PROBABILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD?

Transcription

1 Shemetov, Valery. Probability of Default in Cororate Economic Distress, or What Risk Does Market Reward?. ACRN Oxford Journal of Finance and Risk Persectives 5. (6): PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD? VALERY SHEMETOV Northern Virginia Community College Abstract: The article suggests a quantitative model describing develoment of a cororate economic distress when a firm is not burdened with a long-term debt yet. The model introduces new variables related to the crisis dynamics, market trend and volatility, and cororate features. For the economic distress left unattended and for the recovery stage when the firm tries to restore its stability, the robability of default as a function of time and roblem arameters is given, and the distance to default and the oint of no return for launching a recovery rogram are estimated. The model hels select the rogram minimizing the robability of default over a set of available recovery rograms. For a steady develoing cororation, it is estimated how much money can be withdrawn from the business for dividend ayments and other needs without exosing the cororation to an extra risk of default. In the aroximation of firms having no long-term debt, the model demonstrates the limits of validity of the Caital Assets Pricing Model. (JEL G3) Keywords: Cororate Economic Distress; Recovery Program; Probability of Default; Distance to Default; Sustainable Cororate Develoment; CAPM Introduction In this aer we consider develoment of a cororate economic distress which is usually the first stage of a more general and dangerous henomenon of the financial distress (see, for examle, Altman & Hotchkiss (6), Asquith, Gertner, et.al. (994), ibeault (98), Gordon (97), Wruck (99)). Following Gorbenko & Strebulaev (), we interret the cororate distress as a ermanent shock generated by an external/internal cororate event and setting a long-term adverse factor in a cororate business environment that makes the cororate return on assets (ROA) decrease over time. In a volatile business environment, the first stage of a crisis develos imercetibly for the comany during an incubation eriod making the comany loose recious time. If the cororation fails to identify the roblem and find an adequate resonse to it, the comany sustains ever-increasing losses whose cumulative effect threatens a cororate market osition and can lead to default. A good recovery lan launched romtly and imlemented strictly to the schedule minimizes ossible damages and has a good chance to restore cororate stability. The question is what characteristics the recovery lan must have to be good, and how they are related to arameters of the cororate business environment. 83

2 PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD? Crisis management focuses on the following issues:. Crisis recognition, i.e. registration of a mismatch between a current cororate strategy and a new environment trend germinated by external/internal events. Weak signals of the newborn crisis are concealed by fluctuations in the cororate environment; so, a comany must have an early diagnostics rocedure for detecting those signals as soon as ossible.. Crisis identification. The management team reviews the comany s business to diagnose the crisis, localize its causes, study their mechanisms, and estimate ossible threats and oortunities (Pearson & Claire, 998). 3. Develoment and imlementation of a recovery rogram. Any recovery rogram must meet secific challenges of a articular business and industry attern, and, therefore, cannot be comrehensively described here. However, all rograms have the following in common. The objective of a recovery rogram is getting a crisis under control with a minimal loss and robability of default. Decision-making occurs under ressure of losses, uncertainty, and time deficit. ecause of the uncertainty, only robabilistic estimations of a cororate develoment are ossible. Any recovery rogram starts with a delay about the crisis onset and has some efficiency in restoring cororate ROA. For a set of recovery rograms available, the team selects the best one and takes stes to its imlementation such as fundraising, making necessary organizational and oerational rearations, etc. When ready, the cororate team starts imlementation of the chosen lan trying to restore a safe business osition. 4. Post-crisis management. If the comany succeeds, the new strategy outlined in the crisis gets further develoment carrying the changes in organizational values, mission, structure, olicies, business rocesses to their logical conclusions. We share the Roux-Dufort s osition (7) that this holistic aroach can create a comany s new strategic osition in the market increasing its long-term survivability. In a crisis the cororate team meets a challenge: they must solve the roblem which is quite new and maybe even ill-structured in the current aradigm, and they must do it fast. ut how fast the cororate reaction must be, and how arameters of the comany, business environment, crisis, and recovery rogram affect the robability of survival the crisis, these questions still wait for their answers. This aer tries to answer them. For more than fifty years of intensive study of financial distress, a lot of techniques have been develoed redicting cororate default based on the multivariate discriminant analysis (Altman, 968), logit and robit analysis (Asquith, Gertner, et.al., 994), cumulative sums methodology (Kahya & Theodossiou, 999)), neural networks (Salchenberger, Cinar, et.al., 99), genetic algorithms (Shin & Lee, ) and some others. All those methods belong to a set of classifying algorithms seeking for time-indeendent criteria for attributing a firm under consideration to a cluster of healthy firms or to a cluster of distressed ones. They do not consider dynamics of a cororate crisis and efforts the comany undertakes to survive it. Therefore, these methods cannot calculate the robability of default as a function of time and industry, comany, crisis, and recovery rogram arameters. Structural models estimating the robability of cororate default as a function of time from the creditor s oint of view are considered in many aers starting with the Merton s seminal work (974) (e.g. lack & Cox (976), Geske (977), Lando (998)). All those structural models use the otion ricing model develoed by lack & Scholes (97) and consider develoment of a default at a financially distressed firm as a Markov rocess (a rocess without rehistory). Financially distressed comanies, however, do have a rehistory due to their accumulated long- 84

