Stat homework

PREDICTION OF FINANCIAL DISTRESS Statistical Financial Modeling (P. Theodossiou)

1. Testing the Importance of Financial Variables as Predictors of Financial Distress There are several financial variables for distressed firms that are, on average, different from those of healthy firms; in some occasions they are higher in other occasions they are lower (see the answer to question 2 for a list of such variable and financial reasons). Regression analysis could be used to test whether the population means of a variable or a ratio for distressed and healthy firms are the same or not. Consider the following sample regression

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i, ˆˆ ˆ

i DX a bY  , where Xi is firm’s i value for variable X, YD,i is a dichotomous (dummy) variable taking the value of one for distressed firms and the value of zero otherwise. The sample regression for Xi implies that

,

,

ˆ for 0 (healthy firms) ˆ

ˆˆ for 1 (distressed firms)

H D i

i

D D i

a X Y

X

a b X Y

   

     

,

where HX is the mean of the variable in the healthy sample, DX is the mean of the variable in the distressed sample, and

ˆ ˆˆ ˆ( )D HX X a b a b     is the difference of the two sample means.

The issue of whether the means of a variable for healthy and distressed firms are equal or not can be addressed by testing the null hypothesis

0 : 0H b  , against the alternative hypothesis

1 : 0H b  using standard hypothesis testing for the slope of a regression line, here denoted by the letter b. Note that a statistically significant negative slope would imply that the mean of a variable for distressed firms is higher, and vice versa. A statistically insignificant slope would imply that the mean of the variable for distressed firms is equal to that of healthy firms. In the latter case we can claim that the variable is not a good predictor of financial distress. Question 1. (a) Are the means of the above variables statistically different in the healthy and distressed samples? (b) Which of these variables are useful in discriminating financially distressed from healthy firms? (c) Which of the variables is the least (most) significant? (Question 1a) Testing Differences in the means

Total Debt to Total Assets (TDTA) The regression for the variable (ratio) of total debt to total assets is

2 ,0.4694 0.1884 0.1805

(22.7) (6.28) i D iTDTA Y R

    .

The regression implies that the sample means of TDTA for healthy firms is

0.4694HTDTA  and for distressed firms is

0.4694 0.1884 0.6578DTDTA    . Is the mean of the ratio for distressed firms statistically different from that of healthy firms? This question is the same as “is the slope of the above regression model different from zero?” The above question is answered by testing the null hypothesis of a zero slope against the alternative hypothesis of a non-zero slope. Note that the slope’s t-value is 6.28 and is greater than its critical value at the five-percent level of significance of 1.96. On this basis, the null hypothesis is rejected and the alternative hypothesis is accepted (i.e., the slope is statistically significant). The fact that the slope is positive implies that, on average, distressed firms have, on statistical basis, greater TDTA ratios than healthy firms. Annual Employment Growth (GEMPL) The regression for the variable of annual employment growth is

2 ,0.0303 0.0653 0.0936

(2.90) ( 4.29) i D iGEMPL Y R

   



The regression implies that the sample means of GEMPL for healthy firms is

0.0303HGEMPL  or 3.03% and for distressed firms is

0.0303 0.0653 0.035DGEMPL     or –3.5%. The slope’s absolute t-value is 4.29 > 1.96, thus the null hypothesis is rejected. The latter implies that, on average, distressed firms exhibit lower (negative) employment growth rates. Operating Income to Total Assets (OPITA) The regression for the ratio operating income to total assets is

2 ,0.1578 0.1017 0.1799

(14.1) ( 6.27) i D iOPITA Y R

   

 .

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The regression implies that the sample means of OPITA for healthy firms is

0.1578HOPITA  or 15.78% and for distressed firms is

0.1578 0.1017 0.0561DOPITA    or 5.61%. The absolute t-value of the slope is 6.26 > 1.96, thus the null hypothesis is rejected. The latter implies that, on average, distressed firms exhibit lower profitability than healthy firms. Inventory to Sales (INVSLS) The regression for the ratio of inventory to sales

2 ,0.1567 0.0357 0.032

(15.61) (2.44) i D iINVSLS Y R

    .

