Financial Analysis, Planning and Forecasting Theory and Application

Financial Analysis, Planning and ForecastingTheory and Application Chapter 4 Application of Discriminant Analysis and Factor Analysis in Financial Management By Cheng F. Lee Rutgers University, USA John Lee Center for PBBEF Research, USA

Outline • 4.1 Introduction • 4.2 Credit analysis • 4.3 Bankruptcy and financial distress analysis • 4.4 Applications of factor analysis to select useful financial ratios • 4.5 Bond ratings forecasting • 4.6 Bond quality ratings and the change of quality ratings for the electric utility industry • 4.7. Other Model for Estimating Default Probability • 4.8 Summary • Appendix 4A. Jackknife method and its application in MDA analysis • Appendix 4.B. LogisticModel and ProbitModel • Appendix 4.C. SAS Code for Hazard Model in Bankruptcy Forecasting

4.2 Credit analysis (4.1) where Yi = Index value for the ith account; = ith firm’s quick ratio; = ith firm’s total sales/inventory ratio; and A and B are the parameters or weights to be determined.

4.2 Credit analysis (4.2) (4.3) (4.4a)

4.2 Credit analysis (4.4b) Where = Variance of X1; = Variance of X2; = Covariance between X1 and X2; = Difference between the average of X1’s for good accounts and the average of X1’s for bad accounts; and = Difference between the average of X2 for good accounts the average of X2 for bad accounts.

4.2 Credit analysis TABLE 4.1 Status and index values of the accounts

4.2 Credit analysis

4.3 Bankruptcy and financial distress analysis • Discriminant Model (Y is the value of z-score) (4.5) TABLE 4.2 Mean ratios of bankrupt / nonbankrupt firms From Altman, E. I., “Financial ratios, discriminantAnalysis, and the prediction of corporate bankruptcy,”Journal of Finance23 (1968), p. 596, TableI. Reprinted by Permission of Edward I. Altman and Journal of Finance. Z-score >2.99 : non-bankrupt sector; Z-score < 1.81 : bankruptcy; Z-score between 1.81 and 2.99 : gray area.

Empirical • When we apply Equation (4.5) to calculate financial Z-score, the model should be defined as • Here we use JNJ in 2005 as an example, • Then, the z-score for JNJ is 1.2(0.3233)+1.4(0.7147)+3.3(0.2353)+0.6(8.8683)+1.0(0.8706) =8.3567

4.3 Bankruptcy and financial distress analysis

4.3 Bankruptcy and financial distress analysis TABLE 4.3 Profile analysis for problem banks From Sinkey, J.F., “A multivariate statistical analysis of the characteristics of problem banks,” Journal of Finance 30 (1975), Table 3. Reprinted by permission. This paper was written while the author was a Financial Economics at the Federal Deposit Insurance Corporation, Washington, D.C. He is currently Professor of Banking and Finance at College of Business Administration, University of Georgia.

4.3 Bankruptcy and financial distress analysis

4.3 Bankruptcy and financial distress analysis (4.6) where = 0: Unsecured loan, 1: Secured loan; = 0: Past interest payment due, 1: Current loan; = 0: Not audited firm, 1: Audited firm; = 0: Net loss firm 1: Net profit firm = Working Capital/Current Assets; = 0: Loan criticized by bank examiner, 1: Loan not criticized by bank examiner.

4.3 Bankruptcy and financial distress analysis (4.7) where = Agents’ balances/Total assets; a measure of the firms’ accounts receivable management; = Stocks at cost (preferred and common)/Stocks at market (preferred and common); measures investment management; = Bonds at cost/Bonds at market; measures the firm’s age; = (Loss adjustment expenses paid + underwriting expenses paid) / Net premiums written; a measure of a firm’s funds flow from insurance operations; = Combined ratio; traditional measure of underwriting profitability; and = Premiums written direct/Surplus; a measure of the firm’s sales aggressiveness.

4.4 Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categoriesfor industrial firms

4.4 Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categories for industrial firms (Cont.)

4.4 Applications of factor analysis to select useful financial ratios TABLE 4.4a Cross-sectional comparison of financial ratios and factor loadings defining eight financial ratio categories for industrial firms (Cont.) From Johnson, W.B., “The cross-sectional stability of financial ratio patterns,” Journal of Financial and Quantitative Analysis 14 (1979), Table 2. Reprinted by permission of W. Bruce Johnson and JFQA. a Indicates variables having a within-sample cross-loading of between 0.50 and 0.70 on one other factor. *t-test of untransformed data significant at p 0.05.