3 ACRN Oxford Journal of Finance and Risk Persectives Secial Issue of Finance Risk and Accounting Persectives, Vol.5 Issue, March 6,.83-5 ISSN term debt. Therefore, strictly seaking, structural models describe the develoment of default of economically distressed firms having no long-term debt. The main difference of this aer from the creditor s aroach to the roblem of cororate default is that it considers a cororate distress from the inside using information which hel the team not only estimate the distance to default, but also choose a recovery rogram roviding for the highest robability of survival among all available rograms. Outecheva (7) determines a cororate default as an event occurring when (i) a comany fails to meet its financial obligations, (ii) a comany files bankrutcy, (iii) an exchange is distressed. This aer considers just the first two cases when a comany becomes unable to ay its obligatory ayments, or files bankrutcy. The following analysis is based on the assumtions: A) cororate ROA changes uniformly in a crisis A) market fluctuations are normally distributed, time-invariant, and delta-correlated with slowly changing (constant at the interval of the distress develomen arameters A3) a rate of cororate obligatory ayments is a iecewise constant function. Assumtion (A) reflects our aroximate descrition of a crisis. Of course, decrease in cororate ROA can vary during the crisis making cororate managers adjust a chosen recovery rogram to changing conditions. So, an anti-crisis rogram is not a one-time act, but a controlling rocedure reacting to the signals coming from the cororate business environment. Assumtions (A) and (A3) are discussed in Section. The remainder art of the aer is organized as follows. Section describes the model, considers develoment of cororate economic distress left unattended u to the moment of default, and estimates the distance to default. Section contains an analysis of a cororate recovery in a distress and estimates the robability of default during the recovery, the oint of no return, and the maximum tolerable delay for a recovery rogram securing a given recovery rate of cororate ROA. Section 3 considers conditions for a steady cororate develoment and estimates the effect of taxes and a dividend olicy on cororate long-term survival. Section 4 estimates the limits for changes in market risks and ROA that generate more free (unbounded) money for comany needs and dividend ayments. The last section contains a brief discussion of results and conclusions. Model Descrition A cororate strategy includes many comonents: strategic, financial, and organizational managements, marketing, etc. Its success results in a steady increase of cororate assets over a long-term eriod. For continuous time, asset dynamics x( can be symbolically resented by the model: dx [ r( n ( ] x (, x() x. (.) dt Function r( is cororate return on assets (ROA) at time t, ( is a rate of cororate obligatory ayments at time t including fixed oerating costs, long-term debts, R&D exenditures, marketing exenses, and all kinds of overheads like non-rofile assets, etc. We suose ( to be a iecewise constant function: 85

4 PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD?, t t,, t t t, (... (.) i, ti t ti,... here i is a rate of cororate obligatory ayment at interval [ t i, t i ). So, a comany s state at this interval is affected by continuing debt ayments, investments into R & D rojects, and also current obligatory ayments like fixed costs. Term n ( shows an effect of market fluctuations on cororate assets; it is suosed to be a normal random rocess with the roerties: (Aa) n ( m; (Ab) n ( is time-invariant and delta correlated: n ( t ) m][ n ( t ) m] C ( t ), t, t t ( t, and, t t ( t dt for any ε >. t [ t Constant C is a measure of the effect that market fluctuations make on cororate assets. Parameter C reflects a balance between the fluctuations intensity and the comany s caability to run her business in rough conditions limiting an adverse effect of market fluctuations on cororate assets. Oerator denotes averaging over n ( at time t. Assumtion (Ab) means that a great number of non-correlated random fluctuations occur in a characteristic eriod of ROA change. Assumtion (Aa) actually reflects the effect that the market exercises on any comany. Process n( includes all random market imacts on a comany, both diversifiable (unique risks) and non-diversifiable ones (market risks). The market risks contain a drift with the market that means the resence of a non-zero regular comonent in n ( for time eriods: m for recessive markets, m for stagnating markets, and m for raising markets. With a rocess n(: n ( n( m which is normal, time-invariant, delta-correlated, and has a zero mean, equation (.) becomes dx dt which can be rewritten as the geometric rownian model [ r( m n( ] x (, x() x, (.3) dx [ r ( x ( ] dt Cx W, x() x, r ( r( m, (.4) where W is a Wiener rocess. For the last stochastic equation one can write a Fokker - Planck equation for the robability distribution f ( x, 86