The regression implies that the sample means of INVSLS for healthy firms is

0.1567HINVSLS  or 15.67% and for distressed firms is

0.1567 0.0357 0.1924DINVSLS    or 19.24%. The t-value of the slope is 2.44 > 1.96, thus the null hypothesis is rejected. The latter implies that, on average, distressed firms exhibit higher inventory to sales ratios than healthy firms. Natural Logarithm of Deflated Sales (LSLS) The regression for the variable of log-of-sales is

2 ,5.9740 0.5165 0.0249

(35.8) ( 2.14) i D iLSLS Y R

   



The regression implies that the sample means of LSLS for healthy firms

5.974HLSLS  and for distressed firms is

5.9701 0.5165 5.4536.DLSLS   

The slope’s absolute t-value is 2.14 > 1.96, thus the null hypothesis is rejected. Rejection of the null hypothesis implies that, on average, distressed firms exhibit lower sales activity than healthy firms. Natural Logarithm of Deflated Total Assets (LTA) The regression for the variable of log-of-total assets (used as proxy for size) is

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2 ,5.5855 0.4647 0.0195

(32.9) ( 1.88) i D iLTA Y R

   

 .

The regression implies that the sample means of LTA for healthy firms is

5.5855HLTA  and for distressed firms is sample is

5.5855 0.4647 5.1208.DLTA    The absolute t-value of the slope is 1.88 < 1.96, thus the null hypothesis is rejected. The latter implies that distressed and healthy firms have similar LTA (size). Net Working Capital to Total Assets (NWCTA) The regression for the ratio of NWCTA is

2 ,0.2939 0.0487 0.0188

(16.2) ( 1.85) i D iNWCTA Y R

   



The regression implies that the sample means of NWCTA for healthy firms is

0.2939HNWCTA  and for distressed firms is

0.2939 0.0487 0.2452.DNWCTA    The absolute t-value of the slope is 1.85 < 1.96, thus the null hypothesis is rejected. The latter implies that distressed and healthy firms have similar NWCTA ratios. Current Assets to Current Liabilities (CACL) The regression for the ratio of current assets to current liabilities is

2 ,2.3945 0.3689 0.0296

(22.0) ( 2.34) i D iCACL Y R

   



The above regression implies that the sample means of CACL for healthy firms is

2.3944HCACL  and for distressed firms is

2.3944 0.3689 2.0255.DCACL    The absolute t-value of the slope is 2.34 > 1.96, thus the null hypothesis is rejected. The latter implies that, on average distressed firms, exhibit lower current assets to current liabilities ratios (liquidity) than healthy firms.

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Quick Assets to Current Liabilities (QACL) The regression for the ratio of quick assets (current assets–inventory) to current liabilities is

2 ,1.3778 0.2448 0.0201

(15.7) ( 1.92) D iiQACL Y R

   



The regression implies that the sample mans of QACL for healthy firms is

1.3778HQACL  and for distressed firms is

1.3778 0.2448 1.133.DQACL    The slope’s absolute t-value is 1.92 < 1.96, thus null hypothesis is accepted. The latter implies that, on average, distressed and healthy firms exhibit similar liquidity (QACL). Earnings Before Interest and Tax to Total Assets (EBITA) The regression for the ratio of EBIT to total assets is

2 ,0.1126 0.0980 0.1523

(9.45) ( 5.67) i D iEBITA Y R

   



The regression implies that the sample means of EBITA for healthy firms is

0.1126HEBITA  and for distressed firms is

0.1126 0.0980 0.0146.DEBITA    The slope’s absolute t-value is 5.67 > 1.96, thus the null hypothesis is rejected. The latter implies that, on average, distressed firms exhibit lower profitability than healthy firms. Retained Earnings to Total Assets (RETA) The regression for the ratio of retained earnings to total assets is

2 ,0.3577 0.2255 0.1624

(13.6) ( 5.89) i D iRETA Y R

   



The regression implies that the sample means of RETA for healthy firms is

0.3577HRETA  and for distressed firms is

0.3577 0.2255 0.1322.DRETA   

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The absolute t-value of the slope is 5.89 > 1.96, thus the null hypothesis is rejected. Rejection of the null hypothesis implies that, on average, distressed firms exhibit lower RETA than healthy firms. Fixed Assets to Total Assets (FATA) The regression for the ratio of fixed assets to total assets is

2 ,0.3649 0.0522 0.0251

(21.8) ( 2.15) i D iFATA Y R

   



