Bankruptcy Prediction: The Hidden Impact of Derivatives

Brian N. Gibson

April 15, 1998

ACCT 5341

Introduction

Consider a scenario: a securities broker asks you to allow him to invest $100,000, your entire life’s savings, on your behalf. You are told that you will reap great returns from this investment and your investment is financially secure. However, when you ask for more information about the way in which he/she will invest your money, you are told only the broadest of information. "I’ll put about $75,000 in various equity investments and the remainder will be in bonds of various grades." You push to know more detail, but the broker continues to answer in vagaries and refuses to share details. Moreover, comments he/she makes about the types of investments to be made make you wonder exactly what your broker is up to. For example, when you asked for more specific information on the securities, he/she answered, "I’ll invest your money in securities that will maximize your returns and eliminate significant risks."

Most investors would balk at such an investment "opportunity." With so much at stake, the investor has a critical need to evaluate the risk associated with investment. Not only is this important in determining the probability that the investor may lose the investment, but it also determines the expected return on investment. Properly evaluating risk requires information, and lots of it. Did the scenario described above sound hard to imagine? It shouldn’t. American companies have been doing this exact some thing every year when they publish their annual reports. Of course, the investor is told about the operations and is given quite a bit of detail on the assets used in the operations of the business. However, until recently a company might have millions of dollars at risk in derivative securities with only the slightest mention of them in the annual report. Usually, disclosure in the notes to the financial statements would state the equivalent of, "The company is involved with investments in derivative securities to maximize gains and eliminate significant market risks." Now, does that sound familiar?

The Need for Risk Measurement

In years past, the analyst would rely principally on the financial statements to evaluate risks associated with the investment. For example, simple ratio analysis was performed to consider if the company was sufficiently liquid and to see how well it managed its assets and debt. Ratio analysis is fairly meaningless taken alone, but when compared to peer companies, it can be very informative about the effectiveness of management and the quality of the investment. Also, risk has been measured in terms of a company’s beta. Beta gives the investor a comparison of the nondiversifiable risk (that risk which cannot be eliminated simply through investing in a diversified portfolio of investments) between two or more investment alternatives.

The use of derivatives has complicated the investor’s traditional risk assessment. Derivatives represent a complication because they are generally not present in the financial statements. For example, two common types of derivatives include options and interest rate swaps. Employee stock options are prevalent in today’s companies. These options are still generally accounted for under Accounting Principles Board Opinion No. 25 which does not require booking outstanding options as a liability of the company. Luckily, Statement on Financial Accounting Standards No. 123 has increased the disclosure associated with employee stock options. In the case of swaps, the Financial Accounting Standards Board (FASB) will soon require reporting their fair value on the balance sheet (ED 162-B). However, the FASB has not been clear on valuation methods for these instruments. Thus, the investor may have to question the valuation used by the company.

Efforts are being made on behalf of investors. Both the Securities and Exchange Commission (SEC) and FASB have recently developed more stringent disclosure requirements for companies using derivatives. For example, the SEC has issued a series of quantitative and qualitative risk disclosure requirements in Item 305 of Regulation S-K and Item 9A of Form 20-F (SEC Questions and Answers, introduction). One very popular quantitative disclosure is likely to be value-at-risk. "‘Value at risk’ describes a general class of probabilistic models that measure the risk of loss in market risk sensitive instruments" (SEC Questions and Answers, paragraph 57). A good discussion of the value-at-risk model is published by the Federal Reserve Bank of New York and is available at www.ny.frb.org/rmaghome/econ_pol/ 496end.html.

These disclosures and risk assessment tools are very important to users of financial statements. However, the impact of derivatives on risk assessment should also be viewed in the context of their impact on the company as a whole, and not just the riskiness of the derivatives viewed separately. They become a part of the portfolio of "assets" the company is invested in; the investor might want to know how much risk is associated with the entire company. "Several research streams have defined risk in terms of financial distress. . . . Analysts concerned with the economic loss of a portion or all of the amount lent to or invested in a firm would examine financial distress risk" (Stickney 1996, 505 - 506). One possible tool to measure this risk is bankruptcy prediction. Derivative instruments may materially change the probability of bankruptcy for a company.