5 ACRN Oxford Journal of Finance and Risk Persectives Secial Issue of Finance Risk and Accounting Persectives, Vol.5 Issue, March 6,.83-5 ISSN f t x x ( r ( x ) f Cx f. (.5) Introducing a new function V and a new variable z V xf ( x,, z ln x, (.6) the equation (.5) becomes V t V C V r ( e z z V z z V, r ( r( m / (.7) C In this aer we consider the marginal case of, described by the equation W t W C W r ( z z (.8) with the initial condition W ( z,) z H ex, H z t. (.8a) This roblem has a solution z H( W ( z, ex, (.9a) ( C ( C t H( H r ( ) d (.9b) which is a normal distribution arametrically deending on time. Equation (.9b) shows an evolution of the distribution center (the distribution mean) over time. One can see from (.7) that function V ( z, deviates from the normal distribution the more the larger arameter. Solution (.9) suoses that cororate assets can assume any value from zero to infinity. However, there is a minimal value xmin, DL ln xmin, at which default occurs. For a small business (a rorietorshi), xmin is an asset value at which the rorietors sto their struggle for the firm survival and file bankrutcy trying to confine damages to their ersonal roerty. For a ublic firm, xmin is a level at which a noteworthy art of cororate shareholders anicking sells their shares out in a short time interval making the share rice dro shar. Even if that dro does not lead to a cororate default immediately, the roblem of cororate survival must be restated for the 87

6 PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD? new (obviously worse) conditions. Observe that xmin deends on both objective factors (a value of the accumulated debt, the rate of the assets decrease, etc.) and subjective factors (the management averse to risk, shareholders confidence in the cororate team, etc.). Subjective factors add more ambiguity to the roblem of cororate survival. For the roblem (P) described by equation (.8) with the boundary conditions. There is an absorbing screen at the default line : W ( DL,. W( z, decays fast enough as z tends to infinity: W (, and the initial condition meeting the boundary conditions a solution is W ( z,) ex z H DL z H ex z H( DL z H( W ( z, ex ex ( ) ( C ( C Ct, (.8b). (.S) The hysical meaning of the absorbing screen becomes clear if one considers rownian articles whose concentration is roortional to W( z, travelling in the semi-sace of [DL, ). When a article touches the screen, it sticks to the screen (the article erishes ). To see the financial meaning of that screen, let us find the intensity of the robability to erish for the articles with the robability distributions determined by the roblem (P): P [ H( ] D x min x dx (ln x H( ) ex ( C ( C H( DL, (.a) Ct z DL ln xmin, ( z) ex( t / ) dt. (.b) At the screen H( DL, and the intensity of the article s robability to erish is P D ( DL). The case when the mean logarithm of assets hit DL-line, we call the hard default. The other case when a default occurs because of fluctuations while the mean logarithm of assets stays over DLline, we call the soft default. The robability of the soft default, PRD, as the assets decline is determined as Suose that a cororation develos with a constant ROA: t PRD( P [ H( ] dt. (.) D r R R m /, (.) ( C 88

7 ACRN Oxford Journal of Finance and Risk Persectives Secial Issue of Finance Risk and Accounting Persectives, Vol.5 Issue, March 6,.83-5 ISSN and average cororate assets grow exonentially over time. Here R is observable cororate ROA in current market conditions, and R is unobservable ROA in sterile conditions with m, C. Let a crisis onset at moment TA and since that time the mean cororate ROA uniformly decreases over time: r ( t R wt, (.3) ) where w is a rate of ROA decrease caused by the crisis (Fig. ). Values T A and w can be determined using cororate statistics collected due to monitoring of cororate assets. Positive asset dynamics together with an effective asset structure determine a cororate long-term stability. If the asset structure is not otimal for a current business conditions, in other words some assets cannot be used, one must use in the analysis effective assets x eff x(,. From the equation P D (, time TChwhen the mean logarithm of assets hits DL-line (the distance to the hard defaul is T T ( H DL) w, (.4a) Ch / T R / w, H H( T ) H wt /. (.4b) A T is the moment when cororate assets becomes maximum, and trajectory of cororate decline. The distance to a soft default is given by the equation H is the highest oint in the T T Cs (/ w)[ H / DL ( CT CT ) ], (.5.a) ( ) T T, / ), (.5.b) where is a given intensity of default considered as dangerous. The equation can be solved numerically using iterative rocedure starting with T in the right art of the equation. As one can easily see, TCs( ) TCh and tends to T Ch, as. ( 89

