Business Cycle and the Riskiness of Italian Firm: An Empirical Analysis

Journal of Modern Accounting and Auditing, ISSN 1548-6583 January 2012, Vol. 8, No. 1, 66-76 Business Cycle and the Riskiness of Italian Firm: An Empirical Analysis Filippo Di Pietro University of Seville, Spain Giuseppe Lusignani University of Bologna, Italy Dolores Oliver Alfonso University of Seville, Spain Given the importance of the relationship between default rates and business cycles, we examine the ability of macroeconomic variables, explaining changes on the default rate of Italian companies. Via a VAR (vector autoregressive) model and an analysis of individual equations, we find a significant influence of short-term interest rates, and the growth rate of gross domestic product (GDP) in the euro area, on the default rate of Italian companies in the period 1985-2004. Using the selected macroeconomic variables, we build a credit cycle index (CCI) in order to infer the state of credit in the Italian market in future periods. The construction of this “credit cycle index” is based on a robust econometric structure with a minimum number of parameters and a minimum number of required data. Keywords: credit risk, business cycle, econometrics, endogenous, estimation, ordinary least squares (OLS) Introduction What most influences the performance of a credit portfolio is the systematic risk (Jarrow, Lando, & Yu, 2000; Frey & McNeil, 2002; Lucas, Klaassen, Spreij, & Straetmens, 2001; Giesecke, 2003). In a loan portfolio, the level of risk is primarily represented through the credit cycle, which in turn is characterized by deterioration or improvement. Despite this, the most popular portfolio models such as those of CreditMetrics (Gupton, Finger, & Bhatia, 1997) and CreditRisk (Credit Suisse, 1997) did not take into account the cycle and its effects on risk. An exception is the CreditPortafolioView (Wilson, 1997a, 1997b) model, which attempted to assess the relationship between the conduct of business failures and the macroeconomic indicators of the economic cycle. In fact, systematic credit risk factors are usually associated with macro-economic conditions. Empirical studies revealed that long-term trends of the average default rates of large company groups highly diversified between each other, relative to a given country are highly volatile and have cyclical factors. It was recognized, indeed, that environmental factors may cause a correlation between the actual default rates of a set of companies (e.g., Asamow & Edwards, 1995; Wilson, 1997a, 1997b). This is evident both from theoretical models (Williamson, 1987; Kiyotaki & Moore, 1997; Bernanke, Gertler, & Gilchrist, 1999; Kwark, 2002) on the real business cycle, either by empirical evidence (Nickell, Perraudin, & Varotto, 2000; Bangia, Diebold, Kronimus, Schagen, & Schuermann, 2002; Kavvathas, 2001; Marcucci & Quagliarello, 2005). The general conclusion of these models is that the probability of default tends to be higher in times of Filippo Di Pietro, assistant professor, Department of Financial Economics and Operations Management, University of Seville. Giuseppe Lusignani, professor, Department of Economics, University of Bologna. Dolores Oliver Alfonso, professor, Department of Financial Economics and Operations Management, University of Seville. DAVID PUBLISHING D BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM 67 economic downturn. Hence, there is a general acceptance that the state of the economy of a country has a direct impact on the observed rate of insolvency. In this work, we analyze the relationship between the default rate and the macroeconomic variable, examining how macroeconomic variables affect the movements in the default rates of Italian companies. Via a VAR model and an analysis of individual equations, we find a significant influence of short-term interest rates, and the growth rate of the GDP in the euro area on the default rate of Italian companies in period 1985 to 2004. Using the selected macroeconomic variables, we build a credit cycle index (CCI) in order to infer the state of credit in the Italian market in future periods. The paper is organized as follows. In the second section, the difficulty of good correlation estimation between macroeconomic variables and default rates is explained. In the third section, a literature review of this item is made. In the fourth section, the data used for this work are presented. The empirical model and the results are presented in section five. The results are backtested in the sixth section. And the last section is the conclusions of the paper. The Difficulty of a Good Correlation Estimation The results obtained from the estimated correlation between macroeconomic variables and default rates are