Bankruptcy Prediction Models

Bankruptcy prediction models are more generally known as measures of financial distress. Three stages in the development of financial distress measures exist: univariate analysis, multivariate analysis, and logit analysis. Univariate analysis assumes "that a single variable can be used for predictive purposes" (Cook and Nelson 1998). The univariate model as proposed by William Beaver achieved a "moderate level of predictive accuracy" (Sheppard 1994, 9). Univariate analysis identified factors related to financial distress; however, it did not provide a measure of the relevant risk (Stickney 1996, 507). In the next stage of financial distress measurement, multivariate analysis (also known as multiple discriminant analysis or MDA) attempted to "overcome the potentially conflicting indications that may result from using single variables" (Cook and Nelson 1998). The best-known, and most-widely used, multiple discriminant analysis method is the one proposed by Edward Altman, Professor of Finance at the Stern School of Business, New York University. Altman’s z-score, or zeta model, combined various measures of profitability or risk. The resulting model was one that demonstrated a company’s risk of bankruptcy relative to a standard. Altman’s initial study proved his model to be very accurate; it correctly predicted bankruptcy in 94% of the initial sample (Altman 1968, 609).

Despite the positive results of his study, Altman’s model had a key weakness: it assumed variables in the sample data to be normally distributed. "If all variables are not normally distributed, the methods employed may result in selection of an inappropriate set of predictors" (Sheppard 1994). Chistine Zavgren developed a model that corrected for this problem. Her model used logit analysis to predict bankruptcy. Due to its use of logit analysis, her model is considered "more robust" (Lo 1986, 151). Further, logit analysis actually provides a probability (in terms of a percentage) of bankruptcy. Also, the probability calculated might be considered a measure of the effectiveness of management, i.e. effective management will not lead a company to the verge of bankruptcy.

During the 1980s and 1990s, the trend has been to use logit analysis in favor of multiple discriminant analysis (Stickney 1996, 510). More recently, logit analysis has been compared to a more advanced analytical tool, neural networks. Research has found that the approaches perform similarly and should be used in combination (Altman, Marco, and Varetto 1994, 505).

Logit Analysis: The Model

Application of the logit model requires four steps. First, a series of seven financial ratios are calculated. Second, each ratio is multiplied by a coefficient unique to that ratio. This coefficient can be either positive or negative. Third, the resulting values are summed together (y). Finally, the probability of bankruptcy for a firm is calculated as the inverse of (1 + e^y). "Explanatory variables with a negative coefficient increase the probability of bankruptcy because they reduce e^y toward zero, with the result that the bankruptcy probability function approaches 1/1, or 100 percent. Likewise, independent variables with a positive coefficient decrease the probability of bankruptcy" (Stickney 1996, 511). Table 1 shows the financial ratios used in the logit model and their respective coefficients.

TABLE 1

Derivatives' Impact on Logit Analysis

As mentioned earlier, derivatives can impact a company’s solvency. Logit analysis has not traditionally taken into consideration derivatives used by a firm in calculating the firm’s probability of bankruptcy. This is due to the fact that derivatives have not been on the balance sheet and therefore not reflected in the financial ratios used in the calculation. The significant impact that derivatives can have on solvency is clearly portrayed through an example in which logit analysis is performed both with and without inclusion of derivative instruments.

First, consider the partial financial statements of XYZ Company. These financial statements were the basis of the logit analysis conducted. Please note, the financial statements presented below are exclusively for the purpose of demonstration and bear no resemblance to any specific company’s financial statements.

Application of the logit analysis model to these financial statements resulted in a 51.5% probability of bankruptcy. This result might make the analyst watch the company’s actions closely, especially in terms of liquidity and solvency, but would not be a reason for alarm.

If the analyst had known the Company’s position in two types of derivative instruments, the results would have differed significantly. The XYZ Company has engaged in an interest rate swap to receive LIBOR plus 1.5% and pay 9% fixed; the Company believes interest rates are going to rise. However, at year end LIBOR is 6.5%. Therefore, XYZ Company has a net payable position. Also, XYZ Company has issued stock options to key employees as part of an incentive program. On the date options were issued, the stock price was equal to the exercise price. Therefore, under APB No. 25 XYZ has not recorded any compensation expense related to the options.