8 PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD? Cororate recovery Let a recovery rogram be launched at time T raising cororate ROA at rate u. At T, the recovery initial conditions are: r ( T ) w( T CT. H H( T ) H T A ), wt T wt So, for t measured from T, we have in the recovery / H w( T T ) /, (.) r ( ut w( T T ), H H w( T T ) t ut / H ( ), ( t (.) H( H A wtt wt /, H( H ( t ) H w( T T ) t ut /, t T t t T, t T If T T, a critical oint exists in the recovery trajectory in which a mean logarithm of cororate assets is minimal: T cr w/ u)( T T ), H H ( w / u)( T T ) H ut /. (.3) ( cr cr The intensity of the robability of default in the recovery when a mean logarithm of assets is H ( can be comuted as H( DL P D ( H) Ct, (.4) and the robability of cororate default is determined by the integral t PRD( t; T H u P,, ) D[ H( t )] dt. (.5) T 9

9 ACRN Oxford Journal of Finance and Risk Persectives Secial Issue of Finance Risk and Accounting Persectives, Vol.5 Issue, March 6,.83-5 ISSN It becomes clear from (.), (.4) and (.5) that the main contribution to the robability of soft default is made by the art of the recovery trajectory closest to the critical oint where the intensity of the robability of default is high and the vertical velocity is low; the time that the mean logarithm of assets sends in the dangerous area deends inversely on recovery rate u. If the objective of the recovery rogram is to restore the re-crisis ROA: r ( Tr ) R, then one can find the recovery time Tr and mean logarithm of assets H r as T r ( w/ u) T, Hr H ( w / u)(t T ) T (.6) For T T, however, H r H. If H r is too close to DL-line, and the intensity of the default robability remains intolerably high then the objective of the recovery can be redefined as to achieve a safe state where the intensity of the robability of cororate default is less than a redetermined value. Now recovery time Tr is determined by the equations Tr Tcr x, x ( / u) cr Cx Hcr DL, (.7a), / ) (.7b) cr CT cr ( here ( ) is the inverse function for (z). max The marginal delay with a launch of the recovery rogram, T, for which the hard default still occurs, can be found as a time for which the numerator in Eq. (.4) turns zero at the critical oint, that is H cr DL. This condition has two consequences. For the rogram with a fixed exected recovery rate u, the marginal delay for its launch T max ( ) is u T u T ( TCh T ), (.8) u w max max and for any T T there is no hard default in the recovery. For the rogram with a fixed delay T, the minimal rate u min T ) reventing the hard default in the recovery is ( u min H w H H. (.9) DL 9

10 PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD? For management uroses, however, it is more ractical to know the maximum tolerable delay for max chosen for the maximum intensity of the robability of default T T P ) which is a solution to the equation: The maximum tolerable delay T T T, / ), ( ( D u Cw T H DL ( T T ) w( u w). (.) u T determines the timeliness of the anti-crisis decision for given environment, crisis, cororate, and recovery rogram s arameters and a chosen intensity of the default robability ; for any delay T the maximum intensity of the robability of default T remains less than. In the same way, Eq. (.) determines the minimal recovery rate min max u T ) u ( P ) roviding a chosen level of the maximum intensity of the robability ( D of cororate default for a given delay T. The usual cororate reaction to a ossible default is to increase cororate assets borrowing money from banks (the small enterrises tactics) or from the market as large firms do. However, this leads to regular debt ayments that is the rate of ayments becomes non-zero, (. We consider this case in another study. Conditions for steady cororate rogress Let us return to a firm whose assets increase over time with a constant ROA, R. ecause a standard deviation of cororate assets continuously grows over time, a question arises about the conditions roviding for a steady cororate develoment. The intensity of the robability of default for that cororation is H ( DL P D ( H), H( H R t, Ct / (3.) where H z t and are the mean logarithm and variance of the logarithm of cororate assets at the initial time. A cororate develoment is considered as steady one if at any time t the intensity of the robability of default remains less than a chosen. This requirement is equivalent to C t C C t C( H DL), (3.) R R 9

11 ACRN Oxford Journal of Finance and Risk Persectives Secial Issue of Finance Risk and Accounting Persectives, Vol.5 Issue, March 6,.83-5 ISSN and / ). The inequality is true for any t when the following requirement is met: ( C R C( H DL). (3.3) R So, for ratio Q C /( R ) roviding a steady cororate rogress, one gets the interval K ( ms) Q K( ms), (3.4a) K ( ms) ms ( ms ), (3.4b) DL ms. (3.4c) H As one can see in Fig.3, K(ms) (the uer branch) monotonously grows over ms from to infinity, and K (the lower branch) tends from one to zero. The condition (3.4c) means that H must be high enough over DL-line, or else a default can occur soon after the start of cororate activities. Thus, variable ms can be interreted as the margin of cororate safety. The right limit in (3.4a) seems very natural: the mean logarithm of cororate assets must rise faster than the standard deviation keeing a low intensity of the robability of default. The left inequality in (3.5a) limits ROA from above. When ROA is high, cororate assets grow fast and asset fluctuations become also high because they are roortional to the assets (see (.4). The greater fluctuations need the greater margin of safety, therefore on the lower branch (high ROA) ms increases fast. Any business is created as a source of income for its rorietors and/or investors, and any firm (not a rorietorshi) finishing a year with rofits ays taxes. Suose that a rorietorshi has successfully comleted its business year staying within the region of stability. As time runs, a osition of a steady firm shifts right along ms axis due to accumulated assets (a mean logarithm of cororate assets in the end of the financial year is H (T ) ). How much money can the rorietors take out of their business without taking an extra risk of default in the next business cycle? Figure 3 answers this question. First, arameter Q is calculated for cororate arameters and a chosen intensity of the robability of default : Q C /( R ), / ), (3.5) ( 93