4.5 Bond ratings forecasting TABLE 4.4b Cross-sectional congruency coefficients for eight financial-ratio dimensions for 1974

4.5 Bond ratings forecasting Ratio found useful in study; (X) Ratio mentioned in study; (1) Net Income plus Depreciation, Depletion, Amortization; (2) No Credit Interval = Quick Assets minus CL/Operating Expense minus Depreciation, Depletion, Amortization; (3) Quick Flow = C + MS + AR + (Annual Sales divided by 12)/[CGS = Depreciation + Selling and Administration + Interest] divided by 12]; (4) Cash Interval = C + MS/Operating Expense minus Depreciation, Depletion, Amortization;

4.5 Bond ratings forecasting (5) Defensive Interval = QA/Operating Expense Minus Depreciation, Depletion, Amortization; (6) Capital Expenditure/Sales; (7) Nonoperating Income before Taxes/Sales. From Chen, K. H., and T. A. Shimerda, “An empirical analysis of useful financial ratios,” Financial Management (Spring 1981), Exhibit 1. Reprinted by permission.

4.5 Bond ratings forecasting From Chen, K. H., and T. A. Shimerda, “An empirical analysis of useful financial ratios,” Financial Management (Spring 1981), Exhibit 5. Reprinted by permission. * Ratio not included in the final factors of the PEMC studies. ** Ratio not in the 48 ratios included in the PEMC study.

4.5 Bond ratings forecasting

4.5 Bond ratings forecasting TABLE 4.7 Variable means, test of significance, and important ranks

4.6 Bond quality ratings and the change of quality ratings for the electric utility industry The multivariate-analysis technique developed by Pinches and Mingo for analyzing industrial bond ratings has also been used to determine bond quality ratings and their associated changes for electric utilities. Pinches, Singleton, and Jahakhani (1978) (PSJ) used this technique to determine whether fixed coverages were a major determinant of electric utility bond ratings. Bhandari, Soldofsky, and Boe (1979) (BSB) investigate whether or not a multivariate discriminant model that incorporates the recent levels, past levels, and the instability of financial ratios can explain and predict the quality rating changes of electric utility bonds. PSJ (1978) found that fixed coverage is the only (and not the dominant) financial variable that apparently influences the bond ratings assigned to electric utility firms. Other important variables are the climate of regulation, total assets, return on total assets, growth rate or net earnings, and construction expenses/total assets.2 The major finding of BSB’s study is that the MDA method can be more successful in predicting bond rating changes than it had been predicting the bond ratings themselves. These results have shed some light for the utility regulation agency on the determinants of bond ratings and the change of bond ratings for electric utility industries.

4.7. Other Model for Estimating Default Probability4.7.1 Ohlson’s and Shumway’s methods for Estimating Default Probability X1 = Natural log of (Total Assets/ GNP Implicit Price Deflator Index). The index assumes a base value of 100 for 1968; X2 = (Total Liabilities/Total Assets); X3 = (Current Assets – Current Liabilities)/Total Assets; X4 = Current Assets/ Current Liabilities; X5 = One if total liabilities exceeds total assets, zero otherwise; X6 = Net income/total assets; X7 = Funds provided by operations/total liabilities; X8 = One if net income was negative for the last two years, zero otherwise; and X9 = (Net income in year t – Net income in t–1) / (Absolute net income in year t + Absolute net income in year t–1).

4.7.1 Ohlson’s and Shumway’s methods for Estimating Default Probability (4.8) Where , P = the probability of bankruptcy.

4.7.1 Ohlson’s and Shumway’s methods for Estimating Default Probability (4.9) Where , P = the probability of bankruptcy; X1 = Net Income/Total Assets; X2 = (Total Liabilities/Total Assets); X3 = The logarithm of (each firm’s market capitalization at the end of year prior to the observation year / total market capitalization of NYSE and AMEX market); X4 = Past excess return as the return of the firm in year t-1 minus the value-weighted CRSP NYSE/AMEX index return in year t - 1; and X5 = idiosyncratic standard deviation of each firm’s stock returns. It is defined as the standard deviation of the residual of a regression which regresses each stock’s monthly returns in year t – 1 on the value-weighted NYSE/AMEX index return for the same year.

4.7.2. KMV-Merton Model • The KMV Corporation developed the KMV-Merton model, which now sees frequent use in both practice and academic research. This model is an application of Merton’s model in which the equity of the firm is a call option on the underlying value of the firm with a strike price equal to the face value of the firm’s debt. The KMV-Merton Model estimates the market value of debt by applying the Merton (1974) bond-pricing model. The Merton model makes two particular important assumptions. The first is that the total value of a firm follows geometric Brownian motion. The second critical assumption is that the firm has issued only one discount bond maturing in T periods. Based on these assumptions, the equity of the firm is a call option on the underlying value of the firm with a strike price equal to the face value of the firm’s debt and a time-to-maturity of T. The Black–Scholes– Merton Formula can describe the value of equity as a function of the total value of the firm. By put-call parity, the value of the firm’s debt equals the value of a risk-free discount bond minus the value of a put option written on the firm, again with a strike price equal to the face value of debt and a time-to-maturity of T. If the assumptions of the Merton model hold, theKMV-Merton model should give accurate default forecasts.