This information might be found by the investor or analyst in the notes to the financial statements. Under SFAS 123, the information about the options should already be disclosed. However, this information might also be available via disaggregated reporting. If investors were given access to a database of contract and transaction information, they would be able to create their own queries to discover this information. For example, the investor could have generated a query for these derivative types and received all of the information needed to evaluate risk.

After obtaining the necessary information, either in a disaggregated database or in the notes to the financial statements, the analyst must value the derivatives. The accepted method of valuing options is the Black-Scholes option pricing model. XYZ’s options are valued below (Schroeder and Clark 1998, 709).

Click here to see how the call option value was calculated using Microsoft Excel.

While the method for valuing options is relatively agreed upon, much debate exists on the proper method to value interest rate swaps. The method used below is the Legal Settlement Method as proposed by Professor Robert Jensen of Trinity University, San Antonio, Texas, in his Working Paper 231.

The net payable position on the swap and the issuance of stock options both represent liabilities to the firm. These liabilities, up to this point, are off balance sheet and therefore not represented in the previously conducted logit analysis. The analyst might choose to view these liabilities as "quasi long-term debt." These items are not specifically long-term debt in the same way as notes payable, but they are in effect a way of financing the operations of the company that benefits more than one period. The interest rate swap would most properly be divided by the analyst into long-term and current portions, but for the sake of simplicity, this analysis will include the full amount as "quasi long-term debt." The inclusion of these liabilities in long-term debt is significant because of the negative sign and the size of its coefficient in the logit model. Further, the value of options issued in the current year (50 options at $5 each) is deducted from income as compensation expense.

The result is dramatic. XYZ was previously thought to only have a 51.5% probability of bankruptcy; under further analysis, it has an 86.9% probability.

As this analysis has shown, derivatives’ impact on solvency cannot be ignored. They significantly impact the risk of financial distress that a company faces. On the other hand, they can benefit the company. For example, if the swap had been a net receivable position, the probability of bankruptcy would have declined. Nevertheless, the point remains: ignoring the existence of derivative instruments can materially mislead the analyst.

Application for Audits

Bankruptcy prediction, or financial distress risk, has a clear application in going concern audit procedures. "The auditor has a responsibility to evaluate whether there is substantial doubt about the entity’s ability to continue as a going concern . . ." (AU §341.02). Logit analysis is an easily implemented analytical procedure available to auditors. In fact, logit analysis has already been applied in audits. "Dugan and Zavgren (1988) describe . . . [the] application of bankruptcy prediction models by auditors in a major public accounting firm: Auditors in that instance use the model mostly in situations where other sources of audit evidence already indicate the existence of a going concern problem" (Poston, Harmon, and Gramlich 1994, 41). In other words, bankruptcy prediction models were being used as a corroborative tool. This rather defeats the purpose of logit analysis as an "early warning system" (Cook and Nelson 1998). Rather, it would be more helpful to auditors if this model were applied during the planning process in order to determine if more testing was necessary on the going concern evaluation. Use of the model will help auditors to know that the going concern exception has been issued properly. (An interesting discussion of auditor going concern modifications is found at www.usc.edu/dept/accounting/midyraud/louwers.html.) Most importantly, as this paper has demonstrated, the bankruptcy prediction model applied must account for use of derivative instruments - both on and off-balance sheet.

Conclusion

The logit model of bankruptcy prediction is a useful model to investors, analysts, and auditors. However, its results are only as accurate as the completeness of the data in the model. Therefore, it is essential that derivatives be accounted for in calculations. This should become easier with increased disclosure in the notes to financial statements and in disaggregated reporting. However, it should be noted that bankruptcy prediction is not a complete solution to risk measurement. It is just one of many tools that the analyst should consider in evaluating the effectiveness of management and the risk associated with an investment opportunity. Finally, this measure of risk might be considered by the SEC or FASB as a required disclosure under the SEC’s "quantitative" and "forward-looking information" disclosure requirements. Bankruptcy prediction with logit analysis has been shown to be effective up to five years ahead of failure (Zavgren 1985, 19); this early warning system would give management and investors improved disclosure of trouble ahead.

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