12 PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD? using for the standard deviation the value achieved in the end of the business year. Then a horizontal line Q Q is drawn in Grah 3 to a oint of intersection with curve K (ms), and oint ms *( Q ) shows the least margin of safety for the next business cycle, that is the minimal initial value of the logarithm of assets guaranteeing the intensity of the robability of default less than. The amount of money W which the rorietors can withdraw without increasing the risk of default in the next business cycle is lnw [ ms ms*( Q )], (3.6) here msis the margin of safety in the end of the year. We can call W unbounded or free money understanding that this money is not bounded by the requirement of securing the cororate stability. Now let us consider a ublic cororation aying taxes and dividends. If after tax cororate assets are less than the least margin of safety for given conditions ms ( Q ) * ms T) [ln[ X T( X X )] DL]/( ) (3.7a) ( F F ms T) ms*( Q ) (3.7b) ( ( X X F and T are before taxes cororate income and an effective tax rate, ms(t ) is the after tax margin of safety), the business is already under an elevated risk in the next cycle, and the investors cannot ay any dividends without increasing the risk of default. If the after tax margin of safety ms (T ) is greater than the least ossible margin of safety ms *( Q ), the amount of dividends D that can be aid to the investors without increasing the risk of default in the next business cycle is ln D [ ms( T) ms*( Q )]. (3.8) ecause the assets variance grows linearly over time, the margin of safety increases from year to year reducing the sum that rorietors/investors can withdraw from the business for their needs. Therefore the rocedure of general cleaning F(, in the organization is necessary on a regular basis (a cyclic rocedure) to control its entroy level and bring the asset variance down to about the initial value. The cororate team must do it in arallel with a ermanent struggle to kee arameter C as low as ossible. Solving roblem (P) in the next time interval with new initial data, one again gets the robability distribution for cororate assets as a comosition of two lognormal distributions ln x H( DL ln x H( f ( x, ex ex x ( ) ( C ( Ct C. (3.9) 94

13 ACRN Oxford Journal of Finance and Risk Persectives Secial Issue of Finance Risk and Accounting Persectives, Vol.5 Issue, March 6,.83-5 ISSN In the end of the next business cycle the rorietors reeat one-time money withdrawal from their business observing the conditions of the cororate steady develoment. The robability distribution will have the same structure (3.9) in a business cycle interval for any number of comleted cycles. However, for a time interval much greater than a business cycle, the robability distribution averaged over that interval will deviate from the distribution (3.9). Due to regular money withdrawals, cororate assets send more time in a region of low values in comarison to the distribution (3.9) swelling the low art of the effective robability distribution. To determine that true robability distribution with heavier tails, one has to consider the case with nonzero ayments (. What risks does the market reward? There is a oular statement made within the frames of Caital Asset Pricing Model (CAPM) that the market rewards market risks meaning that investors investing in ortfolios with higher market risks have higher returns due to increase in rices of their shares and received dividend ayments (see, for examle, realey & Mayers, 996). Higher ortfolio market risks come from higher cororate market risks. Here we try to understand what market risks are rewarded by the market at the cororate level resuming that the considered above sustainable cororate develoment is effective. It was shown that dividends are aid from free money which a comany earns at the market. So, taking extra market risks must result in the growth of free money. elow we derive requirements which must be met to have more money for dividend ayments. Let at a time t a cororate kee a osition ( ms, Q ) in the area of cororate sustainable develoment (Fig. 4). This osition is characterized by the minimal ermissible margin of safety * ms (see (3.4) for Q K ) and available free money W ( w lnw ) ms * Q ) / ( Q, (4.a) * w /( ) ms ms ms ( Q ) /(Q ). (4.b) Suose that at a time tthe cororate osition has changed to ( ms, Q ) with the minimal * ermissible margin of safety ms and the available free money W ( w lnw ). An initial logarithmic variance of cororate assets consists of the market and individual variances: m i. Let the individual volatility relate to the market volatility as i a m, then m ( ). When the firm changes its osition, its market volatility changes to a m b m, b. If the ratio a i / m remains the same in the transition than b, and the margin of safety is ms H DL) /( ) ms / b, (4.a) ( 95