4.7.2. KMV-Merton Model • Bharath and Shumway (2004) examined two hypotheses: (i) the probability of default implied by the Merton model is a sufficient statistic for forecasting bankruptcy; and (ii) the Merton model is an important quantity to consider when predicting default. This study hypothesizes that a reasonable set of simple variables cannot completely replace the information in ΠKMV (The KMV-Merton probability), or that a sufficient statistic for default probability cannot neglect ΠKMV . • Bharath and Shumway (2004) incorporated ΠKMV into a hazard model that forecasts default from 1980 through 2003. Using this hazard model, they compared ΠKMV to a naive alternative (ΠNaive), which is much simpler to calculate, but retains some of the functional form of ΠKMV . • In conclusion, they examined the accuracy and the contribution of the KMV-Merton default-forecasting model. Looking at hazard models that forecast default, the KMV-Merton model does not produce a sufficient statistic for the probability of default, and it appears to be possible to construct a sufficient statistic without solving the simultaneous non-linear equations required by the KMV-Merton model.

4.7.3. Empirical Comparison • Mai’s dissertation (2010) have re-examined the four most commonly employed default prediction models: Z-score model (Altman (1968), logit model (Ohlson (1980)), probit model (Zmijewski (1984)), and hazard analysis (Shumway (2001)). Her empirical results show that the discretetime hazard model adopted by Shumway (2001), combined with a new set of accounting-ratio and market-driven variables improves the bankruptcy forecasting power.

4.7.3. Empirical Comparison • By using a hand-collected business default events from Compustat Annual Industrial database and publicly available press-news, Mai’s (2010) has constructed a sample of publicly-traded companies in one of the three U.S. stock markets between 1991 and 2006. With cautiously chosen cutoff at 0.021 implied bankruptcy probability level, the out-of-sample hazard model with stepwise methodology results in classifying 82.7% of default firms and 82.8% of non-default firms. Comparing to the best results in Shumway (2001), which provides 76.5% classification of default firms, 55.2% in Altman (1993), 66.1% in Ohlson (1980), and 65.4% in Zmijewski (1984). • It can be concluded that resolve from her dissertation did better than the other 4 models. The specification of Logit and Probit Models can be found in Appendix 4.B, and SAS Code for Hazard Model in Bankruptcy Forecasting can be found in Appendix 4.C.

4.8 Summary In this chapter, we have discussed applications of two multivariate statistical methods in discriminant analysis and factor analysis. Examples of using two-group discriminant functions to perform credit analysis, predict corporate bankruptcy, and determine problem banks and distressed P-L insurers were discussed in detail. Basic concepts of factor analysis were presented, showing their application in determining useful financial ratios. In addition, the combination of factor analysis and discriminant analysis to analyze industrial bond ratings was discussed. Finally, Ohlson’s and Shumway’s methods for estimating default probability were discussed. In sum, this chapter shows that multivariate statistical methods can be used to do practical financial analysis for both managers and researchers.

Appendix 4A. Jackknife method and its application in MDA analysis (4.A.1) (4.A.2) (4.A.3)

Appendix 4A. Jackknife method and its application in MDA analysis

Appendix 4.B. Logistic Model and Probit Model The likelihood function for binary sample space of bankruptcy and nonbankruptcy is where P is some probability function, 0 ≤ P ≤ 1; and P(Xi, β) denotes probability of bankruptcy for any given Xi and β. Since it is not easy to solve the selecting probability function P, for simplicity, one can solve the likelihood function in (4.B.1) by taking the natural logarithm. The logarithm of the likelihood function then is where S1 is the set of bankrupt firms; and S2 is the set of non-bankrupt firms.

Appendix 4.B. Logistic Model and Probit Model The maximum likelihood estimators for βs can be obtained by solving MaxβL(l). In Logistic model, the probability of company i going bankrupt given independent variables Xi is defined as The two implications here are (1) P(.) is increasing in βXi and (2) βXi is equal to logP(1−P). We then classify bankrupt firms and non-bankrupt firms by setting a “cut-off” probability attempting to minimize Type I and Type II errors. In Probit models, the probability of company i going bankrupt given independent variables Xi is defined as the cumulative standard normal distribution function. Maximum likelihood estimators from Probit model can be obtained similarly as in the Logistic models. Although Probit models and Logistic models are similar, Logistic models are preferred to Probit models due to the nonlinear estimation in Probit models (Gloubos and Grammatikos, 1998).

Financial Analysis, Planning and Forecasting Theory and Application