Stat homework

HW 6 – FINANCIAL DISTRESS AND ACQUISITION MODELS – LOGIT REGRESSION Statistical Financial Modeling (Prof. P. Theodossiou)

1. Develop a logistic model of financial distress. Explain the procedure used to build your model. Interpret the coefficients of the model. The best Logistic model for financial distress includes five explanatory variables as follows:

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i

D TDTA GEMPLi i  

  

15087 1 44

4 8133 3 95

6 1228 3 09

. ( . )

. ( . )

. ( . )

 

  

51431 2 18

3 6199 153

0 2151 1 72

. ( . )

. ( . )

. ( . )

OPITA INVSLS LSLSi i i

ly,

where Di is an index of financial distress for firm i. The identification of the above model is accomplished by estimating models based on various combinations of variables and by keeping that combination for which all coefficients for the variables are statistically significant at the five percent level and consistent with financial theory. Note that the ratio of inventory to sales and the variable for size have low t-values. However, they are statistically significant at the five percent level using a multivariate log-likelihood ratio test. The log- likelihood ratio statistic can be used to test the significance of the two variables in the model. This is specified as LR = –2 (L1 –L0 ), where L1 is the log-likelihood value of the five-variable Logistic model and L0 is the log-likelihood value of the (nested) three variable logistic model. Specifical

LR = –2 (–90.56 – (–93.93)) = 6.74 > χ2(2)= 5.99.

Thus, the hypothesis that the additional two variables are significant is accepted. The probability of financial distress for firm i is calculated using the (cumulative) logistic probability function

1

1 exp( ) i

i

F D

  

,

where Di is as specified above. Note that the distress index Di and the probability Fi are positively related. That is, the larger the value of Di, the larger the probability of distress. Moreover, positive coefficients of for the variables in Di, imply a positive relationship between the variables and the

ize, and the ratio of operating come to total assets have a negative impact on the probability of distress.

ed firms. Explain the procedure used build your model. Interpret the coefficients of the model.

The best Logistic model for acquisition includes six explanatory variables as follows:

i

probability of distress. The above index indicates that the ratios of total debt to total assets and inventory to sales have a positive impact on the probability of distress, while employment growth, s in 2. Develop a logistic acquisition model for financially distress to

3.6875 1.5235 9.3671 0.0458 ( 2.13) (3.50) (2.76) ( 2.69)

i i iM SLSTA INVSLS INSIDR      

5.3880 0.6485 2.6727 (2.34) (1.61) ( 1.79)

i i iFATA NIFA TDTA   

,

d on various combinations of variables and by keeping that combination for which

are statistically significant at the five-percent level using a multivariate log- kelihood ratio test. Specifically, the log-likelihood ratio statistic for testing the significance of the two

variables in the mod

11.52 > χ2(2)= 5.99,

he two variables in the model is justified. The probability of acquisition for firm i is calculated sing the (cumulative) logistic probability function as follows:

where Mi is an index of acquisition for firm i. The identification of the above model is accomplished by estimating models base all variables’ coefficients are statistically significant at the five percent level as well as they are consistent with financial theory. Note that the ratios of net income to fixed assets and total debt to total assets have low t-values. However, both variables li

el is

LR = –2 (L1 –L0 ) = –2 (–43.06 –(–48.82)) = thus, the addition of t

u

1

1 exp( ) i

i

G M

 .

related. That is, larger values for imply larger probabilities of acquisitions. Moreover, positive coefficients imply a positive relationship

. Given the data below for two financially distressed and two healthy firms, the probability of eloped previously with a cut-off point of 0.5 and reclassify the firms.

The index of financial

D1 = –1.5 1 (0.10)

(0.08) –0.2151 (5.04) = –0.6646.

The probability of distress for firm 1 is

  Note that the acquisition index Mi and the probability Gi are positively Mi between the variables and the probability of acquisition and vice versa. 3 distress model dev Distressed Firms

distress for the first firm is

087 + 4.8133 (0.46) –6.1228 (0.01) –5.143

+3.6199

1 1

0.3397. 1 exp( ) 1 exp( ( 6646))

F D    

1 1

  

remaining three firms are:

D = 3.4393 and F = 0.9689

ealthy Firms

Similarly, the distress indices and probabilities for the 2 2 H D3 = –0.6349 and F3 = 0.3464 D4 = 0.6417 and F4 = 0.6551

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Note that firms 1 and 3 above are miss-classified by the model.

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for two acquired and two non-acquired distressed firms, use the probability of cquisition model developed previously with a cut-off point of 0.5 and reclassify the firms.

cquired Firms

he index of acquisition for the first firm is

M1 = –3.6857 + 1.5235 (1.04) +9.3671 (0.32) –0.0458 (4.9)

+5.3880 (0.32) +0.6485 (–0.04) –2.6727 (0.39) = 1.3277.

on for firm 1 is

4. Given the data a A T

The probability of acquisiti

G1 1 1

0 7905   . . M11 1 1 3277   exp( ) exp( . )

imilarly, the acquisition indices and probabilities for the remaining three firms are:

M3 = –2.0632 and G3 = 0.1127,

M4 = –1.0563 and G4 = 0.2580.

ote that all firms above are classified correctly by the model.

te the of 0.40, 0.45, 0.50, 0.55 and 0.60.