valid only if the statistical time series of default rates of loans are sufficiently long and sufficiently numerous groups. This, unfortunately, is not frequently found in banks. One of the solutions which can be proposed is to perform an analysis of the correlations not on the bank’s internal data, but on very large databases, such as loans and credits of the whole system. Then, once we get the matrix of variances and covariance, apply this to the bank’s portfolio to assess the riskiness1. The series that are available to banks are limited, partly because the nature of non-short-term credit risks prevent daily or monthly observations, being having considered to lengthen the horizon of historical analysis necessarily includes distortions due to structural modifications of long-term economies of production and consumption. Instead, the analysis of correlations needs a high abundance of data to distinguish “structural correlations”, related to strong phenomena, from the “temporary correlations”, valid only at certain periods so, in addition to the problem of being able to estimate the correlation between the losses of loans, it is important to be able to validate the hypothesis that the correlation between loans tends to remain stable over time. The identification of macroeconomic variables that produce significant volatility in default rates to the economic cycle is important, because it can be used to condition the expected default rates and the matrix migration to the state of the economy. Then, macroeconomic variables can be inserted in forecasting internal rating systems. Literature Review The main question facing Nickell et al. (2000)2 in their work is: given that the transition probabilities of the ratings vary for different borrowers at different times of the economic cycle, what are the causes of these variations? 1 A bank according to Basel II, in fact, may use both internal data and external data, but the population of exposures represented in the data, should be the same or at least be comparable with that of the actual exposure of the bank; the bank must also demonstrate that the economic and market conditions that underlie the data are consistent with the current situation and perspective. 2 Helwege and Klieman (1996); McDonald and Van de Gucht (1999). The results of these two studies have benn confirmed and extended by Nickell et al. (2000). BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM 68 The issue is faced calculating the non-conditional matrix and the conditional matrix of transition ratings in a standardized manner, and through a model “probit” logical in which the transitions are driven by realizations of a latent variable that incorporates a series of “dummies” by types of borrowers and the status of the business cycle. The approach taken by Nickell et al. (2000) is to estimate the parameters by taking the entire universe of events of migration as a single sample, and considering the variables sector/area/state of the business cycle as dummy variables (the business cycle is considered by simply dividing the year into “favorable”, “normal” and “unfavorable”)3. The conclusions of this study confirmed what has previously been assumed. In fact, the authors found that the frequency of downgrade and default of counterparties to counterparts assigned to rating classes with a high risk increases in the early stages of economic downturn, it is less predictable and more contradictory than a second result obtained from their model, namely, for counterparts with better rating the impact of negative phases of the cycle seems to increase not only the probability of “downgrade” but also “upgrade”, thus affecting the volatility more than the direction of the rating process migration. Bikker and Metzemakers (2005), using a panel of 26 Organization for Economic Co-operation and Development [OECD] countries over the period 1979-1999, found that the activity of the bank loan is highly dependent on the demand for money measured by cyclic variables, such as the rate of real growth, inflation, unemployment and real supply money. Hackbarth, Miao, and Morellec (2006) developed a framework for analyzing the impact of macroeconomic conditions on credit risk and the choice of the dynamic structure of capital chosen by the company, demonstrating that this simple observation has a wide range of implications for business. Closer to the Italian case we work on: Marotta, Pederzoli, and Torricelli (2005), applying a model developed by Pederzoli and Torricelli using the default data of Italian firms provided by the Bank of Italy. The basic idea of the model is to use a measure of risk that grows just before a recession on the credit horizon, and vice versa decreases just before a period of expansion. The