14 PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD? If that ratio changes to a margin of safety becomes /, than / b( a ) ( a ) b, and the i / m ms H DL) /( ) ms / b (4.b) ( b b( a (4.c) / / ) ( a ) Further we consider the case (4.a) understanding that we can always extend results on the case (4.b) using correction (4.c). The change in Q is caused by changes in volatility, ROA ( R cr ), and in arameter C which within one industry characterizes an intensity of cometition and caability of the cororate team to resist adverse effects of market fluctuations: Q C /( R ) Q /( bc), (4.3a) * w /( ) b( ms ms ) ms ( Q b c ) /(Q c). (4.3b) Our goal is to determine conditions for b and c when the cororate osition is not worsened by changes of arameters b and c ( w w ) /( ) ( Q ) /(Q ) ( Q b c ) /(Q c). (4.4) The last inequality can be rewritten as b c ( Q ) c Q. (4.5) To have a meaningful solution to the inequality (4.5), the following conditions must be met Q b, (4.6a) Q [ ms. (4.6b) / / ( ms ) ] Q ms ( ms ) Solving inequality (4.5), we derive a condition for c as a function of b Q ) / b Q c [ ( A / ( A ) b ( / ) ], (4.7a) A Q b/( Q ). (4.7c) 96

15 ACRN Oxford Journal of Finance and Risk Persectives Secial Issue of Finance Risk and Accounting Persectives, Vol.5 Issue, March 6,.83-5 ISSN The grahs for the areas securing imrovement in cororate free money are given in Fig. 5 and Fig. 6. From the condition (4.7), it follows immediately that for Q and any ms, b and c, what means that the osition withq and any ms is the best, and any shift from it reduces available free money. For other cororate ositions, an extra market risk is rewarded only within the limits of one and Maxb ( Q, ms ). If for a fixed value of ROA (fixed c) the market volatility goes over the maximum, it makes the available cororate free money to diminish. Using the method, one can numerically estimate a threshold for the risk the firm can take in its secific conditions at which decrease in free money will relace its increase. ut how can a firm raise her ROA? There are two ways. The first is to create a highly rofitable market niche rotected by atents, know-hows, etc. After that the firm for some time can enjoy high monoolistic rices on her roduction securing high ROA, moderate C, and low Q value at aroximately the same level of the margin of safety ms, thus, generating more free money and creating the ossibility to ay higher dividends to her shareholders. The second way is to intrude an existing market niche with ROA higher than an industry s mean ROA. The usual reaction from the niche residents to the intervention is to offer resistance to the intruder imlying an intensive cometition. It is interesting to note that a cometition in this model looks similar to the Jaanese Sumo wrestling where two wrestlers try to ush each other out from the ring. In the market cometition the firms try to ush each other out from the area of cororate stability reserving high ROA for the survivors. Intensive cometition raises market and individual cororate risks. With temorarily low ROA so characteristic for a bitter commercial struggle, they drive fast all the cometitors to the boundary of the region of cororate stability until one or several of them leave the region and sto their struggle for a lace in the niche and begin a new struggle for their own survival (see the first two sections of the aer). So, we see that in general the intensity of cometition increases as ROA grows from the to to bottom of the area of sustainable develoment. Most develoing firms cannot afford large margins of safety for any ROA and run their business in the narrow boundary layer of the area of cororate stability from time to time leaving it and returning back. When firms leave the area of cororate stability their robability to default increases and they fill themselves distressed. If they stay outside the area for a longer time and at a longer distance, they may come to default. A significant share of distressed firms comes from the to of the area of cororate stability where ROA is low. Of course, all these hyotheses need exerimental roofs from market observations. Now we can interret the grah in the Fig. 6. For a fixed margin of safety, for any osition in the uer art of the area of cororate sustainability there is a osition in the bottom art of this area conjugated about a osition with Q. For examle, for a cororate osition with Q 3, a conjugated osition has Q / 3and its ROA is nine times higher. Firm assets in that second osition grow very fast, but to secure the same margin of safety the firm must kee big bounded resources hardly leaving anything for free money. The firm belongs to stars in the terminology of the usiness Consulting Grou Growth-Share matrix (Henderson, 97). When the firm s to management decides that the cororation is big enough, they begin to descend from the area of intensive cometition to the areas with lesser ROA and lesser cometition (the star turns to a cash cow ). oth for the firms moving to the areas with higher ROA and higher cometition, and for the firms moving in the oosite direction, for any change in ROA c there is a maximum reasonable risk Maxb searating the states securing more free money from those for which an 97

