Moody’s in April 2002. Before the merger, Moody’s model to assess default proba-}

bility is a hybrid one that combines BSM structural model and a statistical model determined on the basis of historical data. Details of the model can be found in Sobehart and Stein (2000).

fault possibilities. In their model, they assume an exogenously determined threshold level of

asset value, below which default occurs. In contrast to the Merton model, default can occur

at any time. The same idea was employed by Longstaff and Schwartz (1995). Alternatively,

default thresholds can be determined endogenously, which allows the stockholders to de-

cide when to default so that they maximize firm’s value. Examples are Leland (1994), Leland

and Toft (1996), and Anderson et al. (1996). The difference between exogenous and endoge-

nous default barrier models are in the assumption underlying the default decision. While

these studies focus on addressing early default issues, other studies try to relax one of the

Merton model assumptions by considering stochastic interest rates. Examples are Kim et al.

(1993), Nielsen et al. (1993), and Longstaff and Schwartz (1995).

Such market-based structural models provide an appealing alternative because it coun-

ters most of the criticisms about accounting ratio based models. It provides guidance about

theoretical determinants of bankruptcy risk and structure to extract information from mar-

ket prices. Market data should reflect all information contained in accounting data and

also contain information not in accounting statements, and it reflects investors’ expecta-

tions about a firm’s future performance and hence should be more appropriate in prediction

context. Market prices are less influenced by management than are accounting statements.

Over the past decade, both practitioners and researchers have examined the contribution

of the Merton model. The very first authors are practitioners employed by either KMV or

Moody’s before they merged. Falkenstein and Boral (2001) find that the Merton model is a

powerful measure of default risk, and Kealhofer and Kurbat (2002) show that the model out-

performs alternatives and it captures all information contained in accounting and agency

ratings. Other papers, including Sobehart and Keenan (1999), Stein (2000), Sobehart and

Stein (2000) argue that Merton-type models are not sufficient to predict bankruptcy proba-

with accounting ratios and agency ratings, an example is Moody’s hybrid model in Sobehart

and Stein (2000).

A number of studies have addressed empirically the relevance of accounting-based mod-

els and market-based models in explaining bankruptcy. Shumway (2001) develops a sim-

ple hazard model using three market-driven variables to determine firm’s bankruptcy risk,

and finds adding market variables on top of previously identified accounting variables helps

improve forecasting accuracy. Hillegeist et al. (2004) extend Shumway’s method by using

Merton’s option model in a discrete hazard framework to examine the predictive ability of

accounting-based variables. They take into account dividend rate and replace the continu-

ous compounded risk free rate by continuous compounded expected return on assets,µ, to adjust for actual risk. In order to estimate BSM bankruptcy probability,VA,σA,andµmust

be estimated since these values are not directly observable. Hillegeist et al. (2004) estimate

VA andσA by simultaneously solving equation (2.1) and the optimal hedge equation, and

the estimates ofVAare then used to estimateµ. They find that traditional accounting-based

variables do not add incremental information beyond standard option variables. Another

study by Vassalou and Xing (2004) uses a similar approach that adopts an iterative proce-

dure to estimateVAandσA. However Vassalou and Xing (2004) do not adjust for dividends,

and as pointed out by Hillegeist et al. (2004), their method for calculatingµoften results in negative numbers which is inconsistent with asset pricing theory. Studies by Du and Suo

(2007) and Bharath and Shumway (2008) examine the model’s predictive power in a similar

way. While Hillegeist et al. (2004) find BSM model provides significantly more information

than Altman’s Z-Score and Ohlson’s O-Score, Du and Suo (2007) and Bharath and Shumway

(2008) have negative conclusions about the accuracy of the model forecast. Campbell et al.

(2008) estimate hazard models incorporating the BSM bankruptcy probability measure but

Though appealing as the structural model is over accounting-based models, it suffers

from a number of strict assumptions which are not true in reality. For example, it assumes

normality of stock returns, does not distinguish between types of debt, and assumes that

the firm only has a zero coupon debt and the default happens only at maturity. It is not

surprising that the empirical evidence on the performance of market-based models is mixed.