purpose of the proposed model is to include a forecast of the economic cycle in the measures of credit risk. Other empirical studies incorporate macroeconomic variables in forecasting models of credit risk, such as the models proposed by H. Platt and M. Platt (1991) that attempted to isolate the dynamics of sectorial indices through the use of the “relative” value calculated by relating the obtained value by the company and that observed by the sector of membership. Lennox (1999) used macroeconomic variables to improve the performance of the models of credit risk. The results look encouraging, both in terms of efficiency rating, and for the possibility of estimating the effect of a macroeconomic shock on the probability of company default. A work of considerable importance for the analysis carried out here, and which draws on the empirical analysis, is that done by Zazzara and Rotondi (2005a). In their work, the ability of macroeconomic variables to explain the default rates of firms in the Italian banking market is examined. Via a VAR and analysis of individual equations, they found significant influences interest rates in the short term, the difference between potential GDP and real GDP (output gap), the real value of assets, and inflation on the default rate of Italian firms over the period 1990-2004. Using these macro variables, they built a “Credit Cycle Index” in order to infer the state of credit in the Italian market in future periods. 3 Dummy variables for the four locations considered: U.S., UK, Japan, and Europe (including England), dummy variables for 10 industry categories, dummy variables for the current state of the economy and that which is expected (one year). See Nickell et al. (2000), p. 216. BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM 69 Data Sample4 The data available for the preliminary univariate and multivariate analysis, in order to find the most important macroeconomic variables are yearly. We take 1985 as the starting year for our estimation period, since for the series of default rates are not available prior data. The default rate series cover all Italian companies. The default rates are a moving average, centered at three years. This allows an easier processing of such data. Starting from a sample of 12 series of macroeconomic variables, we arrive at the selection of the most significant ones for our analysis. The variables are: (1) Public demand (public administration expenditure in real terms): DPA. (2) Taxes paid by enterprises (share to GDP): TPE. (3) Taxes paid by households (share to GDP): TPH. (4) Social security contributions (share of GDP): SC. (5) Wages and salaries per capita industry: WpC. (6) Brent crude oil prices: PBC. (7) Price index for non-energy commodities (USD currency): PNC. (8) Change $/€: CH. (9) US GDP: USGDP. (10) Euro GDP: EGDP. (11) GDP in developing countries (developing countries): DCGDP. (12) Three-month interest rate: IR3. Univariate analysis was based on the verification of the stationarity of data via the ADF (Augmented Dickey-Fuller) test on the levels, log-levels, first differences and second differences, and if shocks are permanent or stationary. Multivariate analysis was based on the significance of the regressors and the correlation of errors. At this stage, the choice of variables to be used may be based on subjective assessments, perhaps guided by theoretical assessments or maybe just from the results highlighted by other studies. Then, thanks to the econometric work, it is possible to identify the optimal classification rule, identifying variables that can be eliminated as not relevant in determining the effectiveness of the model. It is noted, however, that almost all proposed studies on the subject have used iterative procedures that can identify the significant variables among a large set of selected variables. After carrying out an iterative process in which all possible VAR models were estimated, including the first with five variables, then four and then three, and have felt the significance of all variables in the following estimates of ordinary least squares (OLS). At the end of the analysis, we consider only the following variables: the default rate of Italian companies, such as the autoregressive term, the logarithm of GDP in the euro area and interest rates in the short term. Estimation Methodology and Results Starting from the papers of Zazzara and Rotondi (2005b), we build a credit cycle index of Italian 4 Data provided by Prometeia Association—one of the largest Italian companies in financial and economic research. BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM 70 companies. A two-stage approach is used. We start from the identification of macroeconomic variables, and via a VAR