The regression implies that the sample means of FATA for healthy firms is

0.3648HFATA  and for distressed firms is

0.3649 0.0522 0.3127.DFATA    The slope’s absolute t-value is 2.15 > 1.96, thus the null hypothesis is rejected. The latter implies that, on average, distressed firms exhibit lower FATA than healthy firms. Question 1b. Which of these variables are useful in discriminating financially distressed from healthy firms? The useful variables are those with significant differences in their means in the healthy and distressed samples. Question 1c. Which of the variables is the least (most) significant? The most significant variable is the one with the highest absolute t-value (i.e., TDTA). The least significant is the one with the lowest absolute t-value (i.e., NWCTA). Question 2. Discuss your previous findings from the "financial analysis" point of view. The statistical findings above indicate the following: Financial Leverage Financially distressed firms, on average, exhibit higher total debt to total assets ratios. This finding is consistent with theoretical bankruptcy models showing leverage to be positively related to the probability of bankruptcy (financial distress). This is because financial leverage (short- and long-term debt) involves mandatory commitments in the form of interest and principal payments. Unlike dividend payments, interest and principal payments cannot be postponed without significant negative implications for the firm. In this respect, firms possessing high leverage ratios are more prone to failure during low income or recessionary periods. Profitability

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Financially distressed firms, on average, exhibit lower ratios of operating income to total assets, EBIT to total assets, and retained earnings to total assets ratios. Various theoretical bankruptcy models postulate a positive relationship between profitability and the value of the firm and a negative relationship to the probability of bankruptcy. This is because the income (profit) stream generated by a firm's operations provides funds for future investments and enables the firm to meet its short- and long-term obligations. Note that the ratios of operating income to total assets and EBIT to total assets are proxies for short-term profitability. The ratio of retained earnings to total asset is a proxy for long-term profitability. Firm Growth Financially distressed firms, on average, exhibit lower (negative) annual employment growth while healthy firms exhibit positive employment growth. The firm's growth is directly related to the firm's future cash flow stream and is expected to be negatively related to the probability of distress. Liquidity The liquidity ratios tested are NWCTA, CACL, and QACL. Only the ratio of CACL appears to be statistically different in the two samples. These mixed results raise serious questions as to the usefulness of liquidity measures in discriminating financially distressed from healthy firms. Finance theory postulates that firms possessing insufficient liquidity often experience problems meeting their short-term obligations as they become due, thus impairing their ability to obtain commercial credit and interferes with their normal operations. Moreover, creditors may force such firms into bankruptcy proceedings. Perhaps, liquidity measures are important indicators for small firms than large firms as the ones in our sample. Firm Size According to finance theory, larger firms are more diversified and have greater market power than smaller firms, therefore, their earnings level and stability are expected to be greater. In addition, they have better access to capital markets and face proportionally lower flotation costs than smaller firms when raising additional funds for new projects or meeting debt obligations. Two size measures are considered, that is the log-of-deflated total assets and the log-of-sales. The results are mixed. Note that our sample includes firms listed on NYSE and AMEX, which are relatively large firms. Management Inefficiency Financially distressed firms exhibit higher inventory to sales ratio. This ratio is used as a proxy for management inefficiency. That is, the ratio measures the management's ability to turn inventory into sales. Higher values for this ratio are indicative of management inefficiency. Inefficiently run firms are expected to possess lower profitability than comparable efficiently run firms, therefore they are more likely to fail. Firm Productive Assets Financially distressed firms exhibit lower fixed assets to total assets ratios. This is because distressed firms frequently sell tangible (productive) assets to improve their liquidity position. Question 3. Is it correct to assume the most significant variables must “always” enter the model as explanatory variables? Relate your answer to the variables’ correlation matrix.

Not necessarily. The extent of correlation of two variables determines of whether both variable will be included in a financial distress model or not. For example, the correlation between the ratios of OPITA and EBITA is 0.98 indicating a very strong positive relationship. The latter is strong evidence that the two ratios reveal almost identical information with respect to a firms profitability. The inclusion of one variable in the model makes the inclusion of the other unnecessary. Other examples, include the ratios of log-of-sales and log-of-total assets, NWCTA, CACL and QACL. 2. Linear Probability Model The linear probability model (LPM) is a regression of the dichotomous variable YD,i against explanatory variables for financial distress, such as those presented previously. That is,

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,i

i

e a

viously.