ial Distr l f )/2

.50 0.1474 0.3488 0.2481 68 0.4419 0.2894

f

.50 0.2449 0.2973 0.2711

0.1429 0.4324 0.2876

. Calculate the elasticities of the coefficients of the two models

S M2 = 2.5291 and G2 = 0.9262, Non-Acquired Firms N 5. Calcula models’ error rates for the cut-off points Financ ess Mode Cut-of EH ED (EH+ED 0.40 0.3158 0.2093 0.2625 0.45 0.2105 0.2907 0.2506 0 0.55 0.13 0.60 0.1263 0.4419 0.2841 Acquisition Model Cut-of EN EA (EN+EA)/2 0.40 0.3673 0.1892 0.2783 0.45 0.3061 0.2703 0.2882 0 0.55 0.1837 0.4054 0.2945 0.60 6

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inancial Distress Model The elasticity formula for the financial distress model is

F

Elasti D

i i   cityi  L NM

O 1

QP 

1

1 exp( )  

D X      X X i iand mean and standard deviation for variable  are the Xi in the

f

0 1 1 5 5 , and where healthy and distressed samples. Substitution o the values below gives D  0.0193. i iX i Elasticities Intercept –1.5087 n/a n/a n/a TDTA 4.8133 0.5589 0.2220 0.5291 GEMPL –6.1228 –0.0007 0.1069 0.3241 OPITA –5.1431 0.1094 0.1201 0.3059

as the highest elasticity (0.5291) nd as such it is the most important explanatory variable in the model. The second most important

ent growth (0.3241), followed by the ratios of operating income to total assets .3059), inventory to sales (0.1780), and log of deflated sales (0.1746).

cquisition Model The elasticity formula for the acquisition model is

INVSLS 3.6199 0.1736 0.0993 0.1780 LSLS –0.2151 5.7286 1.6388 0.1746 It appears from the table above that the ratio of total debt to total assets h a variable is employm (0 A

1 1

1 exp( ) i iElasti

M icity      

  

Where 0 1 1 6 6M Z Z      , and andi iZ  are riable Zi in the ubstitution e values be ives

the mean and standard deviation for va

M  –0.5774. acquired and non-acquired samples. S of th low g i iZ i Elasticity

ATA 5.3880 0.3127 0.1560 0.5383

The ratio of sales to total assets has the highest explanatory power (elasticity is 0.9420), followed by the ratio of inventory to sales (0.7001), the variable for insider control (0.5729), and the ratios of fixed assets to total assets (0.5383), net income to fixed assets (0.4283) and total debt to total assets (0.4177).

Intercept –3.6857 n/a n/a n/a SLSTA 1.5235 1.6250 0.9654 0.9420 INVSLS 9.3671 0.1923 0.1167 0.7001 INSIDR –0.0458 19.9521 19.5296 0.5729 F NIFA 0.6485 –0.2800 1.0312 0.4283 TDTA –2.6727 0.6578 0.2440 0.4177

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HW 6 – FINANCIAL DISTRESS AND ACQUISITION MODELS – LOGIT REGRESSION Statistical Financial Modeling (Prof. P. Theodossiou)

Distressed Sample The sample includes 86 financially distressed firms from the NYSE or AMEX. Of these firms, 37 were acquired and 49 were not. A firm was characterized as financially distressed if it exhibited one or more of the following signs of distress: (1) debt default, (2) debt renegotiation attempts with creditors and financial institutions and (3) inability to meet fixed payment obligations on debt. The “distressed date” was defined as that date at which the firm experienced, for the first time, any of the above sign of distress. Data for distressed firms were extracted at about one year prior to the distressed date. Data cover the period 1981-89 and were extracted from COMPUSTAT. YD = XD YD= 0 for healthy firms and YD= 1 for distressed firms TDTA = TL/TA Total debt (liabilities) to total assets GEMPL Employment growth rate OPITA = OPI/TA Operating income to total assets ratio INVSLS = INV/SLS Inventory to sales ratio LSLS = ln(Sales) Natural logarithm of deflated sales (sales in millions of $) LTA = ln(TA) Natural logarithm of deflated total assets (total assets in millions of $) NWCTA = NWC/TA Net working capital to total assets CACL = CA/CL Current assets to current liabilities QACL = (CA-INV)/CL Quick assets to current liabilities EBITA = EBIT/TA Earnings before interest and tax (EBIT) to total assets RETA = RE/TA Retained earnings to total assets FATA = FA/TA Fixed assets to total assets NIFA = NI/FA Net Income to fixed assets INSIDR Insider control 1. Develop a logistic model of financial distress. Explain the procedure used to build your model. Interpret the coefficients of the model. 2. Develop a logistic aquisition model for financially distressed firms. Explain the procedure used to build your model. Interpret the coefficients of the model. 3. Given the data below for two financially distressed and two healthy firms, the probability of distress model developed previously with a cut-off point of 0.5 and reclassify the firms. Distressed Firms NWCTA=0.13, OPITA=0.10, TDTA= 0.46, INVSLS=0.08, LTA=5.06, SLS=5.04, GEMPL=0.01 NWCTA=0.18, OPITA=-0.11, TDTA=1.00, INVSLS=0.16, LTA=6.29, SLS=6.12, GEMPL=-0.05 Healthy Firms NWCTA=0.23, OPITA=0.14, TDTA=0.62, INVSLS=0.18, LTA=7.60, SLS=8.07, GEMPL=0.05 NWCTA=0.37, OPITA=0.10, TDTA=0.61, INVSLS=0.21, LTA=4.86, SLS=5.65, GEMPL=-0.03 4. Given the data below for two acquired and two non-acquired financially distressed firms, use the probability of acquisition model developed previously with a cut-off point of 0.5 and reclassify the firms. 5. Calculate the error rates of both models for the cut-off points of 0.40, 0.45, 0.50, 0.55, and 0.60. 6. Calculate the elasticities of the coefficients of the two models