model, we find the number of variables to use and the lag. The VAR approach avoids a structural model, modeling each endogenous variable in the system as a function of lagged values of all endogenous variables. The equation is: tt-1 pt-ptt ΥΑΥ ΑΥ ΒΧε = +⋅⋅⋅+ + + (1) After careful analysis and various tests we choose among all the series of macroeconomic variables. t t t-1 DF DR PL = where DRt is the default rate; LNRt is loans not repaid at time t; ELt-1 is the existing loans in time t-1; IRshort = interest rates in the short term. LEGDPEURO = the logarithm of gross domestic product in the euro area. The estimated VAR model tells us that the best model is one that uses few variables with a single lag, this gets the most significance of the regression. Table 1 shows the statistical regression performed with the VAR. The first terms in parentheses are the “standard error” variable regression. The second terms in parentheses are the t-statistic. Table 1 VAR Estimation DRt Tbrev LPILEURO DRt (-1) 0.857553 (20.9909) -0.966055 (-1.67830) -11.99617 (-1.01158) IRshort (-1) 0.246329 (4.93865) 0.607240 (0.86407) -0.911236 (-0.06294) LPILEURO (-1) -0.008187 (-2.97555) 0.020297 (0.52357) 1.046109 (1.30981) C 0.003160 (1.83458) 0.010666 (0.43951) 0.221320 (0.44265) R-squared 0.981412 0.776045 0.746792 Adj. R-squared 0.977694 0.731254 0.696150 Sum sq. resids 1.06E-05 0.002099 0.890716 S.E. equation 0.000839 0.011828 0.243682 F-statistic 263.9913 17.32594 14.74661 Log Likelihood 196.9403 Akaike information criteria -19.46740 Schwarz criteria -18.87091 Notes. Sample (adjusted): 1986-2004; included observations: 19 after adjusting endpoints. Standard errors and t-statistics are in parentheses. The R-squared has a very high value confirming the validity of the regression. In all the VAR models estimated with more variables and/or more “lags” we found problems of low significance of the regressors and multicollinearity. So, the first results of estimation indicate that for the construction of the CCI and, more generally, to explain the relationship between macroeconomic performance and the default rates of the loans, it is more efficient to work with a select few one-lag macro variables. Figure 1 traces the impulse response function, the dependent variable (in our case, default rate), which BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM 71 corresponds to a shock in the standard deviation of each explanatory variable. As expected, the default rates respond negatively to an exogenous shock of the standard deviation of GDP in the euro area, but respond positively to a shock in the standard deviation of interest rates in the short term. Figure 1. Responses on impulse function of DR. Selecting the macro variables, we monotonically transform the default rates. The transformation is as follows: Logit( ) Ln( ) 1 t tii,t-jt i t DR DR βΧ ε DR α = =+ × + −∑ (2) We transform the variable GDP: 1 (Ln ) Ln( ) tt D GDP GDP GDP− = − (3) where D refers to the first difference, and Ln to the natural logarithm, so we turned the GDP series in the first difference of its natural logarithm. We make this change for several reasons. First because we are not very interested in how the levels of GDP affect the default rate but rather than the GDP growth rate influences the default rate. The transformation in first differences is performed for a better stabilization of the variable and to make it more significant in the regression. As shown above the natural logarithm of ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −t t DR DR 1 is linearly regressed with macroeconomic explanatory variables jti X−,. The i β coefficients are therefore estimated using the method of ordinary least squares (OLS). 1 2 3 4 5 6 7 8 9 10 0.000 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Response of DR to one S.D. IR innovation -0.002 -0.004 0.000 0.002 0.004 0.006 -0.003 -0.002 -0.001 0.001 0.004 0.003 0.002 0.001 0.000 -0.001 -0.002 0.002 Res p onse of DR to one S.D. LEGDP innovation Res p onse of DR to one S.D. DR innovation BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM 72 Table 2 Regression Analysis Variable Coefficient Std. error t-statistic Prob. C -1.192346 0.162762 -7.325686 0.0000 Logit(DRt) (-1) 0.754341 0.040127 18.79895 0.0000 IRshort (-1) 4.940155 0.438420 11.26808 0.0000 DLGDPEURO (-1) -0.158821 0.040396 -3.931564 0.0015 R-squared 0.986202 Mean dependent var. -3.727850 Adjusted R-squared 0.983245 S.D. dependent var. 0.242755 S.E. of regression 0.031423 Akaike info criterion -3.889449 Sum squared resid. 