, 1 1, ˆ ˆˆ ˆ

i D i i k kP Y a X X      ,

where YD,i is the dummy (dichotomous) variable (YD,i = 1 for each distressed firm and YD,i = 0 for each healthy firm), Xk,i are values of the variables for firm i. The dependent variable YD,i can be interpreted as the probability that firm i with attributes X1,i, X2,i, ..., Xk,i will be distressed. The slope of each variable measures the marginal impact of the variable on the probability of distress. A positive coefficient implies that, other things being equal, an increase in the value of variable Xk,i will result in an increase for the probability of distress. The intercept of the model, is just a scaling constant, and has no particular meaning.

In most cases, the identification of LPM’s explanatory variables is a “fishing” expedition. That is, the dependent variable YD,i is regressed on various combinations of the variables to arrive at a combination for which all explanatory variables are statistically significant and have coefficients which are consistent with financial theory. Question 4. Use regression analysis and the above variables to develop a financial distress model (linear probability model). Interpret the model’s coefficients. Explain how you came up with this model. Using such a procedure, the best model is

, ˆ 0.1039 0.6199 0.9259

(0.77) (3.73) ( 2.89) i D i iP Y TDTA GEMPL   



20.8203 0.6556 0.2841

( 2.52) (1.97) i iOPITA INVSLS R  



The above regression indicates that the ratios of total debt to total assets (TDTA) and inventory to sales (INVSLS) have a positive marginal impact on the probability of distress (Pi); and the annual employment growth rate (GEMPL) and the ratio of operating income to total assets (OPITA) hav negative marginal impact on the probability of distress. Note that these findings are consistent with the financial distress hypotheses postulated pre Question 5. Use the model developed in (4) to assess (ex-post) the financial condition of the firms below (hint: compute the LPM scores and re-classify the firms using a cut-off probability of 0.5).

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, 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. The estimated probabilities of financial distress for the four firms are: Distressed Firms Firm #1: 1 0.1039 0.6199(0.46) 0.9259(0.01) 0.8203(0.1) 0.6557(0.08) 0.3502,P       Firm #2: 2 0.1039 0.6199(1.00) 0.9259( 0.05) 0.8203( 0.11) 0.6557(0.16) 0.9652,P         Healthy Firms Firm #3: 3 0.1039 0.6199(0.62) 0.9259(0.05) 0.8203(0.14) 0.6557(0.18) 0.4451,P       Firm #4: 4 0.1039 0.6199(0.61) 0.9259( 0.03) 0.8203(0.10) 0.6557(0.21) 0.5665.P        Based on the above probabilities and the cut-off point of 0.5, firms #1 and #4 are mis-classified by the model. That is, the distressed firm #1 is classified as healthy, and the healthy firm #3 is classified as distressed. In general, the percentage of firms mis-classified (classified incorrectly) by the model in the distressed sample is known as type I error and in the healthy sample is known as type II error.

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HW 5 - PREDICTION OF FINANCIAL DISTRESS Statistical Financial Modeling (Prof. P. Theodossiou)

Healthy/Distressed Sample The sample includes 86 financially distressed firms and 95 healthy (non-distressed) firms from the NYSE or AMEX. 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. Data for are from COMPUSTAT and cover the period 1981-89. Data for distressed firms were gathered at about one year prior to the point the firm experienced the first sign of distress. Definition of the Variables YD = 0 for healthy firms and 1 for distressed firms TDTA Total liabilities to total assets ratio GEMPL Employment growth rate OPITA Operating income to total assets ratio INVSLS Inventory to sales ratio LSLS Natural logarithm of deflated sales (millions of $) LTA Natural logarithm of deflated total assets (millions of $) NWCTA Net working capital to total assets ratio CACL Current assets to current liabilities ratio QACL Quick assets to current liabilities ratio EBITA Earnings before interest and tax (EBIT) to total assets ratio RETA Retained earnings to total assets ratio FATA Fixed assets to total assets ratio 1. (a) Are the means of the above variables statistically different in the healthy and distressed samples? (b) Which of these variables are useful in discriminating financially distressed from healthy firms? (c) Which of the variables is the least (most) significant? 2. Discuss your previous findings from the “financial analysis” point of view. 3. Is it correct to assume the most significant variables must “always” enter the model as explanatory variables? Relate your answer to the variables’ correlation matrix. 4. Use regression analysis and the above variables to develop a financial distress model (linear probability model or LPM). Interpret the model’s coefficients. Explain how you came up with this model. 5. Use the model developed in (4) to assess (ex-post) the financial condition of the firms below (hint: compute the LPM scores and re-classify the firms using a cut-off probability of 0.5). 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. Use the xls spreadsheets to answer the questions