16 PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD? amount of free money begins to decrease. In the uer art of the area of stability close to its boundary, one can find dogs, and in the middle art of the area one can see the question marks in terminology of the CG matrix. Fig. 5 and 6 show that increase in the market risk does not always guarantee higher dividend ayments as CAPM states, but there is a limit for the market risk getting over which decreases a cororate caability to ay dividends keeing the same margin of safety. In conclusion we must say that results of this section should be taken with a due caution because they are derived for the case when cororate obligatory ayments equal zero: (. The CAPM is a heuristic model generalizing market observations, and, therefore, taking into account real cases with (. A solution of the general roblem for the cororate financial distress can give real limits of validity of the CAPM. The model also exlains consequences of use of the trial and error method in crisis management when the cororate team tries to subdue the economic distress blindly exerimenting with system arameters. To some extent this way of action is secific for small firms trying to comensate a lack of managerial exerience with the trial and error method. As a consequence, the asset variance increases faster for small comanies comared to medium and large ones managed by rofessionals. This relation between the cororation size and the growth rate of the asset variance together with a low margin of safety so usual for small comanies exlains the higher rate of bankrutcies secific for small comanies comared to medium and large ones, esecially in hard times when adverse effects of market volatility and a negative economic trend strengthen each other ( R R m C /, m, C is always ositive). Conclusion The article suggests a quantitative model of a cororate economic distress studying a cororate crisis which lessens cororate ROA at a fixed statistically estimated rate in a secial case when all comany assets are used to generate a current cash flow (there is no such ayments as fixed costs, long-term debts, R&D exenses, etc.). The comany s environment is described by normallydistributed, time-invariant, and delta-correlated market fluctuations having a measurable intensity C and trend m. The cororate state is identified with assets x(, their structure and variance σ, comany s caability to resist adverse effects of market fluctuations C and eriodical orderrestoring rocedure F(,. The crisis is characterized by the time of its onset TA and rate of ROA decrease w. The recovery rogram is described by its exected rate of ROA raise u and delay T about the crisis onset. It is shown how the robability of default develos in time at various stages of the distress deending on the environment, comany, crisis, and recovery rogram arameters. Maybe the most imortant result of this study is the roof that develoment of a cororate economic distress and a cororate struggle for survival are dynamic roblems essentially deending on roer timing of all measures. Therefore, there is no time-indeendent criterion for the distance to default or the robability of default. To some extent this result is equivalent to the lack & Cox s solution (976), however the entire aroach used in the aer shows the limitations of the results. ecause ( is the cororate exenses which do not generate current cash flow, there is no firm for whom ( = for a sufficiently long time interval. Therefore this solution has mainly a methodological value. The model joins financial (assets, ROA, taxes, and dividends) and organizational (an organization s structure, ersonnel motivation, training, management quality, risk avoidance 98

17 ACRN Oxford Journal of Finance and Risk Persectives Secial Issue of Finance Risk and Accounting Persectives, Vol.5 Issue, March 6,.83-5 ISSN strategy, etc.) characteristics of a comany; the last are integrated in the asset variance σ, its growth rate C, order-restoring rocedure F(,, and default value x min. Effects of financial or organizational arameters on a cororate business taken searately are widely discussed in management science (see, for examle, realey & Myers (), Robbins (99)). The model allows quantitative tracing of the contribution to the robability of default of any extra unit of taxes or dividends, any extra oints of cororate ROA, and also of changes in organization s arameters. Statistically monitoring and analyzing the cororate business one can determine Time of the crisis onset TA and rate of ROA decrease w caused by the crisis roviding for an early crisis detection variance of cororate assets and its growth rate C caused by market fluctuations trend m in a comany industry. These arameters hel determine mean and confidence interval for the distance to default if the crisis is left unattended marginal delay T max ( u) (the oint of no return) for starting a recovery rogram of estimated efficiency u. The rogram launched after this time has a very little chance to succeed recovery time Tr and assets x(tr) and also critical time Tcr for which cororate assets have the minimal value xcr the robability of cororate default PRD as a function of the recovery lan characteristics and roblem s arameters marginal amount of money that can be withdrawn from the business without exosing it to an extra risk of default. Measuring cororate, environment, and crisis arameters and estimating characteristics of suggested recovery rograms, cororate managers can select for imlementation the rogram roviding the highest robability of survival and then estimate its effectiveness in ractice. This technique rovides managers for the quantitative instrument heling them to imrove cororate management in a risky business environment and comlex economic conditions. The next ste in the develoment of this model is to increase a model s reality by including nonzero obligatory ayments ( >. 99