0.013823 Schwarz criterion -3.691588 Log likelihood 39.00504 F-statistic 333.5380 Durbin-Watson stat. 1.927173 Prob (F-statistic) 0.000000 Note. Included observations: 18. The statistical regression in Table 2 shows that the t-statistics of the coefficients are all significant, except the constant. Both the R-squared and the adjusted R-squared have very high values, and then the f-test statistic strongly rejects the null hypothesis of no significance of the estimate as a whole. After estimating the equation above, it standardizes the Logit function and adds a minus sign before the equation, in order to obtain a new variable: Ln 1 Ln 1 Ln 1t t t t t DR tDR DR DR DR DR Z μ σ ⎛⎞ ⎜⎟ − ⎝⎠ ⎛⎞ ⎜⎟ − ⎝⎠ ⎛⎞ − ⎜⎟ − ⎝⎠ =− (4) The variable Z represents the Credit Cycle Index and indicates the status of credit divided by all the borrowers during the period t. By construction, the index is zero when the value of all macroeconomic series is exactly equal to the average over the estimation period. The CCI is rather positive or negative when the macroeconomic series differ from their mean. In particular, it is positive in the good times of the cycle (implying a lower probability of default) and negative in the bad times (implying a higher probability of default). See Figure 2. Figure 2. Relation between DR and CCI. -2 -1 0 1 2 0.015 0.020 0.025 0.030 0.035 86 88 90 92 94 96 98 00 02 04 CCI D R BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM 73 Visual inspection of the Figure 2 (where CCI = CCI estimated, and DR = the default rate in the period observed) above shows an inverse relationship between the default rate and the CCI credit, as assumed in the construction of the index. You can see how the CCI approximates quite well to the trend of default rate in Table 3. Table 3 Comparison Between Actual CCI and CCI Estimated Years Actual Estimate Years Actual Estimate 1987 -0.14994 -0.24479 1996 -0.99943 -0.87965 1988 0.252228 0.081049 1997 -0.54895 -0.49671 1989 0.482398 0.448169 1998 -0.05439 0.031501 1990 0.269926 0.32977 1999 0.678005 0.381685 1991 -0.19697 -0.31965 2000 1.119023 0.878269 1992 -0.99049 -0.87652 2001 1.367896 1.290381 1993 -1.47174 -1.53971 2002 1.421929 1.216358 1994 -1.65872 -1.62648 2003 1.394831 1.30301 1995 -1.31222 -1.39476 2004 1.298784 1.41808 Table 3 shows in the “Actual” column the actual values of the index for each year of the sample, and the “Estimate” column the estimated value. You can see that there is a close proximity of the values for each year of the sample and as for the large majority of the observations the two measures have the same sign, it is very important to note the change of sign, the estimated CCI approximates well two on three, the third anticipate the observation in one year. Backtest and Forecast After building our CCI, we test the robustness of our approach through statistical backtest measures. In particular, we ensure the foresight of our credit cycle index, both “in-the-sample” and “out-of-the-sample”. We use the widely used statistical error “Theil Inequality Coefficient”5. ∑∑ ∑ == = + − = n t n t tt n t n y n n y TIC 11 2 2 2 1 )( λ λ (5) where: = t λ Expected value of the credit cycle index at time t; = t y Realized value of the credit cycle index at time t; =n Number of periods. ∑ = − n t tt n y 1 2 )( λ , the numerator is known as the root mean squared error of the forecast. This coefficient varies from 0 to 1, where 0 indicates a perfect “fit”. Figure 3 shows an almost alignment of the curve representing the expected CCI (ESTIMATE) with that achieved (TRUE). Some small difficulties in the final estimation where the credit cycle index follows a slightly different trajectory than the credit cycle index achieved. 5 It provides a measure of how well a time series of estimated values compares to a corresponding time series of observed values. BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM 74 Figure 3. Comparison between actual CCI and CCI estimated. Table 4 shows a good performance with a good “fit” between the expected CCI and CCI realized. These results are also due to annual data. To “backtest” the model better more representative quarterly data that best suite this type of phenomena would be useful, but, unfortunately, we do not have such data. Table 4 Report of the Robustness of CCI Sample Period Tail inequality Same sign of index Same sign of index in change 1985-2004 0.072 95% 66% Now we try to prove the robustness of our CCI estimating out-of-the-sample. To do this, we divide the sample period (1985-2004) in two, with the first being from 1985 to 2002. We estimate the coefficients as carried out by the regressing Equation (1), and using these estimate the credit cycle index in period (2002-2004). See Figure 4. Figure 4. Comparison between estimated value out of the sample and true value. Figure 4 compares the CCI estimated with the actual, and we can see how the two measures did not substantially differ, and make a good forecast out-of-the-sample.