18 PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD? References Altman, E. I. (968). Financial Ratios, Discriminant Analysis and the Prediction of Cororate ankrutcy. Journal of Finance, 3, Altman, E., & Hotchkiss, E. (6). Cororate Financial Distress and ankrutcy: Predict and Avoid ankrutcy, Analyze and Invest in Distressed Debt (3rd ed.), Hoboken, NJ, USA: John Wiley & Sons. Asquith, P., Gertner, R., & Scharfstein, D. (994). Anatomy of Financial Distress: An Exlanation of Junk ond Issuers. Quarterly Journal of Economics, 9, ibeault, D. (98). Cororate Turnaround: How Managers Turn Losers into Winners. New York, USA: McGraw- Hill. lack, F., & Cox, J. C. (976). Valuing Cororate Securities: Some Effects of ond Indenture Provisions. Journal of Finance, 3, lack, F., & Scholes, M. (97). The Pricing of Otions and Cororate Liabilities. Journal of Political Economy, 8(3), realey, R. A., & Myers, S. C. (). Princiles of Cororate Finance. (6th ed.), New York, USA: McGraw-Hill. R. Geske, R. (977). The Valuation of Cororate Liabilities as Comound Otions. Journal of Financial and Quantitative Analysis,, Gestel, T. V., aesens,., Suykens, J., Poel, D. V., aestaens, D. E., & Willekens, M. (6). ayesian kernel based classification for financial distress detection. Euroean Journal of Oerational Research, 7, Gordon, M. J. (97). Towards a Theory of Financial Distress. Journal of Finance, 6(), Henderson,. (97). The Product Portfolio. htts:// Kahya, E., & Theodossiou, P. (999). Predicting Cororate Financial distress: A Time-Series CUSUM Methodology. Review of Quantitative Finance and Accounting, 3, Lando, D. (998). On Cox Processes and Credit Risky Securities. Review of Derivatives Research,, 99. Merton, R. C. (974). On the Pricing of Cororate Debt: The Risk Structure of Interest Rates. Journal of Finance,, Outecheva, N. (7). Cororate Financial Distress: An Emirical Analysis of Distress Risk. Ph.D. Dissertation, University of St. Gallen, St. Gallen, Germany. Pearson, C. M., & Claire, J. A. (998). Reframing crisis management. Academy of Management Review, 3(), Robbins, S. P. (99). Organization Theory: The Structure and Design of Organizations. Englewood Cliffs, NJ, USA: Prentice Hall. Roux-Dufort, C. (7). A assion for imerfections: revisiting crisis management. In: Pearson, C. M., C. Roux- Dufort, C., & Claire, J. A. (Eds.), International Handbook of Organizational Crisis Management, (. 5). Thousand Oaks, CA, USA: Sage. Salchenberger, L. M., Cinar, E. M., & Lash, N. A. (99). Neural Networks: A New Tool for Predicting Thrift Failures. Decision Sciences, 3, Shin, K., & Lee, Y. (). A Genetic Algorithm Alication in ankrutcy Prediction Modeling. Exert Systems with Alications, 3(3), Gorbenko, A. S., & Strebulaev, I. A. (). Temorary versus Permanent Shocks: Exlaining Cororate Financial Policies. Review of Financial Studies, 3, Wruck, K. (99). Financial Distress, Reorganization, and Organizational Efficiency. Journal of Financial Economics, 7,

19 ACRN Oxford Journal of Finance and Risk Persectives Secial Issue of Finance Risk and Accounting Persectives, Vol.5 Issue, March 6,.83-5 ISSN Figure : Decline in a mean logarithm of cororate assets H over time t in a crisis. Line F is the line of cororate steady rogress before the crisis onset at oint A. T A is the time of the crisis onset; since that moment cororate ROA linearly declines over time. Point is the maximum oint in the trajectory of the mean logarithm of cororate assets, ROA(T ) =. If the crisis is left unattended, a hard default occurs at oint C, x(t C) = x min. Figure : Recovery trajectory for the logarithm of cororate assets assing through the oints H, H cr, and H r.

20 PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD? AREA OF SUSTAINALE CORPORATE DEVELOPMENT Figure 3: The area of a steady cororate rogress, Q C /( R ), ms ( H A DL)/( ). The area of a steady cororate rogress, where the intensity of the robability of default remains less than.5, lies inside the curve.

21 ACRN Oxford Journal of Finance and Risk Persectives Secial Issue of Finance Risk and Accounting Persectives, Vol.5 Issue, March 6,.83-5 ISSN ms Figure 4: Illustration to calculations of the logarithms of available free money w lnw, cororate ositions (ms, Q ) and (ms, Q ). w lnw for different 3

22 PROAILITY OF DEFAULT IN CORPORATE ECONOMIC DISTRESS, OR WHAT RISK DOES MARKET REWARD?,,8,6,4,.,5,5,5 3 3,5 4 Figure 5: Maximum increase of cororate volatility Maxb ( ) securing increase in free money ( m b m w w ) keeing the same robability of default as a function of the initial value Q C /(R ), ms =. 4

23 ACRN Oxford Journal of Finance and Risk Persectives Secial Issue of Finance Risk and Accounting Persectives, Vol.5 Issue, March 6,.83-5 ISSN ,,,3,4,5,6,7. Figure 6: Areas of arameter c ( R cr ) securing increase in free money ( w w ) and keeing the same robability of default as a function of the volatility growth b ( (line ), Q =.5 (line ), Q = 3 (line 3). ) for ms = and three values of Q : Q = m b m 5